question stringlengths 117 269 | answer stringlengths 2 624 | task stringclasses 5 values | noise_type stringclasses 3 values | difficulty stringclasses 3 values | demos stringlengths 4.82k 30.2k | num_demo_thoughts float32 5 17 | num_demo_noisy_thoughts float32 0 7.61 | noise_distribution stringclasses 1 value |
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In base-11, what is 97+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 123 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 67+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 7 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 6 + 7 + 1 = 14 in base 10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 133. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{133}
Question: In base-11, what is 29+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 9 + 8 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. We have 2 + 8 + 1 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 106. Answer:\box{106}
Question: In base-11, what is 95+75? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 5 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have 9 + 7 + 0 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 15A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{15A}
Question: In base-11, what is 9A+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have A + 9 = 19 in base-10. In human biology, the human adult skull is made up of 19 bones when the mandible (a separate bone) is included. Since we're in base-11, that exceeds the maximum value of A for a single digit. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In music, an octave consists of eight notes in the Western musical scale. We have 9 + 6 + 1 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 158. Answer:\box{158}
Question: In base-11, what is 83+3A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 3 + A = 13 in base-10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 8 + 3 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 112. Answer:\box{112}
Question: In base-11, what is 77+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 2 = 9 in base-10. In mythology and religion, there are nine realms in Norse Cosmology. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. We have 7 + 9 + 0 = 16 in base 10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 159. Answer:\box{159}
Question: In base-11, what is 27+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + A = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. We have 2 + 1 + 1 = 4 in base 10. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 46. In geometry, a hexagon is a six-sided polygon. Answer:\box{46}
Question: In base-11, what is 66+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 6 = 12 in base-10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. We have 6 + 7 + 1 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). A leading digit is 1. So the answer is 131. In mathematics, one is the first counting number and the starting point of the natural numbers. Answer:\box{131}
Question: In base-11, what is 52+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 2 + 2 = 4 in base-10. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. We have 5 + 7 + 0 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. So the answer is 114. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{114}
Question: In base-11, what is 92+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 2 + 9 = 11 in base-10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 9 + 1 + 1 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. So the answer is 100. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{100} | 14 | 6 | fixed |
In base-11, what is 92+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 101 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 28+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 8 + 9 = 17 in base-10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. We have 2 + A + 1 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. So the answer is 126. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{126}
Question: In base-11, what is 92+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 2 + 0 = 2 in base-10. In mathematics, an area is a two-dimensional size of a defined part of a surface. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In mathematics, two is the smallest and first prime number. We have 9 + 9 + 0 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. A leading digit is 1. So the answer is 172. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{172}
Question: In base-11, what is 6A+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 8 = 18 in base-10. In the Jewish tradition, the number 18 symbolizes 'chai', which means 'life' in Hebrew. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. We have 6 + 4 + 1 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 107. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Answer:\box{107}
Question: In base-11, what is 91+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 2 = 3 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 3 mod 11 = 3, so the digit is 3 and the carry is 0. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. We have 9 + A + 0 = 19 in base 10. In mathematics, nineteen is a prime number, the 8th prime number in the series. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is a Fibonacci number and a cube number. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 183. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. Answer:\box{183}
Question: In base-11, what is 72+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 2 + 9 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 7 + 8 + 1 = 16 in base 10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 150. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{150}
Question: In base-11, what is 92+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 7 = 9 in base-10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. We have 9 + 8 + 0 = 17 in base 10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. 17 mod 11 = 6, so the digit is 6 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 169. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{169}
Question: In base-11, what is 66+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 6 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 6 + 2 + 1 = 9 in base 10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. 9 mod 11 = 9, so the digit is 9 and the carry is 0. A leading digit is 0. So the answer is 91. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{91}
Question: In base-11, what is 1A+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have A + 7 = 17 in base-10. Seventeen is a Fermat prime, as it is in the form of 2^(2^n) + 1, with n = 2. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 1 + 9 + 1 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. So the answer is 106. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{106}
Question: In base-11, what is 82+31? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 2 + 1 = 3 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 3 mod 11 = 3, so the digit is 3 and the carry is 0. We have 8 + 3 + 0 = 11 in base 10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 103. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{103}
Question: In base-11, what is 14+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 8 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 1 + 2 + 1 = 4 in base 10. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 41. Answer:\box{41} | 14 | 6 | fixed |
In base-11, what is A2+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 182 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 16+27? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 6 + 7 = 13 in base-10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. We have 1 + 2 + 1 = 4 in base 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 42. Two is the base of the binary code, used extensively in computer science. Answer:\box{42}
Question: In base-11, what is A1+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 1 + 9 = 10 in base-10. The number 10 is symbolic in many cultures, often representing perfection or completeness. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have A + 8 + 0 = 18 in base 10. In golf, a standard round consists of 18 holes. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 17A. Answer:\box{17A}
Question: In base-11, what is 14+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 9 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. We have 1 + 2 + 1 = 4 in base 10. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 42. Answer:\box{42}
Question: In base-11, what is A3+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + 5 = 8 in base-10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have A + A + 0 = 20 in base 10. In computer science, the number 20 is often used in benchmarks and tests due to its convenient divisibility. 20 mod 11 = 9, so the digit is 9 and the carry is 1. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 198. Spiders, part of the arachnid family in biology, typically have eight legs. Answer:\box{198}
Question: In base-11, what is 57+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 2 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have 5 + 8 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 129. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Answer:\box{129}
Question: In base-11, what is 40+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 0 + 8 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. We have 4 + 8 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 118. In computer science, a byte is typically made up of 8 bits. Answer:\box{118}
Question: In base-11, what is 18+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 3 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 1 + A + 1 = 12 in base 10. The 12 Zodiac signs represent different personality traits and are used in astrology. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. So the answer is 110. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{110}
Question: In base-11, what is A5+31? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 5 + 1 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have A + 3 + 0 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 126. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Answer:\box{126}
Question: In base-11, what is 2A+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 6 = 16 in base-10. There are 16 ounces in a pound in the avoirdupois system of measurement. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 2 + 9 + 1 = 12 in base 10. The 12 Zodiac signs represent different personality traits and are used in astrology. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 115. Answer:\box{115}
Question: In base-11, what is 27+43? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 7 + 3 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 2 + 4 + 0 = 6 in base 10. In geometry, a hexagon is a six-sided polygon. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 6A. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{6A} | 14 | 6 | fixed |
In base-11, what is 61+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 100 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 63+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 3 + 5 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. We have 6 + 8 + 0 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 138. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Answer:\box{138}
Question: In base-11, what is 46+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 7 = 13 in base-10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Humans have two sets of each of their chromosomes, making us diploid organisms. We have 4 + 9 + 1 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 132. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. Answer:\box{132}
Question: In base-11, what is 97+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 0 = 7 in base-10. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. We have 9 + 9 + 0 = 18 in base 10. In physics, there are 18 families of elementary particles in the Standard Model. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 177. Answer:\box{177}
Question: In base-11, what is 2A+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 9 = 19 in base-10. In human biology, the first 19 elements of the periodic table are all found in the human body. Since we're in base-11, that exceeds the maximum value of A for a single digit. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In physics, eight is the number of vertices of a cube. We have 2 + 3 + 1 = 6 in base 10. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 68. In music, an octave consists of eight notes in the Western musical scale. Answer:\box{68}
Question: In base-11, what is 72+81? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 2 + 1 = 3 in base-10. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 3 mod 11 = 3, so the digit is 3 and the carry is 0. We have 7 + 8 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 143. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Answer:\box{143}
Question: In base-11, what is 70+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 0 + 5 = 5 in base-10. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 5 mod 11 = 5, so the digit is 5 and the carry is 0. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. We have 7 + 8 + 0 = 15 in base 10. In mathematics, a group of 15 is known as a pentadecagon, which is a polygon with 15 sides and 15 angles. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. So the answer is 145. Humans have five basic senses: sight, hearing, smell, taste, and touch. Answer:\box{145}
Question: In base-11, what is 95+12? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 5 + 2 = 7 in base-10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. We have 9 + 1 + 0 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is A7. Answer:\box{A7}
Question: In base-11, what is 71+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + A = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 7 + 9 + 1 = 17 in base 10. Seventeen is a Fermat prime, as it is in the form of 2^(2^n) + 1, with n = 2. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 160. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). Answer:\box{160}
Question: In base-11, what is 98+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 8 + 7 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 9 + 1 + 1 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 104. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{104}
Question: In base-11, what is 84+30? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 4 + 0 = 4 in base-10. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 8 + 3 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 104. In geometry, a square has four equal sides and four right angles. Answer:\box{104} | 14 | 6 | fixed |
In base-11, what is 89+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 125 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 38+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 2 = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 3 + A + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 12A. Answer:\box{12A}
Question: In base-11, what is 6A+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 3 = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 6 + A + 1 = 17 in base 10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 162. Answer:\box{162}
Question: In base-11, what is 37+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 3 = 10 in base-10. The decimal system, which is the most commonly used number system in the world, has a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 3 + 6 + 0 = 9 in base 10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 0. So the answer is 9A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{9A}
Question: In base-11, what is 1A+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have A + 3 = 13 in base-10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. We have 1 + 3 + 1 = 5 in base 10. Humans have five basic senses: sight, hearing, smell, taste, and touch. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In mathematics, five is the third prime number, after two and three. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 52. Answer:\box{52}
Question: In base-11, what is 43+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + 3 = 6 in base-10. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In geometry, a hexagon is a six-sided polygon. We have 4 + 7 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. So the answer is 106. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{106}
Question: In base-11, what is 51+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 1 + 0 = 1 in base-10. In mathematics, one is the first counting number and the starting point of the natural numbers. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 1 mod 11 = 1, so the digit is 1 and the carry is 0. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have 5 + 7 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 111. Answer:\box{111}
Question: In base-11, what is 59+84? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 4 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. We have 5 + 8 + 1 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 132. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{132}
Question: In base-11, what is 49+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 9 + 4 = 13 in base-10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 4 + 5 + 1 = 10 in base 10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. So the answer is A2. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{A2}
Question: In base-11, what is 49+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 9 = 18 in base-10. In golf, a standard round consists of 18 holes. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 18 mod 11 = 7, so the digit is 7 and the carry is 1. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. We have 4 + 6 + 1 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 107. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. Answer:\box{107}
Question: In base-11, what is 92+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + A = 12 in base-10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. We have 9 + 5 + 1 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. A leading digit is 1. So the answer is 141. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{141} | 14 | 6 | fixed |
In base-11, what is 92+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 151 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 6A+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have A + 5 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. We have 6 + 3 + 1 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A4. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. Answer:\box{A4}
Question: In base-11, what is 33+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 9 = 12 in base-10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. We have 3 + 4 + 1 = 8 in base 10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 81. Answer:\box{81}
Question: In base-11, what is 4A+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + 7 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 4 + 4 + 1 = 9 in base 10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 96. Answer:\box{96}
Question: In base-11, what is 53+75? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 3 + 5 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 5 + 7 + 0 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 118. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Answer:\box{118}
Question: In base-11, what is 38+43? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 3 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 3 + 4 + 1 = 8 in base 10. In computer science, a byte is typically made up of 8 bits. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 80. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{80}
Question: In base-11, what is 96+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 6 + 1 = 7 in base-10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 7 mod 11 = 7, so the digit is 7 and the carry is 0. We have 9 + 7 + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 157. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{157}
Question: In base-11, what is 13+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 7 = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 1 + 1 + 0 = 2 in base 10. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 2A. Answer:\box{2A}
Question: In base-11, what is 2A+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 8 = 18 in base-10. In the Jewish tradition, the number 18 symbolizes 'chai', which means 'life' in Hebrew. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. We have 2 + 1 + 1 = 4 in base 10. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 47. Answer:\box{47}
Question: In base-11, what is 87+21? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 1 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have 8 + 2 + 0 = 10 in base 10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. So the answer is A8. In physics, eight is the number of vertices of a cube. Answer:\box{A8}
Question: In base-11, what is A3+30? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 3 + 0 = 3 in base-10. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 3 mod 11 = 3, so the digit is 3 and the carry is 0. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). We have A + 3 + 0 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. So the answer is 123. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{123} | 14 | 6 | fixed |
In base-11, what is 37+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 117 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 94+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 4 = 8 in base-10. In physics, eight is the number of vertices of a cube. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. We have 9 + A + 0 = 19 in base 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. Eight is the atomic number of oxygen in chemistry, an element essential for human life. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 188. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{188}
Question: In base-11, what is 9A+23? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + 3 = 13 in base-10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 9 + 2 + 1 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 112. Answer:\box{112}
Question: In base-11, what is 12+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 2 + 9 = 11 in base-10. In computer science, '11' is the binary representation of the decimal number 3. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 1 + 4 + 1 = 6 in base 10. Six is the atomic number of carbon in chemistry, a key element for life as we know it. 6 mod 11 = 6, so the digit is 6 and the carry is 0. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. A leading digit is 0. So the answer is 60. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). Answer:\box{60}
Question: In base-11, what is 56+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 7 = 13 in base-10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. We have 5 + 7 + 1 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. So the answer is 122. In mathematics, an area is a two-dimensional size of a defined part of a surface. Answer:\box{122}
Question: In base-11, what is 99+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + 8 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 17 mod 11 = 6, so the digit is 6 and the carry is 1. We have 9 + 4 + 1 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 136. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{136}
Question: In base-11, what is A6+75? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 6 + 5 = 11 in base-10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have A + 7 + 1 = 18 in base 10. In Tarot, the Moon card is card number 18, representing intuition, dreams, and the unconscious. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In biology, a rainbow is seen in seven colors due to the refraction of light. A leading digit is 1. So the answer is 170. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{170}
Question: In base-11, what is 8A+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 6 = 16 in base-10. In mathematics, sixteen is a square number (4^2), and it is the fourth power of two (2^4). Since we're in base-11, that exceeds the maximum value of A for a single digit. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. We have 8 + 2 + 1 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 105. Answer:\box{105}
Question: In base-11, what is 85+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 8 = 13 in base-10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. We have 8 + A + 1 = 19 in base 10. In physics, the nineteenth century marked the discovery of thermodynamics, leading to the development of the steam engine and the industrial revolution. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. A leading digit is 1. So the answer is 182. In mathematics, two is the smallest and first prime number. Answer:\box{182}
Question: In base-11, what is 27+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 7 + 6 = 13 in base-10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. We have 2 + 7 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A2. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{A2}
Question: In base-11, what is 65+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 3 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. We have 6 + 7 + 0 = 13 in base 10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. A leading digit is 1. So the answer is 128. Answer:\box{128} | 14 | 6 | fixed |
In base-11, what is 91+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 176 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 68+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 8 + 4 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have 6 + 5 + 1 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 111. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{111}
Question: In base-11, what is 57+50? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 0 = 7 in base-10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 7 mod 11 = 7, so the digit is 7 and the carry is 0. We have 5 + 5 + 0 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A7. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{A7}
Question: In base-11, what is A9+93? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 3 = 12 in base-10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have A + 9 + 1 = 20 in base 10. In computer science, the number 20 is often used in benchmarks and tests due to its convenient divisibility. 20 mod 11 = 9, so the digit is 9 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 191. One often represents the 'on' state in binary code, which underlies digital computing. Answer:\box{191}
Question: In base-11, what is 90+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 0 + 8 = 8 in base-10. In physics, eight is the number of vertices of a cube. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. We have 9 + 3 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 118. Answer:\box{118}
Question: In base-11, what is 39+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 9 + 9 = 18 in base-10. In computer science, the UTF-18 character set is a proposed extension of the Unicode standard to include a wider range of characters. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have 3 + 3 + 1 = 7 in base 10. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. A leading digit is 0. So the answer is 77. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{77}
Question: In base-11, what is 33+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + A = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. We have 3 + 1 + 1 = 5 in base 10. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. 5 mod 11 = 5, so the digit is 5 and the carry is 0. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 52. Answer:\box{52}
Question: In base-11, what is 19+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 9 + 0 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. We have 1 + 9 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A9. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{A9}
Question: In base-11, what is 73+65? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 5 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. We have 7 + 6 + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. So the answer is 128. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Answer:\box{128}
Question: In base-11, what is 22+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 2 + 9 = 11 in base-10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 2 + 3 + 1 = 6 in base 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 60. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). Answer:\box{60}
Question: In base-11, what is 36+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 6 + 5 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 3 + A + 1 = 14 in base 10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 130. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{130} | 14 | 6 | fixed |
In base-11, what is A5+A7? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 1A1 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A9+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 9 + 9 = 18 in base-10. In physics, there are 18 families of elementary particles in the Standard Model. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have A + 5 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Humans have five basic senses: sight, hearing, smell, taste, and touch. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 157. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{157}
Question: In base-11, what is 22+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 2 + 9 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 2 + A + 1 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. A leading digit is 1. So the answer is 120. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{120}
Question: In base-11, what is 76+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 7 = 13 in base-10. Thirteen is the atomic number of aluminium in chemistry, a post-transition metal that's widely used for its lightness and resistance to corrosion. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Humans have two sets of each of their chromosomes, making us diploid organisms. We have 7 + 1 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 92. In human anatomy, the body is largely symmetrical with two halves. Answer:\box{92}
Question: In base-11, what is 92+43? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 3 = 5 in base-10. In geometry, a pentagon is a five-sided polygon. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 5 mod 11 = 5, so the digit is 5 and the carry is 0. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. We have 9 + 4 + 0 = 13 in base 10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 125. Answer:\box{125}
Question: In base-11, what is 43+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 3 + 3 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The standard guitar has six strings. We have 4 + 7 + 0 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 106. Answer:\box{106}
Question: In base-11, what is 19+65? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 9 + 5 = 14 in base-10. In mathematics, fourteen is the number of days in a fortnight. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have 1 + 6 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 83. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{83}
Question: In base-11, what is 8A+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 6 = 16 in base-10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. We have 8 + 9 + 1 = 18 in base 10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. A leading digit is 1. So the answer is 175. In geometry, a pentagon is a five-sided polygon. Answer:\box{175}
Question: In base-11, what is 39+27? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 7 = 16 in base-10. In mathematics, sixteen is a square number (4^2), and it is the fourth power of two (2^4). Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 3 + 2 + 1 = 6 in base 10. In geometry, a hexagon is a six-sided polygon. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In astronomy, Saturn is the sixth planet from the Sun in our solar system. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 65. Answer:\box{65}
Question: In base-11, what is 90+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 0 + 9 = 9 in base-10. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 9 + 2 + 0 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. So the answer is 109. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{109}
Question: In base-11, what is 9A+84? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 4 = 14 in base-10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. We have 9 + 8 + 1 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 173. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{173} | 14 | 6 | fixed |
In base-11, what is 66+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 150 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 19+36? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 6 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. We have 1 + 3 + 1 = 5 in base 10. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. 5 mod 11 = 5, so the digit is 5 and the carry is 0. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. A leading digit is 0. So the answer is 54. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Answer:\box{54}
Question: In base-11, what is 97+66? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 7 + 6 = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Humans have two sets of each of their chromosomes, making us diploid organisms. We have 9 + 6 + 1 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. So the answer is 152. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{152}
Question: In base-11, what is 5A+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 4 = 14 in base-10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. We have 5 + 3 + 1 = 9 in base 10. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 93. Answer:\box{93}
Question: In base-11, what is 91+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 1 = 2 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In mathematics, two is the smallest and first prime number. We have 9 + A + 0 = 19 in base 10. COVID-19, which stands for 'Coronavirus Disease 2019', was named for the year it was first identified. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 182. In human anatomy, the body is largely symmetrical with two halves. Answer:\box{182}
Question: In base-11, what is 2A+31? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 1 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 2 + 3 + 1 = 6 in base 10. In geometry, a hexagon is a six-sided polygon. 6 mod 11 = 6, so the digit is 6 and the carry is 0. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 60. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{60}
Question: In base-11, what is 2A+60? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 0 = 10 in base-10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have 2 + 6 + 0 = 8 in base 10. In computer science, a byte is typically made up of 8 bits. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 8A. Answer:\box{8A}
Question: In base-11, what is A7+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 7 = 14 in base-10. In mathematics, fourteen is the number of days in a fortnight. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have A + 9 + 1 = 20 in base 10. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In mythology and religion, there are nine realms in Norse Cosmology. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 193. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{193}
Question: In base-11, what is 94+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 2 = 6 in base-10. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the atomic number of carbon in chemistry, a key element for life as we know it. We have 9 + 8 + 0 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 166. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{166}
Question: In base-11, what is 57+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 5 = 12 in base-10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. We have 5 + 3 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 91. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{91}
Question: In base-11, what is 65+81? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 5 + 1 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 6 + 8 + 0 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 136. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{136} | 14 | 6 | fixed |
In base-11, what is A3+16? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 109 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 69+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 1 = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 6 + A + 0 = 16 in base 10. There are 16 ounces in a pound in the avoirdupois system of measurement. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. So the answer is 15A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{15A}
Question: In base-11, what is 51+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 1 + 8 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. We have 5 + 5 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A9. Answer:\box{A9}
Question: In base-11, what is 16+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 6 + 8 = 14 in base-10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 1 + 2 + 1 = 4 in base 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In geometry, a square has four equal sides and four right angles. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 43. Answer:\box{43}
Question: In base-11, what is 44+62? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 4 + 2 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 4 + 6 + 0 = 10 in base 10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A6. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Answer:\box{A6}
Question: In base-11, what is 81+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 1 + A = 11 in base-10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 8 + 9 + 1 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 170. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{170}
Question: In base-11, what is 98+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 8 + 4 = 12 in base-10. Humans typically have 12 pairs of ribs in their skeletal structure. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. We have 9 + 5 + 1 = 15 in base 10. There are 15 facial bones in the human skull (not including the mandible, or lower jaw bone). 15 mod 11 = 4, so the digit is 4 and the carry is 1. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. A leading digit is 1. So the answer is 141. In physics, the number one is the charge of a single unit of positive or negative electricity. Answer:\box{141}
Question: In base-11, what is 85+65? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 5 + 5 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 8 + 6 + 0 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 13A. Answer:\box{13A}
Question: In base-11, what is A9+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 9 = 18 in base-10. In Tarot, the Moon card is card number 18, representing intuition, dreams, and the unconscious. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have A + 7 + 1 = 18 in base 10. In golf, a standard round consists of 18 holes. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 177. Answer:\box{177}
Question: In base-11, what is 57+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 7 = 14 in base-10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 5 + 1 + 1 = 7 in base 10. In biology, a rainbow is seen in seven colors due to the refraction of light. 7 mod 11 = 7, so the digit is 7 and the carry is 0. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. A leading digit is 0. So the answer is 73. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{73}
Question: In base-11, what is 71+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 2 = 3 in base-10. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 3 mod 11 = 3, so the digit is 3 and the carry is 0. Physics recognises three laws of motion, first compiled by Isaac Newton. We have 7 + 7 + 0 = 14 in base 10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 133. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Answer:\box{133} | 14 | 6 | fixed |
In base-11, what is A2+61? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 153 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 51+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 1 + 4 = 5 in base-10. In mathematics, five is the third prime number, after two and three. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 5 mod 11 = 5, so the digit is 5 and the carry is 0. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 5 + 7 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. So the answer is 115. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{115}
Question: In base-11, what is 43+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 3 + 4 = 7 in base-10. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. We have 4 + 6 + 0 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A7. Answer:\box{A7}
Question: In base-11, what is A8+50? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 8 + 0 = 8 in base-10. In music, an octave consists of eight notes in the Western musical scale. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have A + 5 + 0 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 148. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Answer:\box{148}
Question: In base-11, what is 44+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 4 = 8 in base-10. In music, an octave consists of eight notes in the Western musical scale. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. We have 4 + 7 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. So the answer is 108. In physics, eight is the number of vertices of a cube. Answer:\box{108}
Question: In base-11, what is 78+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 8 + 3 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. We have 7 + 6 + 1 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 130. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{130}
Question: In base-11, what is 63+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 9 = 12 in base-10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. We have 6 + A + 1 = 17 in base 10. In human biology, the kidneys filter about 17 liters of blood every hour. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 161. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{161}
Question: In base-11, what is 64+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 7 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. We have 6 + 7 + 1 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 130. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{130}
Question: In base-11, what is 81+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 5 = 6 in base-10. The standard guitar has six strings. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 8 + 3 + 0 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 106. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{106}
Question: In base-11, what is 95+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 4 = 9 in base-10. The gestation period of a human pregnancy is typically nine months. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. We have 9 + 3 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 119. Answer:\box{119}
Question: In base-11, what is A9+10? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 0 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. We have A + 1 + 0 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. So the answer is 109. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{109} | 14 | 6 | fixed |
In base-11, what is 70+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 145 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 41+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 1 + 2 = 3 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have 4 + A + 0 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 133. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{133}
Question: In base-11, what is A1+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 9 = 10 in base-10. The decimal system, which is the most commonly used number system in the world, has a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have A + 6 + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 15A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{15A}
Question: In base-11, what is 6A+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 2 = 12 in base-10. Humans typically have 12 pairs of ribs in their skeletal structure. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 6 + 9 + 1 = 16 in base 10. In mathematics, sixteen is a square number (4^2), and it is the fourth power of two (2^4). 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 151. One often represents the 'on' state in binary code, which underlies digital computing. Answer:\box{151}
Question: In base-11, what is A5+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 3 = 8 in base-10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. We have A + 3 + 0 = 13 in base 10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 128. Answer:\box{128}
Question: In base-11, what is 6A+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + 8 = 18 in base-10. In mathematics, eighteen is the only number that equals twice the sum of its decimal digits (1+8=9, and 9*2=18). Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have 6 + 2 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 97. Answer:\box{97}
Question: In base-11, what is 18+42? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 8 + 2 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. We have 1 + 4 + 0 = 5 in base 10. In geometry, a pentagon is a five-sided polygon. 5 mod 11 = 5, so the digit is 5 and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 5A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{5A}
Question: In base-11, what is 13+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + A = 13 in base-10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. We have 1 + 6 + 1 = 8 in base 10. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In computer science, a byte is typically made up of 8 bits. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 82. Two is the base of the binary code, used extensively in computer science. Answer:\box{82}
Question: In base-11, what is 62+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 3 = 5 in base-10. In mathematics, five is the third prime number, after two and three. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 5 mod 11 = 5, so the digit is 5 and the carry is 0. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 6 + 6 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 115. Answer:\box{115}
Question: In base-11, what is 35+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 5 + 5 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. We have 3 + 3 + 0 = 6 in base 10. The standard guitar has six strings. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 6A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{6A}
Question: In base-11, what is 73+2A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + A = 13 in base-10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 7 + 2 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is A2. Answer:\box{A2} | 14 | 6 | fixed |
In base-11, what is A9+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 158 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 53+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 5 = 8 in base-10. Spiders, part of the arachnid family in biology, typically have eight legs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, eight is the number of vertices of a cube. We have 5 + A + 0 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 148. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{148}
Question: In base-11, what is 64+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 4 + 0 = 4 in base-10. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 6 + 7 + 0 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. A leading digit is 1. So the answer is 124. Answer:\box{124}
Question: In base-11, what is 70+30? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 0 = 0 in base-10. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 0 mod 11 = 0, so the digit is 0 and the carry is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 7 + 3 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A0. Answer:\box{A0}
Question: In base-11, what is 75+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 3 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. We have 7 + 3 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. So the answer is A8. Spiders, part of the arachnid family in biology, typically have eight legs. Answer:\box{A8}
Question: In base-11, what is 83+99? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 3 + 9 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. We have 8 + 9 + 1 = 18 in base 10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 1. So the answer is 171. Answer:\box{171}
Question: In base-11, what is 84+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 2 = 6 in base-10. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. We have 8 + 8 + 0 = 16 in base 10. There are 16 ounces in a pound in the avoirdupois system of measurement. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 156. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Answer:\box{156}
Question: In base-11, what is AA+30? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 0 = 10 in base-10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. We have A + 3 + 0 = 13 in base 10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 12A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{12A}
Question: In base-11, what is 49+56? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 6 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. We have 4 + 5 + 1 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is A4. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{A4}
Question: In base-11, what is 46+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 2 = 8 in base-10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 4 + 7 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 108. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Answer:\box{108}
Question: In base-11, what is 48+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 8 = 16 in base-10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 4 + 4 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 95. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. Answer:\box{95} | 14 | 6 | fixed |
In base-11, what is 59+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 134 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 75+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 7 = 12 in base-10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. We have 7 + 7 + 1 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 141. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{141}
Question: In base-11, what is 30+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 0 + 9 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. We have 3 + A + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 129. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Answer:\box{129}
Question: In base-11, what is 14+A6? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 6 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have 1 + A + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 10A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{10A}
Question: In base-11, what is 67+41? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 7 + 1 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. We have 6 + 4 + 0 = 10 in base 10. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A8. In physics, eight is the number of vertices of a cube. Answer:\box{A8}
Question: In base-11, what is 93+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + 9 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. We have 9 + 3 + 1 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 121. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. Answer:\box{121}
Question: In base-11, what is 1A+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + 7 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 1 + 1 + 1 = 3 in base 10. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. 3 mod 11 = 3, so the digit is 3 and the carry is 0. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 36. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{36}
Question: In base-11, what is 54+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 4 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 5 + A + 0 = 15 in base 10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 148. Answer:\box{148}
Question: In base-11, what is 26+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 6 = 12 in base-10. Humans typically have 12 pairs of ribs in their skeletal structure. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have 2 + 2 + 1 = 5 in base 10. In mathematics, five is the third prime number, after two and three. 5 mod 11 = 5, so the digit is 5 and the carry is 0. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 0. So the answer is 51. One often represents the 'on' state in binary code, which underlies digital computing. Answer:\box{51}
Question: In base-11, what is 54+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 8 = 12 in base-10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 5 + 1 + 1 = 7 in base 10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 71. In biology, humans have one heart, which pumps blood throughout the body. Answer:\box{71}
Question: In base-11, what is 77+23? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 3 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 7 + 2 + 0 = 9 in base 10. The gestation period of a human pregnancy is typically nine months. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 9A. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{9A} | 14 | 6 | fixed |
In base-11, what is 30+84? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 104 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 90+25? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 5 = 5 in base-10. In geometry, a pentagon is a five-sided polygon. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. We have 9 + 2 + 0 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 105. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{105}
Question: In base-11, what is 87+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 7 + 4 = 11 in base-10. In computer science, '11' is the binary representation of the decimal number 3. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 8 + 7 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 150. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{150}
Question: In base-11, what is 6A+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 5 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. We have 6 + 3 + 1 = 10 in base 10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A4. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Answer:\box{A4}
Question: In base-11, what is 57+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 7 + 5 = 12 in base-10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 5 + 3 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 91. Answer:\box{91}
Question: In base-11, what is 87+81? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 1 = 8 in base-10. In physics, eight is the number of vertices of a cube. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 8 + 8 + 0 = 16 in base 10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 158. In music, an octave consists of eight notes in the Western musical scale. Answer:\box{158}
Question: In base-11, what is 44+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 9 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. We have 4 + 3 + 1 = 8 in base 10. In physics, eight is the number of vertices of a cube. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 82. In astronomy, Mars, the second planet after Earth, has 2 moons. Answer:\box{82}
Question: In base-11, what is AA+60? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 0 = 10 in base-10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. We have A + 6 + 0 = 16 in base 10. In human biology, 16 is the number of chromosomes in the parasite that causes malaria (Plasmodium falciparum). 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 15A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{15A}
Question: In base-11, what is 88+16? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 8 + 6 = 14 in base-10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 8 + 1 + 1 = 10 in base 10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. So the answer is A3. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{A3}
Question: In base-11, what is 94+65? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 4 + 5 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. We have 9 + 6 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 149. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{149}
Question: In base-11, what is 37+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 3 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. We have 3 + A + 0 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 12A. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{12A} | 14 | 6 | fixed |
In base-11, what is 46+25? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 70 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 96+81? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 6 + 1 = 7 in base-10. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. We have 9 + 8 + 0 = 17 in base 10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 1. So the answer is 167. Answer:\box{167}
Question: In base-11, what is 38+43? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 3 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 3 + 4 + 1 = 8 in base 10. In computer science, a byte is typically made up of 8 bits. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 80. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{80}
Question: In base-11, what is 48+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 7 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. We have 4 + 7 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 114. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{114}
Question: In base-11, what is 3A+94? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 4 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. We have 3 + 9 + 1 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 123. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Answer:\box{123}
Question: In base-11, what is 77+66? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 6 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. We have 7 + 6 + 1 = 14 in base 10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 132. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{132}
Question: In base-11, what is 99+30? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 0 = 9 in base-10. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have 9 + 3 + 0 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. So the answer is 119. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Answer:\box{119}
Question: In base-11, what is 72+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 2 + 2 = 4 in base-10. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In geometry, a square has four equal sides and four right angles. We have 7 + 9 + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In mathematics, five is the third prime number, after two and three. A leading digit is 1. So the answer is 154. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{154}
Question: In base-11, what is 51+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 9 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. We have 5 + 7 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. So the answer is 11A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{11A}
Question: In base-11, what is 78+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 8 + 4 = 12 in base-10. Humans typically have 12 pairs of ribs in their skeletal structure. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. We have 7 + A + 1 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 171. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{171}
Question: In base-11, what is 96+68? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 8 = 14 in base-10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. We have 9 + 6 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Humans have five basic senses: sight, hearing, smell, taste, and touch. A leading digit is 1. So the answer is 153. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{153} | 14 | 6 | fixed |
In base-11, what is 12+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 90 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 74+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 9 = 13 in base-10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 7 + 2 + 1 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A2. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. Answer:\box{A2}
Question: In base-11, what is 66+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 8 = 14 in base-10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. We have 6 + 7 + 1 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). A leading digit is 1. So the answer is 133. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{133}
Question: In base-11, what is 48+67? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 8 + 7 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 4 + 6 + 1 = 11 in base 10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 104. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{104}
Question: In base-11, what is 79+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 9 + 3 = 12 in base-10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. We have 7 + 6 + 1 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 131. Answer:\box{131}
Question: In base-11, what is 97+31? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 1 = 8 in base-10. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In music, an octave consists of eight notes in the Western musical scale. We have 9 + 3 + 0 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 118. In physics, eight is the number of vertices of a cube. Answer:\box{118}
Question: In base-11, what is 79+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 5 = 14 in base-10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. We have 7 + 9 + 1 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 163. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{163}
Question: In base-11, what is 90+50? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 0 = 0 in base-10. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 0 mod 11 = 0, so the digit is 0 and the carry is 0. We have 9 + 5 + 0 = 14 in base 10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. 14 mod 11 = 3, so the digit is 3 and the carry is 1. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 130. Answer:\box{130}
Question: In base-11, what is 28+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 8 + 4 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 2 + 7 + 1 = 10 in base 10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is A1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{A1}
Question: In base-11, what is 39+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 9 + 7 = 16 in base-10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 3 + 4 + 1 = 8 in base 10. In physics, eight is the number of vertices of a cube. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 85. Answer:\box{85}
Question: In base-11, what is A1+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 1 + 8 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. We have A + 2 + 0 = 12 in base 10. Humans typically have 12 pairs of ribs in their skeletal structure. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 119. Answer:\box{119} | 14 | 6 | fixed |
In base-11, what is 15+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A2 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 56+55? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 5 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 5 + 5 + 1 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. A leading digit is 1. So the answer is 100. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{100}
Question: In base-11, what is 88+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 8 = 16 in base-10. In human biology, 16 is the number of chromosomes in the parasite that causes malaria (Plasmodium falciparum). Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 8 + 7 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Humans have five basic senses: sight, hearing, smell, taste, and touch. A leading digit is 1. So the answer is 155. In geometry, a pentagon is a five-sided polygon. Answer:\box{155}
Question: In base-11, what is 18+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 6 = 14 in base-10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 1 + 7 + 1 = 9 in base 10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. 9 mod 11 = 9, so the digit is 9 and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 93. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{93}
Question: In base-11, what is 37+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 3 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 3 + A + 0 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. So the answer is 12A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{12A}
Question: In base-11, what is 91+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 1 + 8 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. We have 9 + A + 0 = 19 in base 10. COVID-19, which stands for 'Coronavirus Disease 2019', was named for the year it was first identified. 19 mod 11 = 8, so the digit is 8 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 189. The gestation period of a human pregnancy is typically nine months. Answer:\box{189}
Question: In base-11, what is 5A+51? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 1 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 5 + 5 + 1 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 100. Answer:\box{100}
Question: In base-11, what is 86+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 4 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. We have 8 + A + 0 = 18 in base 10. In golf, a standard round consists of 18 holes. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 17A. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{17A}
Question: In base-11, what is 74+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 0 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 7 + 8 + 0 = 15 in base 10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 144. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Answer:\box{144}
Question: In base-11, what is 9A+24? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + 4 = 14 in base-10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). We have 9 + 2 + 1 = 12 in base 10. Humans typically have 12 pairs of ribs in their skeletal structure. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 113. Answer:\box{113}
Question: In base-11, what is A8+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 7 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have A + 3 + 1 = 14 in base 10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 134. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{134} | 14 | 6 | fixed |
In base-11, what is 87+20? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A7 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 68+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 0 = 8 in base-10. In physics, eight is the number of vertices of a cube. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. We have 6 + 7 + 0 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 128. Answer:\box{128}
Question: In base-11, what is 17+55? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 5 = 12 in base-10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have 1 + 5 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 71. In biology, humans have one heart, which pumps blood throughout the body. Answer:\box{71}
Question: In base-11, what is 4A+A0? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 0 = 10 in base-10. The number 10 is symbolic in many cultures, often representing perfection or completeness. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have 4 + A + 0 = 14 in base 10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 13A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{13A}
Question: In base-11, what is 46+62? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 6 + 2 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 4 + 6 + 0 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A8. In physics, eight is the number of vertices of a cube. Answer:\box{A8}
Question: In base-11, what is 87+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 6 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 8 + 8 + 1 = 17 in base 10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 162. Two is the base of the binary code, used extensively in computer science. Answer:\box{162}
Question: In base-11, what is A0+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 8 = 8 in base-10. Spiders, part of the arachnid family in biology, typically have eight legs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. We have A + 2 + 0 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 118. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{118}
Question: In base-11, what is 19+AA? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + A = 19 in base-10. In mathematics, nineteen is a prime number, the 8th prime number in the series. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is a Fibonacci number and a cube number. We have 1 + A + 1 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 118. Answer:\box{118}
Question: In base-11, what is 46+55? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 5 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. We have 4 + 5 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. Answer:\box{A0}
Question: In base-11, what is 9A+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + 0 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. We have 9 + 7 + 0 = 16 in base 10. In computer science, a 'nibble' is a four-bit aggregation, or half an octet, and two nibbles make up a byte, which is 16 bits. 16 mod 11 = 5, so the digit is 5 and the carry is 1. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 15A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{15A}
Question: In base-11, what is 72+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 2 + 4 = 6 in base-10. The standard guitar has six strings. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 7 + 6 + 0 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 126. Answer:\box{126} | 14 | 6 | fixed |
In base-11, what is 96+50? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 136 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A5+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + 3 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. We have A + A + 0 = 20 in base 10. In physics, the twentieth century saw the development of quantum physics and the theory of relativity, two fundamental shifts in our understanding of the universe. 20 mod 11 = 9, so the digit is 9 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 198. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Answer:\box{198}
Question: In base-11, what is 71+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 8 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 7 + 5 + 0 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 119. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Answer:\box{119}
Question: In base-11, what is 64+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 4 + 9 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 6 + 7 + 1 = 14 in base 10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 132. In mathematics, two is the smallest and first prime number. Answer:\box{132}
Question: In base-11, what is 66+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 8 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. We have 6 + 3 + 1 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is A3. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{A3}
Question: In base-11, what is 54+55? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 4 + 5 = 9 in base-10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. We have 5 + 5 + 0 = 10 in base 10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A9. Answer:\box{A9}
Question: In base-11, what is 48+24? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 4 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. We have 4 + 2 + 1 = 7 in base 10. In biology, a rainbow is seen in seven colors due to the refraction of light. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 71. Answer:\box{71}
Question: In base-11, what is 40+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 0 + 1 = 1 in base-10. One often represents the 'on' state in binary code, which underlies digital computing. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 1 mod 11 = 1, so the digit is 1 and the carry is 0. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have 4 + 7 + 0 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). A leading digit is 1. So the answer is 101. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{101}
Question: In base-11, what is 2A+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 5 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. We have 2 + 3 + 1 = 6 in base 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 64. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{64}
Question: In base-11, what is 97+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 3 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 9 + 6 + 0 = 15 in base 10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 14A. Answer:\box{14A}
Question: In base-11, what is 80+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 0 + 8 = 8 in base-10. In mathematics, eight is a Fibonacci number and a cube number. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have 8 + 4 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 118. Answer:\box{118} | 14 | 6 | fixed |
In base-11, what is 91+25? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 106 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 46+14? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 6 + 4 = 10 in base-10. The number 10 is symbolic in many cultures, often representing perfection or completeness. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. We have 4 + 1 + 0 = 5 in base 10. In mathematics, five is the third prime number, after two and three. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 5A. Answer:\box{5A}
Question: In base-11, what is 68+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + A = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have 6 + 8 + 1 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. A leading digit is 1. So the answer is 147. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. Answer:\box{147}
Question: In base-11, what is 84+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 4 + 5 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 8 + 3 + 0 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 109. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. Answer:\box{109}
Question: In base-11, what is 18+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 3 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 1 + 8 + 1 = 10 in base 10. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. Answer:\box{A0}
Question: In base-11, what is 75+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 9 = 14 in base-10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. We have 7 + 4 + 1 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. So the answer is 113. In astronomy, Earth is the third planet from the Sun in our Solar System. Answer:\box{113}
Question: In base-11, what is 57+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 6 = 13 in base-10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 5 + 8 + 1 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. A leading digit is 1. So the answer is 132. In human anatomy, the body is largely symmetrical with two halves. Answer:\box{132}
Question: In base-11, what is 68+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 8 + 0 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 6 + 7 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 128. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{128}
Question: In base-11, what is 70+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 5 = 5 in base-10. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. We have 7 + 3 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A5. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Answer:\box{A5}
Question: In base-11, what is 94+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + 2 = 6 in base-10. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the atomic number of carbon in chemistry, a key element for life as we know it. We have 9 + 9 + 0 = 18 in base 10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. So the answer is 176. In geometry, a hexagon is a six-sided polygon. Answer:\box{176}
Question: In base-11, what is 70+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 0 + 3 = 3 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 3 mod 11 = 3, so the digit is 3 and the carry is 0. Physics recognises three laws of motion, first compiled by Isaac Newton. We have 7 + 3 + 0 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A3. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{A3} | 14 | 6 | fixed |
In base-11, what is 61+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 131 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 47+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 1 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 4 + A + 0 = 14 in base 10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 138. In mathematics, eight is a Fibonacci number and a cube number. Answer:\box{138}
Question: In base-11, what is 42+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 9 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 4 + A + 1 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 140. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{140}
Question: In base-11, what is 45+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 6 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 4 + 9 + 1 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 130. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{130}
Question: In base-11, what is 95+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 7 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 9 + 7 + 1 = 17 in base 10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 161. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{161}
Question: In base-11, what is 86+81? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 1 = 7 in base-10. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have 8 + 8 + 0 = 16 in base 10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 157. Answer:\box{157}
Question: In base-11, what is 20+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 0 + A = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have 2 + 8 + 0 = 10 in base 10. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. So the answer is AA. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{AA}
Question: In base-11, what is 71+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 1 + 4 = 5 in base-10. In mathematics, five is the third prime number, after two and three. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 5 mod 11 = 5, so the digit is 5 and the carry is 0. We have 7 + 5 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 115. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Answer:\box{115}
Question: In base-11, what is 97+21? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 1 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, eight is the number of vertices of a cube. We have 9 + 2 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 108. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Answer:\box{108}
Question: In base-11, what is 78+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + A = 18 in base-10. Humans have 18 muscles in each hand, which control fine motor movements. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. We have 7 + 9 + 1 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In geometry, a hexagon is a six-sided polygon. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 167. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{167}
Question: In base-11, what is A8+57? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 7 = 15 in base-10. There are 15 facial bones in the human skull (not including the mandible, or lower jaw bone). Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. We have A + 5 + 1 = 16 in base 10. In human biology, 16 is the number of chromosomes in the parasite that causes malaria (Plasmodium falciparum). 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 154. Answer:\box{154} | 14 | 6 | fixed |
In base-11, what is 92+32? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 114 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 17+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + A = 17 in base-10. In human biology, the kidneys filter about 17 liters of blood every hour. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 1 + 9 + 1 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. So the answer is 106. Answer:\box{106}
Question: In base-11, what is 69+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 9 + 0 = 9 in base-10. The gestation period of a human pregnancy is typically nine months. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. We have 6 + 7 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. So the answer is 129. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{129}
Question: In base-11, what is 61+75? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 1 + 5 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 6 + 7 + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 126. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{126}
Question: In base-11, what is 81+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 9 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. We have 8 + 7 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 14A. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{14A}
Question: In base-11, what is 2A+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + A = 20 in base-10. In mathematics, twenty is the basis of vigesimal number systems and is used in scoring many traditional games. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 20 mod 11 = 9, so the digit is 9 and the carry is 1. We have 2 + 1 + 1 = 4 in base 10. In geometry, a square has four equal sides and four right angles. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 49. The gestation period of a human pregnancy is typically nine months. Answer:\box{49}
Question: In base-11, what is 2A+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have A + 2 = 12 in base-10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 2 + A + 1 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 121. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{121}
Question: In base-11, what is 37+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 9 = 16 in base-10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. Since we're in base-11, that exceeds the maximum value of A for a single digit. 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 3 + 8 + 1 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. So the answer is 115. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{115}
Question: In base-11, what is 3A+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + 8 = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. We have 3 + 3 + 1 = 7 in base 10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 77. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Answer:\box{77}
Question: In base-11, what is 43+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 6 = 9 in base-10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 4 + 7 + 0 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 109. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Answer:\box{109}
Question: In base-11, what is 8A+65? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have A + 5 = 15 in base-10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. We have 8 + 6 + 1 = 15 in base 10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 144. Answer:\box{144} | 14 | 6 | fixed |
In base-11, what is 3A+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 88 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 80+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 0 + A = 10 in base-10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 8 + 9 + 0 = 17 in base 10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. 17 mod 11 = 6, so the digit is 6 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 16A. Answer:\box{16A}
Question: In base-11, what is 91+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 1 + 7 = 8 in base-10. Spiders, part of the arachnid family in biology, typically have eight legs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, eight is the number of vertices of a cube. We have 9 + 4 + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. So the answer is 128. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Answer:\box{128}
Question: In base-11, what is A0+3A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 0 + A = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have A + 3 + 0 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. A leading digit is 1. So the answer is 12A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{12A}
Question: In base-11, what is 98+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 8 + 9 = 17 in base-10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 9 + 5 + 1 = 15 in base 10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 146. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Answer:\box{146}
Question: In base-11, what is 98+36? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 6 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 9 + 3 + 1 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 123. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{123}
Question: In base-11, what is 82+22? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 2 = 4 in base-10. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 4 mod 11 = 4, so the digit is 4 and the carry is 0. We have 8 + 2 + 0 = 10 in base 10. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is A4. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{A4}
Question: In base-11, what is 74+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + 8 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. We have 7 + A + 1 = 18 in base 10. In the Jewish tradition, the number 18 symbolizes 'chai', which means 'life' in Hebrew. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 171. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{171}
Question: In base-11, what is 24+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 9 = 13 in base-10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. We have 2 + 2 + 1 = 5 in base 10. In geometry, a pentagon is a five-sided polygon. 5 mod 11 = 5, so the digit is 5 and the carry is 0. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 52. Answer:\box{52}
Question: In base-11, what is A3+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 3 + 7 = 10 in base-10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. We have A + 3 + 0 = 13 in base 10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Humans have two sets of each of their chromosomes, making us diploid organisms. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 12A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{12A}
Question: In base-11, what is A6+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + A = 16 in base-10. In computer science, a 'nibble' is a four-bit aggregation, or half an octet, and two nibbles make up a byte, which is 16 bits. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. We have A + 9 + 1 = 20 in base 10. 20 mod 11 = 9, so the digit is 9 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 195. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. Answer:\box{195} | 14 | 6 | fixed |
In base-11, what is 60+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 13A | Math-11 | Irrelevant | Hard | Question: In base-11, what is 82+52? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 2 + 2 = 4 in base-10. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. We have 8 + 5 + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. So the answer is 124. Answer:\box{124}
Question: In base-11, what is 33+93? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 3 = 6 in base-10. In geometry, a hexagon is a six-sided polygon. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 3 + 9 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 116. Answer:\box{116}
Question: In base-11, what is AA+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 5 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. We have A + 3 + 1 = 14 in base 10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 134. In geometry, a square has four equal sides and four right angles. Answer:\box{134}
Question: In base-11, what is 86+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 6 + 9 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. We have 8 + 7 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 154. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{154}
Question: In base-11, what is 51+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 1 + 3 = 4 in base-10. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. We have 5 + 7 + 0 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. So the answer is 114. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. Answer:\box{114}
Question: In base-11, what is 48+46? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 6 = 14 in base-10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 4 + 4 + 1 = 9 in base 10. The gestation period of a human pregnancy is typically nine months. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 93. Answer:\box{93}
Question: In base-11, what is 84+56? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 4 + 6 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 8 + 5 + 0 = 13 in base 10. Thirteen is the atomic number of aluminium in chemistry, a post-transition metal that's widely used for its lightness and resistance to corrosion. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 12A. Answer:\box{12A}
Question: In base-11, what is 45+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 5 + 6 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. We have 4 + 2 + 1 = 7 in base 10. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. A leading digit is 0. So the answer is 70. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{70}
Question: In base-11, what is 85+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + A = 15 in base-10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 8 + 9 + 1 = 18 in base 10. In golf, a standard round consists of 18 holes. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 174. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{174}
Question: In base-11, what is AA+81? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 1 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have A + 8 + 1 = 19 in base 10. A standard basketball game consists of four quarters, each lasting 19 minutes in many high school associations. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 180. Answer:\box{180} | 14 | 6 | fixed |
In base-11, what is 70+43? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 103 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 54+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 4 + A = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 5 + 9 + 1 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 143. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{143}
Question: In base-11, what is 90+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 0 + 9 = 9 in base-10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 9 + A + 0 = 19 in base 10. In computer science, the ISO-8859-19 standard is used for encoding Baltic languages, among others. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 189. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. Answer:\box{189}
Question: In base-11, what is A6+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 7 = 13 in base-10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. We have A + 8 + 1 = 19 in base 10. In mathematics, nineteen is a prime number, the 8th prime number in the series. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 182. Answer:\box{182}
Question: In base-11, what is 78+12? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 2 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 7 + 1 + 0 = 8 in base 10. In physics, eight is the number of vertices of a cube. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. A leading digit is 0. So the answer is 8A. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Answer:\box{8A}
Question: In base-11, what is 70+A6? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 6 = 6 in base-10. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 7 + A + 0 = 17 in base 10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 166. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Answer:\box{166}
Question: In base-11, what is 92+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 6 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, eight is the number of vertices of a cube. We have 9 + 2 + 0 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 108. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Answer:\box{108}
Question: In base-11, what is A2+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 5 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have A + 9 + 0 = 19 in base 10. Nineteen is the atomic number of potassium in chemistry, an essential mineral for the function of all living cells. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In physics, eight is the number of vertices of a cube. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 187. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{187}
Question: In base-11, what is 87+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 5 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have 8 + 9 + 1 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 171. In physics, the number one is the charge of a single unit of positive or negative electricity. Answer:\box{171}
Question: In base-11, what is 83+53? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 3 + 3 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 8 + 5 + 0 = 13 in base 10. Thirteen is the atomic number of aluminium in chemistry, a post-transition metal that's widely used for its lightness and resistance to corrosion. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. A leading digit is 1. So the answer is 126. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{126}
Question: In base-11, what is 88+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 8 + 8 = 16 in base-10. In computer science, a 'nibble' is a four-bit aggregation, or half an octet, and two nibbles make up a byte, which is 16 bits. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 8 + 2 + 1 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 105. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. Answer:\box{105} | 14 | 6 | fixed |
In base-11, what is 85+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 177 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 94+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 5 = 9 in base-10. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 9 + 8 + 0 = 17 in base 10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 169. Answer:\box{169}
Question: In base-11, what is 72+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 2 + A = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. We have 7 + 7 + 1 = 15 in base 10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 141. Answer:\box{141}
Question: In base-11, what is 57+62? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 2 = 9 in base-10. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 5 + 6 + 0 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 109. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{109}
Question: In base-11, what is 64+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + 7 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 6 + 4 + 1 = 11 in base 10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 100. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. Answer:\box{100}
Question: In base-11, what is 42+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 2 + 2 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 4 + 9 + 0 = 13 in base 10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 124. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{124}
Question: In base-11, what is 83+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 1 = 4 in base-10. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 8 + 7 + 0 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 144. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{144}
Question: In base-11, what is 58+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + A = 18 in base-10. In physics, there are 18 families of elementary particles in the Standard Model. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have 5 + 1 + 1 = 7 in base 10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 0. So the answer is 77. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{77}
Question: In base-11, what is 37+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 7 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. We have 3 + 3 + 1 = 7 in base 10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. 7 mod 11 = 7, so the digit is 7 and the carry is 0. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 73. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Answer:\box{73}
Question: In base-11, what is 66+84? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 4 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. We have 6 + 8 + 0 = 14 in base 10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 13A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{13A}
Question: In base-11, what is A7+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 7 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. We have A + 8 + 1 = 19 in base 10. In human biology, the first 19 elements of the periodic table are all found in the human body. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 183. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. Answer:\box{183} | 14 | 6 | fixed |
In base-11, what is 79+12? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 90 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 96+51? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 1 = 7 in base-10. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 7 mod 11 = 7, so the digit is 7 and the carry is 0. We have 9 + 5 + 0 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 137. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{137}
Question: In base-11, what is 47+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 1 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. We have 4 + 9 + 0 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. So the answer is 128. In physics, eight is the number of vertices of a cube. Answer:\box{128}
Question: In base-11, what is 12+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 9 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. We have 1 + 1 + 1 = 3 in base 10. In colors, there are three primary colors: red, yellow, and blue. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 30. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{30}
Question: In base-11, what is A0+57? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 0 + 7 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. We have A + 5 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. A leading digit is 1. So the answer is 147. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. Answer:\box{147}
Question: In base-11, what is 98+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 8 + 1 = 9 in base-10. The gestation period of a human pregnancy is typically nine months. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. We have 9 + 7 + 0 = 16 in base 10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 1. So the answer is 159. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{159}
Question: In base-11, what is 89+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 9 + 6 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 8 + 7 + 1 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 154. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Answer:\box{154}
Question: In base-11, what is 9A+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + 9 = 19 in base-10. In mathematics, nineteen is a prime number, the 8th prime number in the series. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is a Fibonacci number and a cube number. We have 9 + 7 + 1 = 17 in base 10. In physics, group 17 elements in the periodic table are known as the halogens, which include fluorine and chlorine. 17 mod 11 = 6, so the digit is 6 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 168. Answer:\box{168}
Question: In base-11, what is 65+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 5 + 7 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have 6 + 1 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 81. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{81}
Question: In base-11, what is A2+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 4 = 6 in base-10. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. We have A + 3 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Humans have two sets of each of their chromosomes, making us diploid organisms. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 126. Answer:\box{126}
Question: In base-11, what is 81+27? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 1 + 7 = 8 in base-10. In mathematics, eight is a Fibonacci number and a cube number. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have 8 + 2 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A8. In music, an octave consists of eight notes in the Western musical scale. Answer:\box{A8} | 14 | 6 | fixed |
In base-11, what is A0+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 162 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A7+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 8 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. We have A + A + 1 = 21 in base 10. In mathematics, 21 is a triangular number, meaning it can be depicted as an equilateral triangle with dots. 21 mod 11 = A, so the digit is A and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 1A4. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{1A4}
Question: In base-11, what is 35+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + A = 15 in base-10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 3 + 1 + 1 = 5 in base 10. In mathematics, five is the third prime number, after two and three. 5 mod 11 = 5, so the digit is 5 and the carry is 0. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. A leading digit is 0. So the answer is 54. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Answer:\box{54}
Question: In base-11, what is 11+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 1 + 9 = 10 in base-10. The number 10 is symbolic in many cultures, often representing perfection or completeness. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. We have 1 + 4 + 0 = 5 in base 10. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. 5 mod 11 = 5, so the digit is 5 and the carry is 0. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 5A. Answer:\box{5A}
Question: In base-11, what is 7A+36? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + 6 = 16 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. We have 7 + 3 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 105. In geometry, a pentagon is a five-sided polygon. Answer:\box{105}
Question: In base-11, what is 14+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 8 = 12 in base-10. Humans typically have 12 pairs of ribs in their skeletal structure. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. We have 1 + 5 + 1 = 7 in base 10. In biology, a rainbow is seen in seven colors due to the refraction of light. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. A leading digit is 0. So the answer is 71. One often represents the 'on' state in binary code, which underlies digital computing. Answer:\box{71}
Question: In base-11, what is 64+94? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 4 = 8 in base-10. In physics, eight is the number of vertices of a cube. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. We have 6 + 9 + 0 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 148. In computer science, a byte is typically made up of 8 bits. Answer:\box{148}
Question: In base-11, what is 38+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 5 = 13 in base-10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. We have 3 + 8 + 1 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 112. Answer:\box{112}
Question: In base-11, what is 94+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + 2 = 6 in base-10. The standard guitar has six strings. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the atomic number of carbon in chemistry, a key element for life as we know it. We have 9 + 9 + 0 = 18 in base 10. Humans have 18 muscles in each hand, which control fine motor movements. 18 mod 11 = 7, so the digit is 7 and the carry is 1. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. A leading digit is 1. So the answer is 176. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Answer:\box{176}
Question: In base-11, what is 25+16? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 5 + 6 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. We have 2 + 1 + 1 = 4 in base 10. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 40. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{40}
Question: In base-11, what is 78+13? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 3 = 11 in base-10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. We have 7 + 1 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 90. Answer:\box{90} | 14 | 6 | fixed |
In base-11, what is 90+10? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A0 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A5+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 5 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have A + 8 + 0 = 18 in base 10. In golf, a standard round consists of 18 holes. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 17A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{17A}
Question: In base-11, what is 33+68? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 8 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 3 + 6 + 1 = 10 in base 10. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A0. Answer:\box{A0}
Question: In base-11, what is 56+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 6 + 8 = 14 in base-10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have 5 + A + 1 = 16 in base 10. In computer science, a 'nibble' is a four-bit aggregation, or half an octet, and two nibbles make up a byte, which is 16 bits. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. So the answer is 153. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{153}
Question: In base-11, what is 79+61? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + 1 = 10 in base-10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. We have 7 + 6 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 12A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{12A}
Question: In base-11, what is 40+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 9 = 9 in base-10. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. We have 4 + 8 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 119. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{119}
Question: In base-11, what is 97+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 7 + 4 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 9 + 6 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 150. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{150}
Question: In base-11, what is 81+45? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 5 = 6 in base-10. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In geometry, a hexagon is a six-sided polygon. We have 8 + 4 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 116. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{116}
Question: In base-11, what is 21+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 7 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. We have 2 + 9 + 0 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 108. Answer:\box{108}
Question: In base-11, what is 69+53? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 9 + 3 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. We have 6 + 5 + 1 = 12 in base 10. Humans typically have 12 pairs of ribs in their skeletal structure. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 111. In biology, humans have one heart, which pumps blood throughout the body. Answer:\box{111}
Question: In base-11, what is 15+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 8 = 13 in base-10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. We have 1 + 3 + 1 = 5 in base 10. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In geometry, a pentagon is a five-sided polygon. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 52. In mathematics, an area is a two-dimensional size of a defined part of a surface. Answer:\box{52} | 14 | 6 | fixed |
In base-11, what is 29+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 120 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 86+99? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 9 = 15 in base-10. In computer science, a 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. We have 8 + 9 + 1 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 174. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{174}
Question: In base-11, what is A7+81? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 1 = 8 in base-10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. We have A + 8 + 0 = 18 in base 10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. A leading digit is 1. So the answer is 178. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{178}
Question: In base-11, what is 84+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 4 + 0 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 8 + 8 + 0 = 16 in base 10. In human biology, 16 is the number of chromosomes in the parasite that causes malaria (Plasmodium falciparum). 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. So the answer is 154. In geometry, a square has four equal sides and four right angles. Answer:\box{154}
Question: In base-11, what is 88+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 3 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 8 + A + 1 = 19 in base 10. In human biology, the human adult skull is made up of 19 bones when the mandible (a separate bone) is included. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is a Fibonacci number and a cube number. A leading digit is 1. So the answer is 180. Answer:\box{180}
Question: In base-11, what is 55+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 5 + A = 15 in base-10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. We have 5 + 4 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A4. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. Answer:\box{A4}
Question: In base-11, what is 36+3A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 6 + A = 16 in base-10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 3 + 3 + 1 = 7 in base 10. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 75. Answer:\box{75}
Question: In base-11, what is 14+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + A = 14 in base-10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 1 + 7 + 1 = 9 in base 10. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. 9 mod 11 = 9, so the digit is 9 and the carry is 0. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 93. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Answer:\box{93}
Question: In base-11, what is 15+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + 7 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. We have 1 + 1 + 1 = 3 in base 10. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). 3 mod 11 = 3, so the digit is 3 and the carry is 0. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. A leading digit is 0. So the answer is 31. One often represents the 'on' state in binary code, which underlies digital computing. Answer:\box{31}
Question: In base-11, what is 43+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 4 = 7 in base-10. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have 4 + 6 + 0 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. A leading digit is 0. So the answer is A7. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Answer:\box{A7}
Question: In base-11, what is 85+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 2 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. We have 8 + 9 + 0 = 17 in base 10. Seventeen is the atomic number of chlorine in chemistry, a halogen that's widely used in disinfectants. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In geometry, a hexagon is a six-sided polygon. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 167. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{167} | 14 | 6 | fixed |
In base-11, what is 3A+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | AA | Math-11 | Irrelevant | Hard | Question: In base-11, what is 19+21? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + 1 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. We have 1 + 2 + 0 = 3 in base 10. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. 3 mod 11 = 3, so the digit is 3 and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 3A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{3A}
Question: In base-11, what is 60+50? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 0 + 0 = 0 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 0 mod 11 = 0, so the digit is 0 and the carry is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. We have 6 + 5 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 100. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{100}
Question: In base-11, what is 4A+57? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 7 = 17 in base-10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 4 + 5 + 1 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. So the answer is A6. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Answer:\box{A6}
Question: In base-11, what is 47+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 7 + 9 = 16 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 4 + 4 + 1 = 9 in base 10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 95. Humans have five basic senses: sight, hearing, smell, taste, and touch. Answer:\box{95}
Question: In base-11, what is 26+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 8 = 14 in base-10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 2 + 4 + 1 = 7 in base 10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 73. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. Answer:\box{73}
Question: In base-11, what is 42+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 4 = 6 in base-10. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 4 + 6 + 0 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A6. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Answer:\box{A6}
Question: In base-11, what is 87+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 7 + 8 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 8 + 3 + 1 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 114. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{114}
Question: In base-11, what is 63+98? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 3 + 8 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 6 + 9 + 1 = 16 in base 10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In mathematics, five is the third prime number, after two and three. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 150. Answer:\box{150}
Question: In base-11, what is 52+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 9 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. We have 5 + 2 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 80. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{80}
Question: In base-11, what is 74+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 4 + 8 = 12 in base-10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have 7 + 3 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 101. Answer:\box{101} | 14 | 6 | fixed |
In base-11, what is 76+AA? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 175 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A3+75? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 5 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In music, an octave consists of eight notes in the Western musical scale. We have A + 7 + 0 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 168. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Answer:\box{168}
Question: In base-11, what is A0+24? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 0 + 4 = 4 in base-10. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have A + 2 + 0 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. So the answer is 114. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{114}
Question: In base-11, what is 81+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 1 + 4 = 5 in base-10. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 5 mod 11 = 5, so the digit is 5 and the carry is 0. We have 8 + A + 0 = 18 in base 10. In golf, a standard round consists of 18 holes. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. A leading digit is 1. So the answer is 175. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. Answer:\box{175}
Question: In base-11, what is 68+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 8 + 9 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In geometry, a hexagon is a six-sided polygon. We have 6 + 2 + 1 = 9 in base 10. The gestation period of a human pregnancy is typically nine months. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 96. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Answer:\box{96}
Question: In base-11, what is 99+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 0 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. We have 9 + 8 + 0 = 17 in base 10. Seventeen is the atomic number of chlorine in chemistry, a halogen that's widely used in disinfectants. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 169. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{169}
Question: In base-11, what is 99+65? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 5 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). We have 9 + 6 + 1 = 16 in base 10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 153. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{153}
Question: In base-11, what is 28+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 5 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. We have 2 + A + 1 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 122. In mathematics, two is the smallest and first prime number. Answer:\box{122}
Question: In base-11, what is 43+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 8 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 4 + 5 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{A0}
Question: In base-11, what is A6+66? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 6 + 6 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have A + 6 + 1 = 17 in base 10. Seventeen is a Fermat prime, as it is in the form of 2^(2^n) + 1, with n = 2. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 161. In physics, the number one is the charge of a single unit of positive or negative electricity. Answer:\box{161}
Question: In base-11, what is 52+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 5 = 7 in base-10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. We have 5 + A + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. So the answer is 147. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{147} | 14 | 6 | fixed |
In base-11, what is 93+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 179 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 92+21? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 2 + 1 = 3 in base-10. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 3 mod 11 = 3, so the digit is 3 and the carry is 0. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). We have 9 + 2 + 0 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 103. Answer:\box{103}
Question: In base-11, what is 75+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 6 = 11 in base-10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 7 + 2 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{A0}
Question: In base-11, what is 91+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 1 + 2 = 3 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 3 mod 11 = 3, so the digit is 3 and the carry is 0. Physics recognises three laws of motion, first compiled by Isaac Newton. We have 9 + 9 + 0 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 173. In astronomy, Earth is the third planet from the Sun in our Solar System. Answer:\box{173}
Question: In base-11, what is 82+42? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + 2 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 4 mod 11 = 4, so the digit is 4 and the carry is 0. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. We have 8 + 4 + 0 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 114. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{114}
Question: In base-11, what is 76+62? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 2 = 8 in base-10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. We have 7 + 6 + 0 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 128. Answer:\box{128}
Question: In base-11, what is 12+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 2 + 2 = 4 in base-10. In geometry, a square has four equal sides and four right angles. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. We have 1 + 9 + 0 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. So the answer is A4. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{A4}
Question: In base-11, what is 21+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 1 + 8 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have 2 + A + 0 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 119. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{119}
Question: In base-11, what is 93+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 3 + 9 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 9 + 6 + 1 = 16 in base 10. There are 16 ounces in a pound in the avoirdupois system of measurement. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 151. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{151}
Question: In base-11, what is 84+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 8 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 8 + 2 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 101. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{101}
Question: In base-11, what is A6+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 3 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. We have A + 8 + 0 = 18 in base 10. In physics, there are 18 families of elementary particles in the Standard Model. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 179. Answer:\box{179} | 14 | 6 | fixed |
In base-11, what is 22+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A0 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A5+53? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + 3 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. We have A + 5 + 0 = 15 in base 10. In mathematics, a group of 15 is known as a pentadecagon, which is a polygon with 15 sides and 15 angles. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 148. In computer science, a byte is typically made up of 8 bits. Answer:\box{148}
Question: In base-11, what is 81+36? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 1 + 6 = 7 in base-10. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. We have 8 + 3 + 0 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 107. Answer:\box{107}
Question: In base-11, what is AA+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 7 = 17 in base-10. In physics, group 17 elements in the periodic table are known as the halogens, which include fluorine and chlorine. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have A + 1 + 1 = 12 in base 10. Humans typically have 12 pairs of ribs in their skeletal structure. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. So the answer is 116. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{116}
Question: In base-11, what is 11+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 9 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 1 + 5 + 0 = 6 in base 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In geometry, a hexagon is a six-sided polygon. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 6A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{6A}
Question: In base-11, what is 2A+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have A + 9 = 19 in base-10. In human biology, the human adult skull is made up of 19 bones when the mandible (a separate bone) is included. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is a Fibonacci number and a cube number. We have 2 + 7 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. So the answer is A8. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Answer:\box{A8}
Question: In base-11, what is 91+93? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 1 + 3 = 4 in base-10. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 9 + 9 + 0 = 18 in base 10. In Tarot, the Moon card is card number 18, representing intuition, dreams, and the unconscious. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 174. Answer:\box{174}
Question: In base-11, what is 51+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 1 + 2 = 3 in base-10. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In astronomy, Earth is the third planet from the Sun in our Solar System. We have 5 + 8 + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. So the answer is 123. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{123}
Question: In base-11, what is 47+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 4 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 4 + 3 + 1 = 8 in base 10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In computer science, a byte is typically made up of 8 bits. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 80. Answer:\box{80}
Question: In base-11, what is 95+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 5 + 8 = 13 in base-10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. We have 9 + 8 + 1 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 172. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{172}
Question: In base-11, what is 95+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 0 = 5 in base-10. In geometry, a pentagon is a five-sided polygon. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 5 mod 11 = 5, so the digit is 5 and the carry is 0. We have 9 + 7 + 0 = 16 in base 10. In human biology, 16 is the number of chromosomes in the parasite that causes malaria (Plasmodium falciparum). 16 mod 11 = 5, so the digit is 5 and the carry is 1. In mathematics, five is the third prime number, after two and three. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 155. Answer:\box{155} | 14 | 6 | fixed |
In base-11, what is 61+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 127 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A0+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + A = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have A + 9 + 0 = 19 in base 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. Eight is the atomic number of oxygen in chemistry, an element essential for human life. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 18A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{18A}
Question: In base-11, what is 18+43? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 3 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 1 + 4 + 1 = 6 in base 10. In astronomy, Saturn is the sixth planet from the Sun in our solar system. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 60. Answer:\box{60}
Question: In base-11, what is 87+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + 8 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. We have 8 + 5 + 1 = 14 in base 10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. 14 mod 11 = 3, so the digit is 3 and the carry is 1. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 134. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{134}
Question: In base-11, what is 6A+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + 9 = 19 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In physics, eight is the number of vertices of a cube. We have 6 + 1 + 1 = 8 in base 10. In mathematics, eight is a Fibonacci number and a cube number. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 88. In computer science, a byte is typically made up of 8 bits. Answer:\box{88}
Question: In base-11, what is 94+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 4 + 9 = 13 in base-10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. We have 9 + 4 + 1 = 14 in base 10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. A leading digit is 1. So the answer is 132. In astronomy, Mars, the second planet after Earth, has 2 moons. Answer:\box{132}
Question: In base-11, what is A9+41? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 9 + 1 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have A + 4 + 0 = 14 in base 10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 13A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{13A}
Question: In base-11, what is 66+93? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 6 + 3 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. We have 6 + 9 + 0 = 15 in base 10. There are 15 facial bones in the human skull (not including the mandible, or lower jaw bone). 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 1. So the answer is 149. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Answer:\box{149}
Question: In base-11, what is 90+45? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 0 + 5 = 5 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 5 mod 11 = 5, so the digit is 5 and the carry is 0. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. We have 9 + 4 + 0 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 125. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Answer:\box{125}
Question: In base-11, what is 76+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 1 = 7 in base-10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 7 mod 11 = 7, so the digit is 7 and the carry is 0. We have 7 + 9 + 0 = 16 in base 10. There are 16 ounces in a pound in the avoirdupois system of measurement. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 157. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{157}
Question: In base-11, what is 79+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 8 = 17 in base-10. Seventeen is a Fermat prime, as it is in the form of 2^(2^n) + 1, with n = 2. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. We have 7 + 5 + 1 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 126. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{126} | 14 | 6 | fixed |
In base-11, what is 47+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 10A | Math-11 | Irrelevant | Hard | Question: In base-11, what is 56+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 5 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 5 + 9 + 1 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. A leading digit is 1. So the answer is 140. Answer:\box{140}
Question: In base-11, what is 38+15? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 5 = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 3 + 1 + 1 = 5 in base 10. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. 5 mod 11 = 5, so the digit is 5 and the carry is 0. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 52. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. Answer:\box{52}
Question: In base-11, what is 61+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 1 + 8 = 9 in base-10. In mythology and religion, there are nine realms in Norse Cosmology. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have 6 + 7 + 0 = 13 in base 10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 129. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{129}
Question: In base-11, what is 44+56? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 6 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 4 + 5 + 0 = 9 in base 10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 9A. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{9A}
Question: In base-11, what is 53+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 3 + 3 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 5 + 7 + 0 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 116. Answer:\box{116}
Question: In base-11, what is 66+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 9 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 6 + 7 + 1 = 14 in base 10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. So the answer is 134. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{134}
Question: In base-11, what is 37+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 7 + 2 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. We have 3 + 9 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 119. Answer:\box{119}
Question: In base-11, what is 12+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 1 = 3 in base-10. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 3 mod 11 = 3, so the digit is 3 and the carry is 0. We have 1 + A + 0 = 11 in base 10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. So the answer is 103. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{103}
Question: In base-11, what is 8A+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + 7 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 17 mod 11 = 6, so the digit is 6 and the carry is 1. We have 8 + 3 + 1 = 12 in base 10. Humans typically have 12 pairs of ribs in their skeletal structure. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 116. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Answer:\box{116}
Question: In base-11, what is A1+94? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 1 + 4 = 5 in base-10. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 5 mod 11 = 5, so the digit is 5 and the carry is 0. Humans have five basic senses: sight, hearing, smell, taste, and touch. We have A + 9 + 0 = 19 in base 10. COVID-19, which stands for 'Coronavirus Disease 2019', was named for the year it was first identified. 19 mod 11 = 8, so the digit is 8 and the carry is 1. A leading digit is 1. So the answer is 185. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{185} | 14 | 6 | fixed |
In base-11, what is 73+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 149 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 50+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 2 = 2 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In mathematics, two is the smallest and first prime number. We have 5 + A + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 142. In mathematics, an area is a two-dimensional size of a defined part of a surface. Answer:\box{142}
Question: In base-11, what is 70+41? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 1 = 1 in base-10. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 1 mod 11 = 1, so the digit is 1 and the carry is 0. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. We have 7 + 4 + 0 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 101. In mathematics, one is the first counting number and the starting point of the natural numbers. Answer:\box{101}
Question: In base-11, what is 59+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 8 = 17 in base-10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. We have 5 + 8 + 1 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. A leading digit is 1. So the answer is 136. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{136}
Question: In base-11, what is 43+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 2 = 5 in base-10. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 5 mod 11 = 5, so the digit is 5 and the carry is 0. Humans have five basic senses: sight, hearing, smell, taste, and touch. We have 4 + 9 + 0 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. So the answer is 125. In mathematics, five is the third prime number, after two and three. Answer:\box{125}
Question: In base-11, what is 48+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 8 + 9 = 17 in base-10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 17 mod 11 = 6, so the digit is 6 and the carry is 1. We have 4 + 6 + 1 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 106. Answer:\box{106}
Question: In base-11, what is A4+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 4 + 3 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. We have A + 3 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 127. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{127}
Question: In base-11, what is A0+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 0 + 3 = 3 in base-10. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 3 mod 11 = 3, so the digit is 3 and the carry is 0. We have A + 3 + 0 = 13 in base 10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 123. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{123}
Question: In base-11, what is 16+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 6 + 8 = 14 in base-10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 1 + 5 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 73. Answer:\box{73}
Question: In base-11, what is 57+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 7 + 8 = 15 in base-10. In computer science, a 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 5 + 1 + 1 = 7 in base 10. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 74. In geometry, a square has four equal sides and four right angles. Answer:\box{74}
Question: In base-11, what is 5A+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have A + 4 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 5 + A + 1 = 16 in base 10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Humans have five basic senses: sight, hearing, smell, taste, and touch. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 153. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{153} | 14 | 6 | fixed |
In base-11, what is A1+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 145 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 27+46? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 6 = 13 in base-10. Thirteen is the atomic number of aluminium in chemistry, a post-transition metal that's widely used for its lightness and resistance to corrosion. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. We have 2 + 4 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 72. In human anatomy, the body is largely symmetrical with two halves. Answer:\box{72}
Question: In base-11, what is 47+27? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 7 = 14 in base-10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. We have 4 + 2 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 73. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. Answer:\box{73}
Question: In base-11, what is 45+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 5 + 0 = 5 in base-10. In geometry, a pentagon is a five-sided polygon. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. We have 4 + 8 + 0 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. So the answer is 115. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. Answer:\box{115}
Question: In base-11, what is 67+2A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + A = 17 in base-10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. We have 6 + 2 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 96. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{96}
Question: In base-11, what is 94+23? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 4 + 3 = 7 in base-10. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. We have 9 + 2 + 0 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. So the answer is 107. Answer:\box{107}
Question: In base-11, what is 6A+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + 3 = 13 in base-10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Humans have two sets of each of their chromosomes, making us diploid organisms. We have 6 + 8 + 1 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. A leading digit is 1. So the answer is 142. In mathematics, an area is a two-dimensional size of a defined part of a surface. Answer:\box{142}
Question: In base-11, what is 77+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 7 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have 7 + 8 + 1 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 153. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{153}
Question: In base-11, what is 92+25? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + 5 = 7 in base-10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. We have 9 + 2 + 0 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 107. Answer:\box{107}
Question: In base-11, what is 96+32? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 2 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In music, an octave consists of eight notes in the Western musical scale. We have 9 + 3 + 0 = 12 in base 10. In computer science, '12' is represented as '1100' in binary notation. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. So the answer is 118. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Answer:\box{118}
Question: In base-11, what is 58+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 3 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 5 + 3 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 90. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{90} | 14 | 6 | fixed |
In base-11, what is 95+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 175 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 7A+56? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + 6 = 16 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Humans have five basic senses: sight, hearing, smell, taste, and touch. We have 7 + 5 + 1 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 125. In geometry, a pentagon is a five-sided polygon. Answer:\box{125}
Question: In base-11, what is 63+60? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 0 = 3 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 3 mod 11 = 3, so the digit is 3 and the carry is 0. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. We have 6 + 6 + 0 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 113. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{113}
Question: In base-11, what is 80+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + A = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 8 + 4 + 0 = 12 in base 10. The 12 Zodiac signs represent different personality traits and are used in astrology. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 11A. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{11A}
Question: In base-11, what is 88+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 8 = 16 in base-10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 8 + 1 + 1 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is A5. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{A5}
Question: In base-11, what is 27+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 4 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 2 + 3 + 1 = 6 in base 10. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. 6 mod 11 = 6, so the digit is 6 and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 60. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{60}
Question: In base-11, what is 88+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 7 = 15 in base-10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 8 + 8 + 1 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 164. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Answer:\box{164}
Question: In base-11, what is 5A+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 1 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. We have 5 + 9 + 1 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. A leading digit is 1. So the answer is 140. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{140}
Question: In base-11, what is 53+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 3 + 8 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 5 + A + 1 = 16 in base 10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. So the answer is 150. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{150}
Question: In base-11, what is 52+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 2 + 8 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 5 + 8 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 12A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{12A}
Question: In base-11, what is 68+27? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 7 = 15 in base-10. In computer science, a 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. We have 6 + 2 + 1 = 9 in base 10. The gestation period of a human pregnancy is typically nine months. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 94. Answer:\box{94} | 14 | 6 | fixed |
In base-11, what is A9+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 181 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 58+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 8 + 9 = 17 in base-10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. We have 5 + 4 + 1 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. So the answer is A6. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{A6}
Question: In base-11, what is 92+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 2 + 9 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 9 + 1 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 100. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{100}
Question: In base-11, what is 96+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 3 = 9 in base-10. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 9 + A + 0 = 19 in base 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. Spiders, part of the arachnid family in biology, typically have eight legs. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 189. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{189}
Question: In base-11, what is 17+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 8 = 15 in base-10. There are 15 facial bones in the human skull (not including the mandible, or lower jaw bone). Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. We have 1 + 1 + 1 = 3 in base 10. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). 3 mod 11 = 3, so the digit is 3 and the carry is 0. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 34. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{34}
Question: In base-11, what is 44+75? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 4 + 5 = 9 in base-10. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 4 + 7 + 0 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 109. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Answer:\box{109}
Question: In base-11, what is 53+57? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 3 + 7 = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 5 + 5 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is AA. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{AA}
Question: In base-11, what is 22+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 2 + 9 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 2 + 8 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 100. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{100}
Question: In base-11, what is 43+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 3 = 6 in base-10. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The standard guitar has six strings. We have 4 + A + 0 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 136. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{136}
Question: In base-11, what is 68+23? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 3 = 11 in base-10. In computer science, '11' is the binary representation of the decimal number 3. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 6 + 2 + 1 = 9 in base 10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. A leading digit is 0. So the answer is 90. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{90}
Question: In base-11, what is 36+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 7 = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. We have 3 + 7 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 102. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{102} | 14 | 6 | fixed |
In base-11, what is 50+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 145 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 85+32? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 2 = 7 in base-10. In biology, a rainbow is seen in seven colors due to the refraction of light. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have 8 + 3 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 107. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. Answer:\box{107}
Question: In base-11, what is 51+61? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 1 = 2 in base-10. Two is the base of the binary code, used extensively in computer science. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In human anatomy, the body is largely symmetrical with two halves. We have 5 + 6 + 0 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. A leading digit is 1. So the answer is 102. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{102}
Question: In base-11, what is 20+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 0 + 3 = 3 in base-10. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 3 mod 11 = 3, so the digit is 3 and the carry is 0. We have 2 + 8 + 0 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A3. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Answer:\box{A3}
Question: In base-11, what is 80+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 0 = 0 in base-10. In chemistry, pH 0 on the pH scale represents extreme acidity. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 0 mod 11 = 0, so the digit is 0 and the carry is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 8 + 9 + 0 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 160. Answer:\box{160}
Question: In base-11, what is 48+2A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 8 + A = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. We have 4 + 2 + 1 = 7 in base 10. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. 7 mod 11 = 7, so the digit is 7 and the carry is 0. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 77. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Answer:\box{77}
Question: In base-11, what is 67+44? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 4 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 6 + 4 + 1 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 100. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{100}
Question: In base-11, what is 14+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + 6 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. We have 1 + 8 + 0 = 9 in base 10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 9A. Answer:\box{9A}
Question: In base-11, what is A4+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + A = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. We have A + 9 + 1 = 20 in base 10. In physics, the twentieth century saw the development of quantum physics and the theory of relativity, two fundamental shifts in our understanding of the universe. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. A leading digit is 1. So the answer is 193. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{193}
Question: In base-11, what is 65+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + 2 = 7 in base-10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. We have 6 + 9 + 0 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 147. Answer:\box{147}
Question: In base-11, what is A6+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 6 + 9 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. We have A + 5 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. So the answer is 154. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{154} | 14 | 6 | fixed |
In base-11, what is 7A+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A7 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 91+40? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 1 + 0 = 1 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 1 mod 11 = 1, so the digit is 1 and the carry is 0. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 9 + 4 + 0 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. So the answer is 121. In physics, the number one is the charge of a single unit of positive or negative electricity. Answer:\box{121}
Question: In base-11, what is 27+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 6 = 13 in base-10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 2 + 8 + 1 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 102. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{102}
Question: In base-11, what is 46+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 6 + A = 16 in base-10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. Since we're in base-11, that exceeds the maximum value of A for a single digit. 16 mod 11 = 5, so the digit is 5 and the carry is 1. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. We have 4 + 5 + 1 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is A5. Answer:\box{A5}
Question: In base-11, what is 79+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + A = 19 in base-10. In computer science, the ISO-8859-19 standard is used for encoding Baltic languages, among others. Since we're in base-11, that exceeds the maximum value of A for a single digit. 19 mod 11 = 8, so the digit is 8 and the carry is 1. We have 7 + 6 + 1 = 14 in base 10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 138. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{138}
Question: In base-11, what is 82+61? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 1 = 3 in base-10. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 3 mod 11 = 3, so the digit is 3 and the carry is 0. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. We have 8 + 6 + 0 = 14 in base 10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 133. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{133}
Question: In base-11, what is 75+A6? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 5 + 6 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 7 + A + 1 = 18 in base 10. In computer science, the UTF-18 character set is a proposed extension of the Unicode standard to include a wider range of characters. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 170. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{170}
Question: In base-11, what is 39+36? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + 6 = 15 in base-10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 3 + 3 + 1 = 7 in base 10. In biology, a rainbow is seen in seven colors due to the refraction of light. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. A leading digit is 0. So the answer is 74. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Answer:\box{74}
Question: In base-11, what is 63+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 3 + 4 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have 6 + A + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In mathematics, five is the third prime number, after two and three. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 157. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. Answer:\box{157}
Question: In base-11, what is 58+42? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 2 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. We have 5 + 4 + 0 = 9 in base 10. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. 9 mod 11 = 9, so the digit is 9 and the carry is 0. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 9A. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{9A}
Question: In base-11, what is 32+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + A = 12 in base-10. The 12 Zodiac signs represent different personality traits and are used in astrology. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 3 + 5 + 1 = 9 in base 10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. A leading digit is 0. So the answer is 91. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{91} | 14 | 6 | fixed |
In base-11, what is 76+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 137 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 3A+20? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have A + 0 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 3 + 2 + 0 = 5 in base 10. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. 5 mod 11 = 5, so the digit is 5 and the carry is 0. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 0. So the answer is 5A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{5A}
Question: In base-11, what is 94+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 4 + 5 = 9 in base-10. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. We have 9 + 8 + 0 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 169. The gestation period of a human pregnancy is typically nine months. Answer:\box{169}
Question: In base-11, what is A1+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 1 + A = 11 in base-10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have A + 4 + 1 = 15 in base 10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. 15 mod 11 = 4, so the digit is 4 and the carry is 1. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. A leading digit is 1. So the answer is 140. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{140}
Question: In base-11, what is 33+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 3 + A = 13 in base-10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. We have 3 + 6 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A2. In mathematics, an area is a two-dimensional size of a defined part of a surface. Answer:\box{A2}
Question: In base-11, what is 83+93? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 3 + 3 = 6 in base-10. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. We have 8 + 9 + 0 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. A leading digit is 1. So the answer is 166. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Answer:\box{166}
Question: In base-11, what is 69+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 9 + 3 = 12 in base-10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 6 + 6 + 1 = 13 in base 10. Thirteen is the atomic number of aluminium in chemistry, a post-transition metal that's widely used for its lightness and resistance to corrosion. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 121. In biology, humans have one heart, which pumps blood throughout the body. Answer:\box{121}
Question: In base-11, what is 45+99? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + 9 = 14 in base-10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. We have 4 + 9 + 1 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. A leading digit is 1. So the answer is 133. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Answer:\box{133}
Question: In base-11, what is 27+27? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 7 = 14 in base-10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. We have 2 + 2 + 1 = 5 in base 10. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In mathematics, five is the third prime number, after two and three. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 53. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{53}
Question: In base-11, what is 93+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + 2 = 5 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 5 mod 11 = 5, so the digit is 5 and the carry is 0. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. We have 9 + 7 + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 155. In mathematics, five is the third prime number, after two and three. Answer:\box{155}
Question: In base-11, what is 76+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 6 + 3 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. We have 7 + 6 + 0 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 129. The gestation period of a human pregnancy is typically nine months. Answer:\box{129} | 14 | 6 | fixed |
In base-11, what is 89+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 160 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 56+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 6 + 8 = 14 in base-10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. We have 5 + A + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 153. Answer:\box{153}
Question: In base-11, what is 9A+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + A = 20 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. We have 9 + 7 + 1 = 17 in base 10. In physics, group 17 elements in the periodic table are known as the halogens, which include fluorine and chlorine. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 169. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{169}
Question: In base-11, what is 85+99? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 9 = 14 in base-10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. We have 8 + 9 + 1 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. A leading digit is 1. So the answer is 173. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. Answer:\box{173}
Question: In base-11, what is 59+98? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 9 + 8 = 17 in base-10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 17 mod 11 = 6, so the digit is 6 and the carry is 1. We have 5 + 9 + 1 = 15 in base 10. In computer science, a 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 146. Answer:\box{146}
Question: In base-11, what is 49+60? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 0 = 9 in base-10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. We have 4 + 6 + 0 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A9. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Answer:\box{A9}
Question: In base-11, what is 18+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 7 = 15 in base-10. There are 15 facial bones in the human skull (not including the mandible, or lower jaw bone). Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 1 + 4 + 1 = 6 in base 10. In astronomy, Saturn is the sixth planet from the Sun in our solar system. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 64. In geometry, a square has four equal sides and four right angles. Answer:\box{64}
Question: In base-11, what is 90+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 5 = 5 in base-10. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 5 mod 11 = 5, so the digit is 5 and the carry is 0. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. We have 9 + 8 + 0 = 17 in base 10. Seventeen is a Fermat prime, as it is in the form of 2^(2^n) + 1, with n = 2. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 165. Answer:\box{165}
Question: In base-11, what is 69+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 3 = 12 in base-10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 6 + 7 + 1 = 14 in base 10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. So the answer is 131. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{131}
Question: In base-11, what is A9+20? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 0 = 9 in base-10. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. We have A + 2 + 0 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 119. Answer:\box{119}
Question: In base-11, what is 98+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 8 = 16 in base-10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 16 mod 11 = 5, so the digit is 5 and the carry is 1. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. We have 9 + 2 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 115. Answer:\box{115} | 14 | 6 | fixed |
In base-11, what is 35+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 110 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 99+2A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 9 + A = 19 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. We have 9 + 2 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 118. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Answer:\box{118}
Question: In base-11, what is 98+66? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 6 = 14 in base-10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 9 + 6 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 153. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{153}
Question: In base-11, what is 8A+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + 7 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In geometry, a hexagon is a six-sided polygon. We have 8 + 1 + 1 = 10 in base 10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A6. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Answer:\box{A6}
Question: In base-11, what is 81+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 1 + 4 = 5 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 5 mod 11 = 5, so the digit is 5 and the carry is 0. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 8 + 3 + 0 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. So the answer is 105. In geometry, a pentagon is a five-sided polygon. Answer:\box{105}
Question: In base-11, what is 90+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 9 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. We have 9 + 4 + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 129. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{129}
Question: In base-11, what is 10+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 0 + 5 = 5 in base-10. In mathematics, five is the third prime number, after two and three. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 5 mod 11 = 5, so the digit is 5 and the carry is 0. We have 1 + 9 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A5. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Answer:\box{A5}
Question: In base-11, what is 76+53? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 3 = 9 in base-10. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. We have 7 + 5 + 0 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 119. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{119}
Question: In base-11, what is A4+A0? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 0 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In geometry, a square has four equal sides and four right angles. We have A + A + 0 = 20 in base 10. In physics, the twentieth century saw the development of quantum physics and the theory of relativity, two fundamental shifts in our understanding of the universe. 20 mod 11 = 9, so the digit is 9 and the carry is 1. The gestation period of a human pregnancy is typically nine months. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 194. Answer:\box{194}
Question: In base-11, what is 25+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 5 + 9 = 14 in base-10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 2 + 5 + 1 = 8 in base 10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 83. Answer:\box{83}
Question: In base-11, what is 22+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 2 + 8 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. We have 2 + 7 + 0 = 9 in base 10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 9A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{9A} | 14 | 6 | fixed |
In base-11, what is 39+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 96 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 92+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 6 = 8 in base-10. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In computer science, a byte is typically made up of 8 bits. We have 9 + 7 + 0 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 158. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{158}
Question: In base-11, what is 52+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + 5 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have 5 + 9 + 0 = 14 in base 10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 137. Answer:\box{137}
Question: In base-11, what is 2A+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 4 = 14 in base-10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 14 mod 11 = 3, so the digit is 3 and the carry is 1. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). We have 2 + A + 1 = 13 in base 10. Thirteen is the atomic number of aluminium in chemistry, a post-transition metal that's widely used for its lightness and resistance to corrosion. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 123. In astronomy, Earth is the third planet from the Sun in our Solar System. Answer:\box{123}
Question: In base-11, what is 46+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 9 = 15 in base-10. In mathematics, a group of 15 is known as a pentadecagon, which is a polygon with 15 sides and 15 angles. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. We have 4 + 8 + 1 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 124. Answer:\box{124}
Question: In base-11, what is 8A+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 6 = 16 in base-10. In computer science, a 'nibble' is a four-bit aggregation, or half an octet, and two nibbles make up a byte, which is 16 bits. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. We have 8 + 2 + 1 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 105. Humans have five basic senses: sight, hearing, smell, taste, and touch. Answer:\box{105}
Question: In base-11, what is 48+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 3 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. We have 4 + 6 + 1 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 100. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{100}
Question: In base-11, what is 34+56? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 6 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. We have 3 + 5 + 0 = 8 in base 10. In mathematics, eight is a Fibonacci number and a cube number. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, eight is the number of vertices of a cube. A leading digit is 0. So the answer is 8A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{8A}
Question: In base-11, what is 95+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 2 = 7 in base-10. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have 9 + A + 0 = 19 in base 10. A standard basketball game consists of four quarters, each lasting 19 minutes in many high school associations. 19 mod 11 = 8, so the digit is 8 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 187. Answer:\box{187}
Question: In base-11, what is 86+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 6 + 0 = 6 in base-10. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The standard guitar has six strings. We have 8 + 7 + 0 = 15 in base 10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. So the answer is 146. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{146}
Question: In base-11, what is 9A+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + 8 = 18 in base-10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. We have 9 + 7 + 1 = 17 in base 10. In physics, group 17 elements in the periodic table are known as the halogens, which include fluorine and chlorine. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 167. Answer:\box{167} | 14 | 6 | fixed |
In base-11, what is 67+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 147 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 32+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + 7 = 9 in base-10. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 3 + 8 + 0 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 109. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{109}
Question: In base-11, what is A0+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 0 + 3 = 3 in base-10. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In colors, there are three primary colors: red, yellow, and blue. We have A + 6 + 0 = 16 in base 10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. A leading digit is 1. So the answer is 153. Answer:\box{153}
Question: In base-11, what is 87+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 7 = 14 in base-10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have 8 + 9 + 1 = 18 in base 10. In Tarot, the Moon card is card number 18, representing intuition, dreams, and the unconscious. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 173. Answer:\box{173}
Question: In base-11, what is 52+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + 3 = 5 in base-10. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. We have 5 + 6 + 0 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 105. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. Answer:\box{105}
Question: In base-11, what is A4+A7? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 7 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. We have A + A + 1 = 21 in base 10. Many cultures celebrate the 21st birthday as a significant milestone, marking the transition into full adulthood. 21 mod 11 = A, so the digit is A and the carry is 1. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 1A0. Answer:\box{1A0}
Question: In base-11, what is 62+41? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 2 + 1 = 3 in base-10. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 6 + 4 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A3. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{A3}
Question: In base-11, what is 71+40? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 1 + 0 = 1 in base-10. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 1 mod 11 = 1, so the digit is 1 and the carry is 0. We have 7 + 4 + 0 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. So the answer is 101. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. Answer:\box{101}
Question: In base-11, what is 88+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 1 = 9 in base-10. In mythology and religion, there are nine realms in Norse Cosmology. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have 8 + A + 0 = 18 in base 10. Humans have 18 muscles in each hand, which control fine motor movements. 18 mod 11 = 7, so the digit is 7 and the carry is 1. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. A leading digit is 1. So the answer is 179. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{179}
Question: In base-11, what is 78+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 8 + 9 = 17 in base-10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. We have 7 + 7 + 1 = 15 in base 10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. A leading digit is 1. So the answer is 146. Answer:\box{146}
Question: In base-11, what is 93+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 3 + 9 = 12 in base-10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 9 + 3 + 1 = 13 in base 10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 121. Answer:\box{121} | 14 | 6 | fixed |
In base-11, what is 44+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 82 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 26+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 1 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. We have 2 + 9 + 0 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 107. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. Answer:\box{107}
Question: In base-11, what is 27+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + A = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. We have 2 + 5 + 1 = 8 in base 10. Spiders, part of the arachnid family in biology, typically have eight legs. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 86. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Answer:\box{86}
Question: In base-11, what is 39+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 9 + 3 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have 3 + 8 + 1 = 12 in base 10. The 12 Zodiac signs represent different personality traits and are used in astrology. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 111. In biology, humans have one heart, which pumps blood throughout the body. Answer:\box{111}
Question: In base-11, what is 62+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 2 + 9 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 6 + 5 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 110. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{110}
Question: In base-11, what is 26+57? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 7 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. We have 2 + 5 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, eight is the number of vertices of a cube. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 82. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{82}
Question: In base-11, what is 60+45? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 5 = 5 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In geometry, a pentagon is a five-sided polygon. We have 6 + 4 + 0 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A5. Answer:\box{A5}
Question: In base-11, what is A1+60? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 1 + 0 = 1 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 1 mod 11 = 1, so the digit is 1 and the carry is 0. In biology, humans have one heart, which pumps blood throughout the body. We have A + 6 + 0 = 16 in base 10. There are 16 ounces in a pound in the avoirdupois system of measurement. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 151. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{151}
Question: In base-11, what is 35+68? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 5 + 8 = 13 in base-10. Thirteen is the atomic number of aluminium in chemistry, a post-transition metal that's widely used for its lightness and resistance to corrosion. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. We have 3 + 6 + 1 = 10 in base 10. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. So the answer is A2. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{A2}
Question: In base-11, what is AA+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 9 = 19 in base-10. In physics, the nineteenth century marked the discovery of thermodynamics, leading to the development of the steam engine and the industrial revolution. Since we're in base-11, that exceeds the maximum value of A for a single digit. 19 mod 11 = 8, so the digit is 8 and the carry is 1. We have A + A + 1 = 21 in base 10. In mathematics, 21 is a triangular number, meaning it can be depicted as an equilateral triangle with dots. 21 mod 11 = A, so the digit is A and the carry is 1. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 1A8. In computer science, a byte is typically made up of 8 bits. Answer:\box{1A8}
Question: In base-11, what is 62+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 2 + 9 = 11 in base-10. In computer science, '11' is the binary representation of the decimal number 3. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 6 + 1 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 80. Answer:\box{80} | 14 | 6 | fixed |
In base-11, what is 64+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 133 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 58+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 4 = 12 in base-10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 5 + 7 + 1 = 13 in base 10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 121. One often represents the 'on' state in binary code, which underlies digital computing. Answer:\box{121}
Question: In base-11, what is 32+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 8 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have 3 + 4 + 0 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 7A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{7A}
Question: In base-11, what is 40+62? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 0 + 2 = 2 in base-10. In mathematics, an area is a two-dimensional size of a defined part of a surface. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In astronomy, Mars, the second planet after Earth, has 2 moons. We have 4 + 6 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A2. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{A2}
Question: In base-11, what is 2A+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have A + 9 = 19 in base-10. A standard basketball game consists of four quarters, each lasting 19 minutes in many high school associations. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 19 mod 11 = 8, so the digit is 8 and the carry is 1. We have 2 + 5 + 1 = 8 in base 10. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 88. Answer:\box{88}
Question: In base-11, what is 82+32? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 2 = 4 in base-10. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 4 mod 11 = 4, so the digit is 4 and the carry is 0. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. We have 8 + 3 + 0 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. So the answer is 104. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{104}
Question: In base-11, what is 68+51? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 8 + 1 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. We have 6 + 5 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 109. The gestation period of a human pregnancy is typically nine months. Answer:\box{109}
Question: In base-11, what is 4A+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 1 = 11 in base-10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 4 + 7 + 1 = 12 in base 10. In computer science, '12' is represented as '1100' in binary notation. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 110. Answer:\box{110}
Question: In base-11, what is 17+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + A = 17 in base-10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 1 + 6 + 1 = 8 in base 10. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 86. In geometry, a hexagon is a six-sided polygon. Answer:\box{86}
Question: In base-11, what is 55+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 5 + 9 = 14 in base-10. In mathematics, fourteen is the number of days in a fortnight. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 5 + 5 + 1 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. A leading digit is 1. So the answer is 103. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{103}
Question: In base-11, what is 38+25? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 5 = 13 in base-10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. We have 3 + 2 + 1 = 6 in base 10. Six is the atomic number of carbon in chemistry, a key element for life as we know it. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. A leading digit is 0. So the answer is 62. Two is the base of the binary code, used extensively in computer science. Answer:\box{62} | 14 | 6 | fixed |
In base-11, what is 14+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | AA | Math-11 | Irrelevant | Hard | Question: In base-11, what is 77+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 7 + 2 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. We have 7 + 8 + 0 = 15 in base 10. There are 15 facial bones in the human skull (not including the mandible, or lower jaw bone). 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. A leading digit is 1. So the answer is 149. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{149}
Question: In base-11, what is 73+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 5 = 8 in base-10. In music, an octave consists of eight notes in the Western musical scale. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. We have 7 + 3 + 0 = 10 in base 10. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A8. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Answer:\box{A8}
Question: In base-11, what is 66+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 9 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 6 + 6 + 1 = 13 in base 10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 124. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{124}
Question: In base-11, what is 67+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + 3 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have 6 + 6 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 11A. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{11A}
Question: In base-11, what is 21+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 1 + 3 = 4 in base-10. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. We have 2 + A + 0 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 114. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{114}
Question: In base-11, what is 8A+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + A = 20 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. We have 8 + 8 + 1 = 17 in base 10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. A leading digit is 1. So the answer is 169. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{169}
Question: In base-11, what is 94+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 3 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. We have 9 + 6 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 147. Answer:\box{147}
Question: In base-11, what is 53+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + A = 13 in base-10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. We have 5 + 5 + 1 = 11 in base 10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 102. Answer:\box{102}
Question: In base-11, what is 1A+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + 7 = 17 in base-10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 1 + 4 + 1 = 6 in base 10. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. A leading digit is 0. So the answer is 66. Answer:\box{66}
Question: In base-11, what is 74+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 4 + 4 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have 7 + A + 0 = 17 in base 10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 168. In mathematics, eight is a Fibonacci number and a cube number. Answer:\box{168} | 14 | 6 | fixed |
In base-11, what is 1A+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 93 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 90+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 0 + A = 10 in base-10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. We have 9 + 1 + 0 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is AA. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{AA}
Question: In base-11, what is 17+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 6 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. We have 1 + 9 + 1 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 102. In astronomy, Mars, the second planet after Earth, has 2 moons. Answer:\box{102}
Question: In base-11, what is 67+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 9 = 16 in base-10. In human biology, 16 is the number of chromosomes in the parasite that causes malaria (Plasmodium falciparum). Since we're in base-11, that exceeds the maximum value of A for a single digit. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. We have 6 + 3 + 1 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A5. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Answer:\box{A5}
Question: In base-11, what is 6A+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 5 = 15 in base-10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. We have 6 + A + 1 = 17 in base 10. Seventeen is the atomic number of chlorine in chemistry, a halogen that's widely used in disinfectants. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 164. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Answer:\box{164}
Question: In base-11, what is 95+93? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 5 + 3 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 9 + 9 + 0 = 18 in base 10. Humans have 18 muscles in each hand, which control fine motor movements. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 178. Spiders, part of the arachnid family in biology, typically have eight legs. Answer:\box{178}
Question: In base-11, what is 88+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 3 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 8 + 3 + 1 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. So the answer is 110. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{110}
Question: In base-11, what is 28+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 6 = 14 in base-10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. We have 2 + 7 + 1 = 10 in base 10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A3. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{A3}
Question: In base-11, what is 64+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 4 + A = 14 in base-10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. We have 6 + 1 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 83. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Answer:\box{83}
Question: In base-11, what is 98+22? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 8 + 2 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 9 + 2 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 10A. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{10A}
Question: In base-11, what is 29+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 9 + 7 = 16 in base-10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. We have 2 + 1 + 1 = 4 in base 10. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. A leading digit is 0. So the answer is 45. Answer:\box{45} | 14 | 6 | fixed |
In base-11, what is 73+62? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 125 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 5A+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + 4 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 5 + 6 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 113. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{113}
Question: In base-11, what is 75+75? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 5 + 5 = 10 in base-10. The decimal system, which is the most commonly used number system in the world, has a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. We have 7 + 7 + 0 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 13A. Answer:\box{13A}
Question: In base-11, what is 23+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 3 + 8 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 2 + 7 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). Answer:\box{A0}
Question: In base-11, what is 47+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 3 = 10 in base-10. The decimal system, which is the most commonly used number system in the world, has a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. We have 4 + 7 + 0 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. So the answer is 10A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{10A}
Question: In base-11, what is 45+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 2 = 7 in base-10. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have 4 + 8 + 0 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 117. Answer:\box{117}
Question: In base-11, what is A8+56? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 6 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. We have A + 5 + 1 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 153. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{153}
Question: In base-11, what is 90+94? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 0 + 4 = 4 in base-10. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In geometry, a square has four equal sides and four right angles. We have 9 + 9 + 0 = 18 in base 10. In mathematics, eighteen is the only number that equals twice the sum of its decimal digits (1+8=9, and 9*2=18). 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 1. So the answer is 174. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{174}
Question: In base-11, what is 47+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 8 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 4 + 2 + 1 = 7 in base 10. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 74. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Answer:\box{74}
Question: In base-11, what is 47+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 7 + 4 = 11 in base-10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 4 + 6 + 1 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 100. Answer:\box{100}
Question: In base-11, what is 19+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 9 + 3 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 1 + 7 + 1 = 9 in base 10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 91. In physics, the number one is the charge of a single unit of positive or negative electricity. Answer:\box{91} | 14 | 6 | fixed |
In base-11, what is 31+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 126 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 6A+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have A + 8 = 18 in base-10. Humans have 18 muscles in each hand, which control fine motor movements. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In biology, a rainbow is seen in seven colors due to the refraction of light. We have 6 + A + 1 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 167. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{167}
Question: In base-11, what is 75+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 4 = 9 in base-10. The gestation period of a human pregnancy is typically nine months. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. We have 7 + 3 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is A9. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{A9}
Question: In base-11, what is 37+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + 5 = 12 in base-10. Humans typically have 12 pairs of ribs in their skeletal structure. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have 3 + 9 + 1 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Humans have two sets of each of their chromosomes, making us diploid organisms. A leading digit is 1. So the answer is 121. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. Answer:\box{121}
Question: In base-11, what is 94+57? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 4 + 7 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 9 + 5 + 1 = 15 in base 10. There are 15 facial bones in the human skull (not including the mandible, or lower jaw bone). 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 1. So the answer is 140. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{140}
Question: In base-11, what is 87+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + 9 = 16 in base-10. In mathematics, sixteen is a square number (4^2), and it is the fourth power of two (2^4). Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In mathematics, five is the third prime number, after two and three. We have 8 + A + 1 = 19 in base 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 185. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{185}
Question: In base-11, what is 15+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 5 + 8 = 13 in base-10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 1 + A + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 112. In astronomy, Mars, the second planet after Earth, has 2 moons. Answer:\box{112}
Question: In base-11, what is 63+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 7 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 6 + 4 + 0 = 10 in base 10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is AA. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{AA}
Question: In base-11, what is 67+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 5 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. We have 6 + A + 1 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 161. Answer:\box{161}
Question: In base-11, what is A1+AA? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + A = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have A + A + 1 = 21 in base 10. Many cultures celebrate the 21st birthday as a significant milestone, marking the transition into full adulthood. 21 mod 11 = A, so the digit is A and the carry is 1. The number 10 is symbolic in many cultures, often representing perfection or completeness. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 1A0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. Answer:\box{1A0}
Question: In base-11, what is 60+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 5 = 5 in base-10. In mathematics, five is the third prime number, after two and three. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 5 mod 11 = 5, so the digit is 5 and the carry is 0. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. We have 6 + 8 + 0 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 135. Answer:\box{135} | 14 | 6 | fixed |
In base-11, what is 30+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A9 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 12+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 2 + A = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. We have 1 + 7 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 91. Answer:\box{91}
Question: In base-11, what is 52+A6? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 6 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, eight is the number of vertices of a cube. We have 5 + A + 0 = 15 in base 10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. 15 mod 11 = 4, so the digit is 4 and the carry is 1. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 148. In mathematics, eight is a Fibonacci number and a cube number. Answer:\box{148}
Question: In base-11, what is 65+46? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 6 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. We have 6 + 4 + 1 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 100. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. Answer:\box{100}
Question: In base-11, what is 88+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 8 = 16 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 8 + 8 + 1 = 17 in base 10. In human biology, the kidneys filter about 17 liters of blood every hour. 17 mod 11 = 6, so the digit is 6 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 165. In mathematics, five is the third prime number, after two and three. Answer:\box{165}
Question: In base-11, what is A6+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + A = 16 in base-10. In mathematics, sixteen is a square number (4^2), and it is the fourth power of two (2^4). Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have A + 9 + 1 = 20 in base 10. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 195. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{195}
Question: In base-11, what is 94+52? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 2 = 6 in base-10. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The standard guitar has six strings. We have 9 + 5 + 0 = 14 in base 10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. So the answer is 136. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Answer:\box{136}
Question: In base-11, what is 69+42? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 9 + 2 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 6 + 4 + 1 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 100. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{100}
Question: In base-11, what is 70+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 0 + A = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have 7 + 1 + 0 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 8A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{8A}
Question: In base-11, what is 73+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 9 = 12 in base-10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. We have 7 + 1 + 1 = 9 in base 10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 91. Answer:\box{91}
Question: In base-11, what is 52+94? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 2 + 4 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. We have 5 + 9 + 0 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 136. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{136} | 14 | 6 | fixed |
In base-11, what is 77+2A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A6 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 39+67? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 7 = 16 in base-10. In human biology, 16 is the number of chromosomes in the parasite that causes malaria (Plasmodium falciparum). Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In mathematics, five is the third prime number, after two and three. We have 3 + 6 + 1 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. So the answer is A5. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. Answer:\box{A5}
Question: In base-11, what is A3+A6? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 6 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have A + A + 0 = 20 in base 10. In computer science, the number 20 is often used in benchmarks and tests due to its convenient divisibility. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In mythology and religion, there are nine realms in Norse Cosmology. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 199. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Answer:\box{199}
Question: In base-11, what is 89+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + 5 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. We have 8 + 3 + 1 = 12 in base 10. In computer science, '12' is represented as '1100' in binary notation. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. So the answer is 113. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Answer:\box{113}
Question: In base-11, what is 59+13? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 3 = 12 in base-10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have 5 + 1 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 71. Answer:\box{71}
Question: In base-11, what is A0+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 1 = 1 in base-10. In mathematics, one is the first counting number and the starting point of the natural numbers. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 1 mod 11 = 1, so the digit is 1 and the carry is 0. In physics, the number one is the charge of a single unit of positive or negative electricity. We have A + A + 0 = 20 in base 10. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 191. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{191}
Question: In base-11, what is A6+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 6 + 4 = 10 in base-10. The decimal system, which is the most commonly used number system in the world, has a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. We have A + 6 + 0 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 15A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{15A}
Question: In base-11, what is 83+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 7 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 8 + 7 + 0 = 15 in base 10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. A leading digit is 1. So the answer is 14A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{14A}
Question: In base-11, what is 61+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 1 + 7 = 8 in base-10. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have 6 + 7 + 0 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. So the answer is 128. In physics, eight is the number of vertices of a cube. Answer:\box{128}
Question: In base-11, what is 28+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 8 + 9 = 17 in base-10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 2 + 1 + 1 = 4 in base 10. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 46. Answer:\box{46}
Question: In base-11, what is 63+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 8 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 6 + 3 + 1 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is A0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{A0} | 14 | 6 | fixed |
In base-11, what is 26+98? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 113 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 70+57? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 7 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 7 mod 11 = 7, so the digit is 7 and the carry is 0. We have 7 + 5 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 117. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Answer:\box{117}
Question: In base-11, what is 37+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 2 = 9 in base-10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. We have 3 + 7 + 0 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. So the answer is A9. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{A9}
Question: In base-11, what is 90+42? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 0 + 2 = 2 in base-10. In mathematics, two is the smallest and first prime number. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 2 mod 11 = 2, so the digit is 2 and the carry is 0. Two is the base of the binary code, used extensively in computer science. We have 9 + 4 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 122. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. Answer:\box{122}
Question: In base-11, what is 28+12? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 2 = 10 in base-10. The number 10 is symbolic in many cultures, often representing perfection or completeness. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. We have 2 + 1 + 0 = 3 in base 10. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. 3 mod 11 = 3, so the digit is 3 and the carry is 0. A leading digit is 0. So the answer is 3A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{3A}
Question: In base-11, what is 83+84? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 4 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have 8 + 8 + 0 = 16 in base 10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 157. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Answer:\box{157}
Question: In base-11, what is 25+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 5 + 0 = 5 in base-10. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 5 mod 11 = 5, so the digit is 5 and the carry is 0. Humans have five basic senses: sight, hearing, smell, taste, and touch. We have 2 + 8 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A5. Answer:\box{A5}
Question: In base-11, what is 57+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 7 + 5 = 12 in base-10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 5 + 8 + 1 = 14 in base 10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 131. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{131}
Question: In base-11, what is 25+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 5 + A = 15 in base-10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 2 + 6 + 1 = 9 in base 10. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 94. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{94}
Question: In base-11, what is 27+44? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 7 + 4 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 2 + 4 + 1 = 7 in base 10. In biology, a rainbow is seen in seven colors due to the refraction of light. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 0. So the answer is 70. Answer:\box{70}
Question: In base-11, what is 99+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 9 + 7 = 16 in base-10. In human biology, 16 is the number of chromosomes in the parasite that causes malaria (Plasmodium falciparum). Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Humans have five basic senses: sight, hearing, smell, taste, and touch. We have 9 + 9 + 1 = 19 in base 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. Spiders, part of the arachnid family in biology, typically have eight legs. A leading digit is 1. So the answer is 185. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. Answer:\box{185} | 14 | 6 | fixed |
In base-11, what is 33+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 50 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A8+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 4 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have A + 3 + 1 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 131. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{131}
Question: In base-11, what is 63+65? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 5 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. We have 6 + 6 + 0 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 118. In computer science, a byte is typically made up of 8 bits. Answer:\box{118}
Question: In base-11, what is 75+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 6 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 7 + 8 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. So the answer is 150. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{150}
Question: In base-11, what is 1A+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have A + 7 = 17 in base-10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 17 mod 11 = 6, so the digit is 6 and the carry is 1. We have 1 + 8 + 1 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A6. Answer:\box{A6}
Question: In base-11, what is 37+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 7 + 4 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 3 + A + 1 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 130. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. Answer:\box{130}
Question: In base-11, what is 33+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + 1 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. We have 3 + 9 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. So the answer is 114. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{114}
Question: In base-11, what is 82+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 2 + 0 = 2 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 2 mod 11 = 2, so the digit is 2 and the carry is 0. We have 8 + 8 + 0 = 16 in base 10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 152. In astronomy, Mars, the second planet after Earth, has 2 moons. Answer:\box{152}
Question: In base-11, what is 29+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 7 = 16 in base-10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 2 + 7 + 1 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A5. Answer:\box{A5}
Question: In base-11, what is 6A+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 2 = 12 in base-10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 6 + 8 + 1 = 15 in base 10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 141. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{141}
Question: In base-11, what is 59+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + 8 = 17 in base-10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 5 + 7 + 1 = 13 in base 10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. So the answer is 126. In geometry, a hexagon is a six-sided polygon. Answer:\box{126} | 14 | 6 | fixed |
In base-11, what is 37+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A5 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A0+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 0 + A = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have A + 6 + 0 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. A leading digit is 1. So the answer is 15A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{15A}
Question: In base-11, what is 9A+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 4 = 14 in base-10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 9 + 7 + 1 = 17 in base 10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In geometry, a hexagon is a six-sided polygon. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 163. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Answer:\box{163}
Question: In base-11, what is 79+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 9 + 1 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. We have 7 + 9 + 0 = 16 in base 10. In computer science, a 'nibble' is a four-bit aggregation, or half an octet, and two nibbles make up a byte, which is 16 bits. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. So the answer is 15A. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{15A}
Question: In base-11, what is 17+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + A = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 1 + 8 + 1 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is A6. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{A6}
Question: In base-11, what is 55+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + A = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. We have 5 + 8 + 1 = 14 in base 10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 134. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{134}
Question: In base-11, what is 98+42? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 2 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. We have 9 + 4 + 0 = 13 in base 10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 12A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{12A}
Question: In base-11, what is 86+99? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 6 + 9 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. We have 8 + 9 + 1 = 18 in base 10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 174. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{174}
Question: In base-11, what is 49+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 9 + 8 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. We have 4 + 4 + 1 = 9 in base 10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 96. In geometry, a hexagon is a six-sided polygon. Answer:\box{96}
Question: In base-11, what is 47+55? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 5 = 12 in base-10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 4 + 5 + 1 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A1. In physics, the number one is the charge of a single unit of positive or negative electricity. Answer:\box{A1}
Question: In base-11, what is A4+2A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 4 + A = 14 in base-10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have A + 2 + 1 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. A leading digit is 1. So the answer is 123. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Answer:\box{123} | 14 | 6 | fixed |
In base-11, what is 55+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 80 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 13+67? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 7 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have 1 + 6 + 0 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 7A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{7A}
Question: In base-11, what is 19+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 9 + 4 = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. We have 1 + A + 1 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 112. Answer:\box{112}
Question: In base-11, what is 2A+42? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have A + 2 = 12 in base-10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have 2 + 4 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 71. Answer:\box{71}
Question: In base-11, what is 88+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 0 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have 8 + 9 + 0 = 17 in base 10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 168. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{168}
Question: In base-11, what is A5+41? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 1 = 6 in base-10. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. We have A + 4 + 0 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. A leading digit is 1. So the answer is 136. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{136}
Question: In base-11, what is 37+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 7 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 14 mod 11 = 3, so the digit is 3 and the carry is 1. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). We have 3 + 4 + 1 = 8 in base 10. In music, an octave consists of eight notes in the Western musical scale. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. A leading digit is 0. So the answer is 83. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{83}
Question: In base-11, what is 89+12? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 9 + 2 = 11 in base-10. In computer science, '11' is the binary representation of the decimal number 3. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 8 + 1 + 1 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A0. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{A0}
Question: In base-11, what is 44+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 5 = 9 in base-10. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. We have 4 + A + 0 = 14 in base 10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 1. So the answer is 139. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. Answer:\box{139}
Question: In base-11, what is 53+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 3 + 8 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have 5 + 2 + 1 = 8 in base 10. In computer science, a byte is typically made up of 8 bits. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 80. Answer:\box{80}
Question: In base-11, what is 32+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 2 + 9 = 11 in base-10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 3 + 8 + 1 = 12 in base 10. The 12 Zodiac signs represent different personality traits and are used in astrology. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. So the answer is 110. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{110} | 14 | 6 | fixed |
In base-11, what is 52+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 111 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 19+2A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 9 + A = 19 in base-10. A standard basketball game consists of four quarters, each lasting 19 minutes in many high school associations. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 19 mod 11 = 8, so the digit is 8 and the carry is 1. We have 1 + 2 + 1 = 4 in base 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 48. In physics, eight is the number of vertices of a cube. Answer:\box{48}
Question: In base-11, what is 35+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 5 + A = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. We have 3 + 7 + 1 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 104. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{104}
Question: In base-11, what is 39+3A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + A = 19 in base-10. In human biology, the first 19 elements of the periodic table are all found in the human body. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 19 mod 11 = 8, so the digit is 8 and the carry is 1. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have 3 + 3 + 1 = 7 in base 10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 0. So the answer is 78. Spiders, part of the arachnid family in biology, typically have eight legs. Answer:\box{78}
Question: In base-11, what is 45+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 2 = 7 in base-10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have 4 + 9 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. So the answer is 127. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{127}
Question: In base-11, what is 60+94? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 0 + 4 = 4 in base-10. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. We have 6 + 9 + 0 = 15 in base 10. There are 15 facial bones in the human skull (not including the mandible, or lower jaw bone). 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 144. Answer:\box{144}
Question: In base-11, what is 64+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 2 = 6 in base-10. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 6 + A + 0 = 16 in base 10. In mathematics, sixteen is a square number (4^2), and it is the fourth power of two (2^4). 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 156. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Answer:\box{156}
Question: In base-11, what is 75+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 5 + 2 = 7 in base-10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 7 mod 11 = 7, so the digit is 7 and the carry is 0. We have 7 + A + 0 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 167. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Answer:\box{167}
Question: In base-11, what is 26+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 6 + A = 16 in base-10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Humans have five basic senses: sight, hearing, smell, taste, and touch. We have 2 + 6 + 1 = 9 in base 10. In mythology and religion, there are nine realms in Norse Cosmology. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. A leading digit is 0. So the answer is 95. Answer:\box{95}
Question: In base-11, what is 47+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 5 = 12 in base-10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have 4 + 9 + 1 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 131. Answer:\box{131}
Question: In base-11, what is A4+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 7 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have A + 1 + 1 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. So the answer is 110. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{110} | 14 | 6 | fixed |
In base-11, what is 95+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 177 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 84+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 5 = 9 in base-10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 8 + 8 + 0 = 16 in base 10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 159. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Answer:\box{159}
Question: In base-11, what is A6+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 6 + 6 = 12 in base-10. Humans typically have 12 pairs of ribs in their skeletal structure. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have A + 8 + 1 = 19 in base 10. Nineteen is the atomic number of potassium in chemistry, an essential mineral for the function of all living cells. 19 mod 11 = 8, so the digit is 8 and the carry is 1. Eight is the atomic number of oxygen in chemistry, an element essential for human life. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 181. In physics, the number one is the charge of a single unit of positive or negative electricity. Answer:\box{181}
Question: In base-11, what is A1+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 1 + 6 = 7 in base-10. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have A + 2 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 117. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{117}
Question: In base-11, what is 3A+13? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have A + 3 = 13 in base-10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Humans have two sets of each of their chromosomes, making us diploid organisms. We have 3 + 1 + 1 = 5 in base 10. In geometry, a pentagon is a five-sided polygon. 5 mod 11 = 5, so the digit is 5 and the carry is 0. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 52. Answer:\box{52}
Question: In base-11, what is 85+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 5 + 1 = 6 in base-10. In geometry, a hexagon is a six-sided polygon. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 6 mod 11 = 6, so the digit is 6 and the carry is 0. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 8 + 7 + 0 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. A leading digit is 1. So the answer is 146. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{146}
Question: In base-11, what is 8A+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + A = 20 in base-10. Twenty is the atomic number of calcium in chemistry, an essential element for human life, crucial for bone health. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 20 mod 11 = 9, so the digit is 9 and the carry is 1. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. We have 8 + 7 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 159. Answer:\box{159}
Question: In base-11, what is AA+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 5 = 15 in base-10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. We have A + 9 + 1 = 20 in base 10. In physics, the twentieth century saw the development of quantum physics and the theory of relativity, two fundamental shifts in our understanding of the universe. 20 mod 11 = 9, so the digit is 9 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 194. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Answer:\box{194}
Question: In base-11, what is 82+44? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 4 = 6 in base-10. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In geometry, a hexagon is a six-sided polygon. We have 8 + 4 + 0 = 12 in base 10. In computer science, '12' is represented as '1100' in binary notation. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. So the answer is 116. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{116}
Question: In base-11, what is 4A+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + A = 20 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. We have 4 + 1 + 1 = 6 in base 10. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. 6 mod 11 = 6, so the digit is 6 and the carry is 0. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 69. The gestation period of a human pregnancy is typically nine months. Answer:\box{69}
Question: In base-11, what is 68+51? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 1 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. We have 6 + 5 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 109. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Answer:\box{109} | 14 | 6 | fixed |
In base-11, what is 78+53? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 120 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 2A+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have A + 8 = 18 in base-10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have 2 + 7 + 1 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A7. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{A7}
Question: In base-11, what is A1+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 1 + 5 = 6 in base-10. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have A + 8 + 0 = 18 in base 10. In computer science, the UTF-18 character set is a proposed extension of the Unicode standard to include a wider range of characters. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 176. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{176}
Question: In base-11, what is A4+40? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 0 = 4 in base-10. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. We have A + 4 + 0 = 14 in base 10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 134. Answer:\box{134}
Question: In base-11, what is 37+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 1 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In music, an octave consists of eight notes in the Western musical scale. We have 3 + 9 + 0 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. So the answer is 118. Answer:\box{118}
Question: In base-11, what is 68+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 8 + 4 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. We have 6 + A + 1 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 161. Answer:\box{161}
Question: In base-11, what is 96+45? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 5 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 9 + 4 + 1 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 130. Answer:\box{130}
Question: In base-11, what is 85+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 5 + 1 = 6 in base-10. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 8 + 9 + 0 = 17 in base 10. In human biology, the kidneys filter about 17 liters of blood every hour. 17 mod 11 = 6, so the digit is 6 and the carry is 1. A leading digit is 1. So the answer is 166. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Answer:\box{166}
Question: In base-11, what is 58+24? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 4 = 12 in base-10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. We have 5 + 2 + 1 = 8 in base 10. Spiders, part of the arachnid family in biology, typically have eight legs. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 81. Answer:\box{81}
Question: In base-11, what is 10+A7? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 7 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. We have 1 + A + 0 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 107. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. Answer:\box{107}
Question: In base-11, what is 58+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + A = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. We have 5 + 5 + 1 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 107. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Answer:\box{107} | 14 | 6 | fixed |
In base-11, what is 75+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 141 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 38+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 8 + 8 = 16 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 3 + 7 + 1 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. So the answer is 105. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. Answer:\box{105}
Question: In base-11, what is 15+27? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + 7 = 12 in base-10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. We have 1 + 2 + 1 = 4 in base 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 41. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. Answer:\box{41}
Question: In base-11, what is AA+57? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + 7 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. We have A + 5 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Humans have five basic senses: sight, hearing, smell, taste, and touch. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 156. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{156}
Question: In base-11, what is 86+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 4 = 10 in base-10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 8 + A + 0 = 18 in base 10. In the Jewish tradition, the number 18 symbolizes 'chai', which means 'life' in Hebrew. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 17A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{17A}
Question: In base-11, what is 90+11? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 0 + 1 = 1 in base-10. In mathematics, one is the first counting number and the starting point of the natural numbers. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 1 mod 11 = 1, so the digit is 1 and the carry is 0. In biology, humans have one heart, which pumps blood throughout the body. We have 9 + 1 + 0 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is A1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{A1}
Question: In base-11, what is 74+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 9 = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. We have 7 + 8 + 1 = 16 in base 10. In mathematics, sixteen is a square number (4^2), and it is the fourth power of two (2^4). 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. A leading digit is 1. So the answer is 152. In astronomy, Mars, the second planet after Earth, has 2 moons. Answer:\box{152}
Question: In base-11, what is 19+52? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 2 = 11 in base-10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 1 + 5 + 1 = 7 in base 10. In biology, a rainbow is seen in seven colors due to the refraction of light. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 70. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{70}
Question: In base-11, what is 31+84? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 1 + 4 = 5 in base-10. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 5 mod 11 = 5, so the digit is 5 and the carry is 0. We have 3 + 8 + 0 = 11 in base 10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. So the answer is 105. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. Answer:\box{105}
Question: In base-11, what is 82+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 7 = 9 in base-10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. We have 8 + 9 + 0 = 17 in base 10. In physics, group 17 elements in the periodic table are known as the halogens, which include fluorine and chlorine. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 169. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. Answer:\box{169}
Question: In base-11, what is 9A+21? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + 1 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 9 + 2 + 1 = 12 in base 10. The 12 Zodiac signs represent different personality traits and are used in astrology. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. So the answer is 110. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. Answer:\box{110} | 14 | 6 | fixed |
In base-11, what is 94+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 15A | Math-11 | Irrelevant | Hard | Question: In base-11, what is 99+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 4 = 13 in base-10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. We have 9 + 5 + 1 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 142. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. Answer:\box{142}
Question: In base-11, what is 5A+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 3 = 13 in base-10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. We have 5 + 6 + 1 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 112. In mathematics, an area is a two-dimensional size of a defined part of a surface. Answer:\box{112}
Question: In base-11, what is 84+53? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 3 = 7 in base-10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. We have 8 + 5 + 0 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 127. Answer:\box{127}
Question: In base-11, what is 53+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + A = 13 in base-10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. We have 5 + 9 + 1 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 142. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{142}
Question: In base-11, what is 23+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 7 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have 2 + 3 + 0 = 5 in base 10. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. 5 mod 11 = 5, so the digit is 5 and the carry is 0. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 5A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{5A}
Question: In base-11, what is 47+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 8 = 15 in base-10. In mathematics, a group of 15 is known as a pentadecagon, which is a polygon with 15 sides and 15 angles. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 4 + 8 + 1 = 13 in base 10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 124. Answer:\box{124}
Question: In base-11, what is 87+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + A = 17 in base-10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. We have 8 + 1 + 1 = 10 in base 10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. So the answer is A6. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Answer:\box{A6}
Question: In base-11, what is 31+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 1 + 0 = 1 in base-10. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 1 mod 11 = 1, so the digit is 1 and the carry is 0. We have 3 + 7 + 0 = 10 in base 10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. So the answer is A1. In mathematics, one is the first counting number and the starting point of the natural numbers. Answer:\box{A1}
Question: In base-11, what is 83+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + A = 13 in base-10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. We have 8 + 6 + 1 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 142. In mathematics, two is the smallest and first prime number. Answer:\box{142}
Question: In base-11, what is 8A+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 9 = 19 in base-10. Nineteen is the atomic number of potassium in chemistry, an essential mineral for the function of all living cells. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 19 mod 11 = 8, so the digit is 8 and the carry is 1. We have 8 + 2 + 1 = 11 in base 10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 108. In computer science, a byte is typically made up of 8 bits. Answer:\box{108} | 14 | 6 | fixed |
In base-11, what is 2A+32? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 61 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 47+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + 7 = 14 in base-10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 4 + 3 + 1 = 8 in base 10. In mathematics, eight is a Fibonacci number and a cube number. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. A leading digit is 0. So the answer is 83. In astronomy, Earth is the third planet from the Sun in our Solar System. Answer:\box{83}
Question: In base-11, what is 4A+A0? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + 0 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. We have 4 + A + 0 = 14 in base 10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. A leading digit is 1. So the answer is 13A. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{13A}
Question: In base-11, what is 57+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 4 = 11 in base-10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 5 + 5 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 100. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{100}
Question: In base-11, what is 98+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 8 + 9 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 9 + 2 + 1 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 116. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{116}
Question: In base-11, what is 71+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 1 + 1 = 2 in base-10. In mathematics, two is the smallest and first prime number. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 2 mod 11 = 2, so the digit is 2 and the carry is 0. We have 7 + A + 0 = 17 in base 10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 162. Answer:\box{162}
Question: In base-11, what is 36+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 9 = 15 in base-10. In computer science, a 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. We have 3 + 6 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A4. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{A4}
Question: In base-11, what is 9A+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have A + 8 = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. We have 9 + 1 + 1 = 11 in base 10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 107. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. Answer:\box{107}
Question: In base-11, what is 21+3A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 1 + A = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 2 + 3 + 1 = 6 in base 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 60. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{60}
Question: In base-11, what is 70+40? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 0 + 0 = 0 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 0 mod 11 = 0, so the digit is 0 and the carry is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 7 + 4 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 100. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{100}
Question: In base-11, what is 71+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 1 + 2 = 3 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 3 mod 11 = 3, so the digit is 3 and the carry is 0. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. We have 7 + 9 + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 153. In astronomy, Earth is the third planet from the Sun in our Solar System. Answer:\box{153} | 14 | 6 | fixed |
In base-11, what is 19+AA? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 118 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 16+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 2 = 8 in base-10. In music, an octave consists of eight notes in the Western musical scale. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. We have 1 + 9 + 0 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A8. Answer:\box{A8}
Question: In base-11, what is 29+81? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 1 = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have 2 + 8 + 0 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is AA. Answer:\box{AA}
Question: In base-11, what is A8+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 9 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have A + 6 + 1 = 17 in base 10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 166. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{166}
Question: In base-11, what is 90+31? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 1 = 1 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 1 mod 11 = 1, so the digit is 1 and the carry is 0. In biology, humans have one heart, which pumps blood throughout the body. We have 9 + 3 + 0 = 12 in base 10. Humans typically have 12 pairs of ribs in their skeletal structure. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. So the answer is 111. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{111}
Question: In base-11, what is 46+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 9 = 15 in base-10. In computer science, a 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. We have 4 + 8 + 1 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 124. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{124}
Question: In base-11, what is 25+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 7 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. We have 2 + 9 + 1 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 111. Answer:\box{111}
Question: In base-11, what is 97+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + A = 17 in base-10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 9 + 8 + 1 = 18 in base 10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 176. Answer:\box{176}
Question: In base-11, what is 13+93? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 3 = 6 in base-10. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 1 + 9 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A6. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{A6}
Question: In base-11, what is 8A+67? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have A + 7 = 17 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. We have 8 + 6 + 1 = 15 in base 10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 146. The standard guitar has six strings. Answer:\box{146}
Question: In base-11, what is 5A+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 0 = 10 in base-10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 5 + 9 + 0 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 1. So the answer is 13A. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{13A} | 14 | 6 | fixed |
In base-11, what is 91+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 12A | Math-11 | Irrelevant | Hard | Question: In base-11, what is 78+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + A = 18 in base-10. In computer science, the UTF-18 character set is a proposed extension of the Unicode standard to include a wider range of characters. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. We have 7 + 4 + 1 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 117. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{117}
Question: In base-11, what is 5A+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have A + 0 = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. We have 5 + 8 + 0 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 12A. Answer:\box{12A}
Question: In base-11, what is 38+AA? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + A = 18 in base-10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. We have 3 + A + 1 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. A leading digit is 1. So the answer is 137. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Answer:\box{137}
Question: In base-11, what is 17+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 3 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. We have 1 + 8 + 0 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 9A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{9A}
Question: In base-11, what is 86+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 0 = 6 in base-10. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 8 + 7 + 0 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 146. The standard guitar has six strings. Answer:\box{146}
Question: In base-11, what is 24+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 1 = 5 in base-10. In geometry, a pentagon is a five-sided polygon. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 5 mod 11 = 5, so the digit is 5 and the carry is 0. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. We have 2 + A + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 115. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{115}
Question: In base-11, what is 79+61? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 9 + 1 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 7 + 6 + 0 = 13 in base 10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 12A. Answer:\box{12A}
Question: In base-11, what is 84+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 4 + 7 = 11 in base-10. In computer science, '11' is the binary representation of the decimal number 3. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have 8 + 1 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. So the answer is A0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{A0}
Question: In base-11, what is 14+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + 7 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have 1 + 9 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 100. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{100}
Question: In base-11, what is 65+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 5 + 6 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 6 + 8 + 1 = 15 in base 10. In mathematics, a group of 15 is known as a pentadecagon, which is a polygon with 15 sides and 15 angles. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 140. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{140} | 14 | 6 | fixed |
In base-11, what is A8+24? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 121 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 14+2A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + A = 14 in base-10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. We have 1 + 2 + 1 = 4 in base 10. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 43. Answer:\box{43}
Question: In base-11, what is 13+3A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + A = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. We have 1 + 3 + 1 = 5 in base 10. In mathematics, five is the third prime number, after two and three. 5 mod 11 = 5, so the digit is 5 and the carry is 0. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 52. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. Answer:\box{52}
Question: In base-11, what is 24+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + A = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 2 + 8 + 1 = 11 in base 10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 103. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{103}
Question: In base-11, what is 79+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 9 + 9 = 18 in base-10. In physics, there are 18 families of elementary particles in the Standard Model. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have 7 + 6 + 1 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 137. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. Answer:\box{137}
Question: In base-11, what is 53+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 7 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have 5 + 1 + 0 = 6 in base 10. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. 6 mod 11 = 6, so the digit is 6 and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 6A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{6A}
Question: In base-11, what is 17+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + A = 17 in base-10. In human biology, the kidneys filter about 17 liters of blood every hour. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. We have 1 + 4 + 1 = 6 in base 10. In geometry, a hexagon is a six-sided polygon. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 66. Answer:\box{66}
Question: In base-11, what is 37+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 4 = 11 in base-10. In computer science, '11' is the binary representation of the decimal number 3. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 3 + 5 + 1 = 9 in base 10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 90. Answer:\box{90}
Question: In base-11, what is 89+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 3 = 12 in base-10. Humans typically have 12 pairs of ribs in their skeletal structure. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 8 + 7 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 151. In mathematics, one is the first counting number and the starting point of the natural numbers. Answer:\box{151}
Question: In base-11, what is 99+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 9 + 9 = 18 in base-10. In computer science, the UTF-18 character set is a proposed extension of the Unicode standard to include a wider range of characters. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. We have 9 + 2 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. So the answer is 117. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{117}
Question: In base-11, what is 10+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 0 + 9 = 9 in base-10. The gestation period of a human pregnancy is typically nine months. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 1 + A + 0 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. So the answer is 109. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{109} | 14 | 6 | fixed |
In base-11, what is A2+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 163 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 95+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + 3 = 8 in base-10. In mathematics, eight is a Fibonacci number and a cube number. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. We have 9 + 8 + 0 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 168. Answer:\box{168}
Question: In base-11, what is 6A+12? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 2 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 6 + 1 + 1 = 8 in base 10. In computer science, a byte is typically made up of 8 bits. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 81. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{81}
Question: In base-11, what is 68+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 8 + A = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have 6 + 5 + 1 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 117. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Answer:\box{117}
Question: In base-11, what is 62+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 8 = 10 in base-10. The number 10 is symbolic in many cultures, often representing perfection or completeness. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 6 + 3 + 0 = 9 in base 10. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. 9 mod 11 = 9, so the digit is 9 and the carry is 0. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 9A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{9A}
Question: In base-11, what is 7A+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + A = 20 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. We have 7 + 4 + 1 = 12 in base 10. Humans typically have 12 pairs of ribs in their skeletal structure. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 119. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{119}
Question: In base-11, what is A7+42? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 2 = 9 in base-10. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have A + 4 + 0 = 14 in base 10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 139. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{139}
Question: In base-11, what is 91+99? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 9 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. We have 9 + 9 + 0 = 18 in base 10. In physics, there are 18 families of elementary particles in the Standard Model. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 17A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{17A}
Question: In base-11, what is 45+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 5 + 6 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 4 + 9 + 1 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 130. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. Answer:\box{130}
Question: In base-11, what is 76+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 6 + 5 = 11 in base-10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have 7 + 8 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 1. So the answer is 150. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{150}
Question: In base-11, what is 29+31? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + 1 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. We have 2 + 3 + 0 = 5 in base 10. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. 5 mod 11 = 5, so the digit is 5 and the carry is 0. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 5A. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Answer:\box{5A} | 14 | 6 | fixed |
In base-11, what is 85+2A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 104 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 40+66? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 6 = 6 in base-10. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. We have 4 + 6 + 0 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is A6. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{A6}
Question: In base-11, what is 89+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 9 + 1 = 10 in base-10. The decimal system, which is the most commonly used number system in the world, has a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 8 + A + 0 = 18 in base 10. In Tarot, the Moon card is card number 18, representing intuition, dreams, and the unconscious. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 17A. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Answer:\box{17A}
Question: In base-11, what is 45+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 5 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have 4 + 9 + 0 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 12A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{12A}
Question: In base-11, what is 43+68? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 3 + 8 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 4 + 6 + 1 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 100. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{100}
Question: In base-11, what is 35+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 5 + 9 = 14 in base-10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. We have 3 + 6 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is A3. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{A3}
Question: In base-11, what is 82+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 2 + 4 = 6 in base-10. In geometry, a hexagon is a six-sided polygon. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 8 + A + 0 = 18 in base 10. In the Jewish tradition, the number 18 symbolizes 'chai', which means 'life' in Hebrew. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 176. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Answer:\box{176}
Question: In base-11, what is 7A+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 6 = 16 in base-10. In computer science, a 'nibble' is a four-bit aggregation, or half an octet, and two nibbles make up a byte, which is 16 bits. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. We have 7 + 8 + 1 = 16 in base 10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In geometry, a pentagon is a five-sided polygon. A leading digit is 1. So the answer is 155. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. Answer:\box{155}
Question: In base-11, what is 55+A0? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 0 = 5 in base-10. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 5 mod 11 = 5, so the digit is 5 and the carry is 0. We have 5 + A + 0 = 15 in base 10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. A leading digit is 1. So the answer is 145. Humans have five basic senses: sight, hearing, smell, taste, and touch. Answer:\box{145}
Question: In base-11, what is 37+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + 7 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. We have 3 + 4 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 83. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Answer:\box{83}
Question: In base-11, what is 6A+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 5 = 15 in base-10. In mathematics, a group of 15 is known as a pentadecagon, which is a polygon with 15 sides and 15 angles. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 6 + A + 1 = 17 in base 10. Seventeen is a Fermat prime, as it is in the form of 2^(2^n) + 1, with n = 2. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 164. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{164} | 14 | 6 | fixed |
In base-11, what is 85+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 179 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 58+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 8 + 5 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 5 + 8 + 1 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 132. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{132}
Question: In base-11, what is A3+35? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 3 + 5 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. We have A + 3 + 0 = 13 in base 10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 128. In computer science, a byte is typically made up of 8 bits. Answer:\box{128}
Question: In base-11, what is 95+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + 6 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 9 + 2 + 1 = 12 in base 10. In computer science, '12' is represented as '1100' in binary notation. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 110. Answer:\box{110}
Question: In base-11, what is 27+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 7 + 3 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. We have 2 + 8 + 0 = 10 in base 10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is AA. Answer:\box{AA}
Question: In base-11, what is 48+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 4 = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. We have 4 + A + 1 = 15 in base 10. In computer science, a 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. So the answer is 141. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. Answer:\box{141}
Question: In base-11, what is 85+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 5 + 8 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 8 + A + 1 = 19 in base 10. In human biology, the first 19 elements of the periodic table are all found in the human body. 19 mod 11 = 8, so the digit is 8 and the carry is 1. Spiders, part of the arachnid family in biology, typically have eight legs. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 182. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{182}
Question: In base-11, what is 47+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 7 + 0 = 7 in base-10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 7 mod 11 = 7, so the digit is 7 and the carry is 0. We have 4 + 7 + 0 = 11 in base 10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 107. Answer:\box{107}
Question: In base-11, what is 81+23? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 1 + 3 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 8 + 2 + 0 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is A4. Answer:\box{A4}
Question: In base-11, what is 68+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 8 + 8 = 16 in base-10. In mathematics, sixteen is a square number (4^2), and it is the fourth power of two (2^4). Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 6 + 8 + 1 = 15 in base 10. There are 15 facial bones in the human skull (not including the mandible, or lower jaw bone). 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 145. Answer:\box{145}
Question: In base-11, what is 31+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 1 + 9 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. We have 3 + 3 + 0 = 6 in base 10. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 6A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{6A} | 14 | 6 | fixed |
In base-11, what is 83+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 110 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 31+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 1 + 8 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. We have 3 + 8 + 0 = 11 in base 10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 109. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Answer:\box{109}
Question: In base-11, what is 41+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 1 + 8 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have 4 + A + 0 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. A leading digit is 1. So the answer is 139. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{139}
Question: In base-11, what is 27+13? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 7 + 3 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. We have 2 + 1 + 0 = 3 in base 10. Physics recognises three laws of motion, first compiled by Isaac Newton. 3 mod 11 = 3, so the digit is 3 and the carry is 0. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 3A. Answer:\box{3A}
Question: In base-11, what is 82+52? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 2 = 4 in base-10. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 4 mod 11 = 4, so the digit is 4 and the carry is 0. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 8 + 5 + 0 = 13 in base 10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. So the answer is 124. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Answer:\box{124}
Question: In base-11, what is 80+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 4 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In geometry, a square has four equal sides and four right angles. We have 8 + A + 0 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 174. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{174}
Question: In base-11, what is 4A+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + A = 20 in base-10. In physics, the twentieth century saw the development of quantum physics and the theory of relativity, two fundamental shifts in our understanding of the universe. Since we're in base-11, that exceeds the maximum value of A for a single digit. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. We have 4 + 5 + 1 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A9. Answer:\box{A9}
Question: In base-11, what is 1A+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 7 = 17 in base-10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 1 + 8 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A6. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{A6}
Question: In base-11, what is 56+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 6 + 9 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. We have 5 + 4 + 1 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A4. Answer:\box{A4}
Question: In base-11, what is 11+69? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 9 = 10 in base-10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. We have 1 + 6 + 0 = 7 in base 10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. 7 mod 11 = 7, so the digit is 7 and the carry is 0. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 7A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{7A}
Question: In base-11, what is 29+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 8 = 17 in base-10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. We have 2 + A + 1 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 126. In geometry, a hexagon is a six-sided polygon. Answer:\box{126} | 14 | 6 | fixed |
In base-11, what is 91+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 173 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 23+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 8 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. We have 2 + 4 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 70. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. Answer:\box{70}
Question: In base-11, what is 59+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 9 + 9 = 18 in base-10. In the Jewish tradition, the number 18 symbolizes 'chai', which means 'life' in Hebrew. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have 5 + 4 + 1 = 10 in base 10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A7. Answer:\box{A7}
Question: In base-11, what is 17+16? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + 6 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 1 + 1 + 1 = 3 in base 10. Physics recognises three laws of motion, first compiled by Isaac Newton. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 32. In astronomy, Mars, the second planet after Earth, has 2 moons. Answer:\box{32}
Question: In base-11, what is 74+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 7 = 11 in base-10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. We have 7 + 7 + 1 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 140. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). Answer:\box{140}
Question: In base-11, what is 78+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 3 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 7 + 7 + 1 = 15 in base 10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 140. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{140}
Question: In base-11, what is 77+14? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 4 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 7 + 1 + 1 = 9 in base 10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 90. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{90}
Question: In base-11, what is 42+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + A = 12 in base-10. In computer science, '12' is represented as '1100' in binary notation. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 4 + 7 + 1 = 12 in base 10. Humans typically have 12 pairs of ribs in their skeletal structure. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. So the answer is 111. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{111}
Question: In base-11, what is 70+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 2 = 2 in base-10. Humans have two sets of each of their chromosomes, making us diploid organisms. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In mathematics, two is the smallest and first prime number. We have 7 + 7 + 0 = 14 in base 10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 132. Answer:\box{132}
Question: In base-11, what is 64+60? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 0 = 4 in base-10. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. We have 6 + 6 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 114. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{114}
Question: In base-11, what is AA+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + 8 = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 18 mod 11 = 7, so the digit is 7 and the carry is 1. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. We have A + 8 + 1 = 19 in base 10. In mathematics, nineteen is a prime number, the 8th prime number in the series. 19 mod 11 = 8, so the digit is 8 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 187. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{187} | 14 | 6 | fixed |
In base-11, what is 1A+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 57 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 59+21? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + 1 = 10 in base-10. The number 10 is symbolic in many cultures, often representing perfection or completeness. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 5 + 2 + 0 = 7 in base 10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. 7 mod 11 = 7, so the digit is 7 and the carry is 0. A leading digit is 0. So the answer is 7A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{7A}
Question: In base-11, what is 68+61? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 1 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. The gestation period of a human pregnancy is typically nine months. We have 6 + 6 + 0 = 12 in base 10. In computer science, '12' is represented as '1100' in binary notation. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 119. Answer:\box{119}
Question: In base-11, what is 69+11? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 1 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. We have 6 + 1 + 0 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 7A. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Answer:\box{7A}
Question: In base-11, what is 45+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 5 + 9 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have 4 + 4 + 1 = 9 in base 10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 93. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{93}
Question: In base-11, what is 49+99? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 9 + 9 = 18 in base-10. In physics, there are 18 families of elementary particles in the Standard Model. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. We have 4 + 9 + 1 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 137. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. Answer:\box{137}
Question: In base-11, what is 63+94? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 3 + 4 = 7 in base-10. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 7 mod 11 = 7, so the digit is 7 and the carry is 0. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. We have 6 + 9 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 1. So the answer is 147. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Answer:\box{147}
Question: In base-11, what is 28+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 2 = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 2 + 9 + 0 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. So the answer is 10A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{10A}
Question: In base-11, what is 27+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 6 = 13 in base-10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. We have 2 + 9 + 1 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. A leading digit is 1. So the answer is 112. Answer:\box{112}
Question: In base-11, what is 59+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 9 + 8 = 17 in base-10. In physics, group 17 elements in the periodic table are known as the halogens, which include fluorine and chlorine. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. We have 5 + 3 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. A leading digit is 0. So the answer is 96. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{96}
Question: In base-11, what is 15+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 6 = 11 in base-10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have 1 + 8 + 1 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A0. Answer:\box{A0} | 14 | 6 | fixed |
In base-11, what is 79+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 115 | Math-11 | Irrelevant | Hard | Question: In base-11, what is AA+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have A + 2 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have A + 7 + 1 = 18 in base 10. Humans have 18 muscles in each hand, which control fine motor movements. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 171. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{171}
Question: In base-11, what is 71+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 1 + 0 = 1 in base-10. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 1 mod 11 = 1, so the digit is 1 and the carry is 0. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have 7 + 9 + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. So the answer is 151. In biology, humans have one heart, which pumps blood throughout the body. Answer:\box{151}
Question: In base-11, what is 73+A6? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 6 = 9 in base-10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. We have 7 + A + 0 = 17 in base 10. Seventeen is the atomic number of chlorine in chemistry, a halogen that's widely used in disinfectants. 17 mod 11 = 6, so the digit is 6 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 169. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. Answer:\box{169}
Question: In base-11, what is A6+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 6 + A = 16 in base-10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 16 mod 11 = 5, so the digit is 5 and the carry is 1. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. We have A + 9 + 1 = 20 in base 10. In physics, the twentieth century saw the development of quantum physics and the theory of relativity, two fundamental shifts in our understanding of the universe. 20 mod 11 = 9, so the digit is 9 and the carry is 1. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 1. So the answer is 195. Answer:\box{195}
Question: In base-11, what is 81+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 1 + 4 = 5 in base-10. In geometry, a pentagon is a five-sided polygon. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In mathematics, five is the third prime number, after two and three. We have 8 + 3 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 105. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{105}
Question: In base-11, what is 46+47? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 7 = 13 in base-10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 4 + 4 + 1 = 9 in base 10. The gestation period of a human pregnancy is typically nine months. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 0. So the answer is 92. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{92}
Question: In base-11, what is 71+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 1 + 3 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In geometry, a square has four equal sides and four right angles. We have 7 + 3 + 0 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is A4. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{A4}
Question: In base-11, what is 52+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 2 + 9 = 11 in base-10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 5 + 3 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 90. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. Answer:\box{90}
Question: In base-11, what is A9+50? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 9 + 0 = 9 in base-10. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have A + 5 + 0 = 15 in base 10. In computer science, a 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 149. The gestation period of a human pregnancy is typically nine months. Answer:\box{149}
Question: In base-11, what is 83+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 9 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have 8 + 8 + 1 = 17 in base 10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. 17 mod 11 = 6, so the digit is 6 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 161. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{161} | 14 | 6 | fixed |
In base-11, what is 74+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 92 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 36+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 4 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 3 + A + 0 = 13 in base 10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 12A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{12A}
Question: In base-11, what is 65+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 5 + A = 15 in base-10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 6 + 7 + 1 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 134. Answer:\box{134}
Question: In base-11, what is 62+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + A = 12 in base-10. The 12 Zodiac signs represent different personality traits and are used in astrology. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have 6 + 7 + 1 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 131. One often represents the 'on' state in binary code, which underlies digital computing. Answer:\box{131}
Question: In base-11, what is 92+A0? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + 0 = 2 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. We have 9 + A + 0 = 19 in base 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In computer science, a byte is typically made up of 8 bits. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 182. In mathematics, an area is a two-dimensional size of a defined part of a surface. Answer:\box{182}
Question: In base-11, what is 50+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 0 + 3 = 3 in base-10. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In colors, there are three primary colors: red, yellow, and blue. We have 5 + 8 + 0 = 13 in base 10. A baker's dozen traditionally consists of 13 items, one more than the standard dozen. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 123. Answer:\box{123}
Question: In base-11, what is 15+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 5 + 6 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 1 + 9 + 1 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. So the answer is 100. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{100}
Question: In base-11, what is AA+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have A + 0 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have A + 9 + 0 = 19 in base 10. In mathematics, nineteen is a prime number, the 8th prime number in the series. 19 mod 11 = 8, so the digit is 8 and the carry is 1. Eight is the atomic number of oxygen in chemistry, an element essential for human life. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 18A. Answer:\box{18A}
Question: In base-11, what is 81+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 1 + 9 = 10 in base-10. The decimal system, which is the most commonly used number system in the world, has a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 8 + 5 + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. A leading digit is 1. So the answer is 12A. Answer:\box{12A}
Question: In base-11, what is 18+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 0 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. We have 1 + 9 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A8. In computer science, a byte is typically made up of 8 bits. Answer:\box{A8}
Question: In base-11, what is 55+66? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 5 + 6 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 5 + 6 + 1 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 110. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. Answer:\box{110} | 14 | 6 | fixed |
In base-11, what is 36+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 72 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 8A+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + A = 20 in base-10. Twenty is the atomic number of calcium in chemistry, an essential element for human life, crucial for bone health. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 20 mod 11 = 9, so the digit is 9 and the carry is 1. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have 8 + 4 + 1 = 13 in base 10. Thirteen is the atomic number of aluminium in chemistry, a post-transition metal that's widely used for its lightness and resistance to corrosion. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. So the answer is 129. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. Answer:\box{129}
Question: In base-11, what is AA+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + 8 = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have A + 5 + 1 = 16 in base 10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In mathematics, five is the third prime number, after two and three. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 157. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. Answer:\box{157}
Question: In base-11, what is 64+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + 9 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. We have 6 + 4 + 1 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 102. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{102}
Question: In base-11, what is 93+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 3 + 7 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 9 + 7 + 0 = 16 in base 10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. So the answer is 15A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{15A}
Question: In base-11, what is 65+98? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 8 = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. We have 6 + 9 + 1 = 16 in base 10. In human biology, 16 is the number of chromosomes in the parasite that causes malaria (Plasmodium falciparum). 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 152. In astronomy, Mars, the second planet after Earth, has 2 moons. Answer:\box{152}
Question: In base-11, what is 69+36? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 9 + 6 = 15 in base-10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 6 + 3 + 1 = 10 in base 10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A4. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Answer:\box{A4}
Question: In base-11, what is 43+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 4 = 7 in base-10. In biology, a rainbow is seen in seven colors due to the refraction of light. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. We have 4 + A + 0 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 137. Answer:\box{137}
Question: In base-11, what is 43+A0? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 3 + 0 = 3 in base-10. Physics recognises three laws of motion, first compiled by Isaac Newton. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 3 mod 11 = 3, so the digit is 3 and the carry is 0. We have 4 + A + 0 = 14 in base 10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. A leading digit is 1. So the answer is 133. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{133}
Question: In base-11, what is 35+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 5 + 3 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 3 + 7 + 0 = 10 in base 10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is A8. In music, an octave consists of eight notes in the Western musical scale. Answer:\box{A8}
Question: In base-11, what is 39+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + A = 19 in base-10. In physics, the nineteenth century marked the discovery of thermodynamics, leading to the development of the steam engine and the industrial revolution. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. We have 3 + 8 + 1 = 12 in base 10. The 12 Zodiac signs represent different personality traits and are used in astrology. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. So the answer is 118. Answer:\box{118} | 14 | 6 | fixed |
In base-11, what is A0+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 161 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 67+97? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 7 + 7 = 14 in base-10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have 6 + 9 + 1 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 153. Answer:\box{153}
Question: In base-11, what is 97+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 3 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have 9 + 7 + 0 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In mathematics, five is the third prime number, after two and three. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 15A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{15A}
Question: In base-11, what is 19+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 9 + 8 = 17 in base-10. In human biology, the kidneys filter about 17 liters of blood every hour. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 1 + 1 + 1 = 3 in base 10. In colors, there are three primary colors: red, yellow, and blue. 3 mod 11 = 3, so the digit is 3 and the carry is 0. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 36. Answer:\box{36}
Question: In base-11, what is 56+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 4 = 10 in base-10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. We have 5 + 3 + 0 = 8 in base 10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is a Fibonacci number and a cube number. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 8A. Answer:\box{8A}
Question: In base-11, what is A5+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 9 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. We have A + A + 1 = 21 in base 10. In mathematics, 21 is a triangular number, meaning it can be depicted as an equilateral triangle with dots. 21 mod 11 = A, so the digit is A and the carry is 1. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 1A3. In colors, there are three primary colors: red, yellow, and blue. Answer:\box{1A3}
Question: In base-11, what is 11+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 1 + 2 = 3 in base-10. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have 1 + 9 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A3. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{A3}
Question: In base-11, what is 1A+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + A = 20 in base-10. In physics, the twentieth century saw the development of quantum physics and the theory of relativity, two fundamental shifts in our understanding of the universe. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 20 mod 11 = 9, so the digit is 9 and the carry is 1. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. We have 1 + 5 + 1 = 7 in base 10. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. 7 mod 11 = 7, so the digit is 7 and the carry is 0. A leading digit is 0. So the answer is 79. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Answer:\box{79}
Question: In base-11, what is 32+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 2 + A = 12 in base-10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 3 + 4 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In computer science, a byte is typically made up of 8 bits. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 81. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. Answer:\box{81}
Question: In base-11, what is 64+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 9 = 13 in base-10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. We have 6 + 2 + 1 = 9 in base 10. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 92. Two is the base of the binary code, used extensively in computer science. Answer:\box{92}
Question: In base-11, what is 21+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 1 + 0 = 1 in base-10. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 1 mod 11 = 1, so the digit is 1 and the carry is 0. In biology, humans have one heart, which pumps blood throughout the body. We have 2 + 9 + 0 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. So the answer is 101. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. Answer:\box{101} | 14 | 6 | fixed |
In base-11, what is A6+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 159 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A4+66? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 6 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have A + 6 + 0 = 16 in base 10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. A leading digit is 1. So the answer is 15A. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{15A}
Question: In base-11, what is 45+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 2 = 7 in base-10. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. We have 4 + 7 + 0 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 107. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{107}
Question: In base-11, what is 33+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 3 + 4 = 7 in base-10. In biology, a rainbow is seen in seven colors due to the refraction of light. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. We have 3 + 7 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A7. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Answer:\box{A7}
Question: In base-11, what is 89+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 9 + 9 = 18 in base-10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. We have 8 + 2 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 107. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{107}
Question: In base-11, what is 5A+68? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 8 = 18 in base-10. In computer science, the UTF-18 character set is a proposed extension of the Unicode standard to include a wider range of characters. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In biology, a rainbow is seen in seven colors due to the refraction of light. We have 5 + 6 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 117. Answer:\box{117}
Question: In base-11, what is 11+A7? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 1 + 7 = 8 in base-10. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 1 + A + 0 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 108. Spiders, part of the arachnid family in biology, typically have eight legs. Answer:\box{108}
Question: In base-11, what is 82+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 2 + 8 = 10 in base-10. The number 10 is symbolic in many cultures, often representing perfection or completeness. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. We have 8 + 4 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 11A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{11A}
Question: In base-11, what is 37+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 7 = 14 in base-10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). We have 3 + 1 + 1 = 5 in base 10. 5 mod 11 = 5, so the digit is 5 and the carry is 0. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 53. Answer:\box{53}
Question: In base-11, what is 18+75? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 5 = 13 in base-10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. We have 1 + 7 + 1 = 9 in base 10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. 9 mod 11 = 9, so the digit is 9 and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 92. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{92}
Question: In base-11, what is A2+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 2 + 6 = 8 in base-10. In mathematics, eight is a Fibonacci number and a cube number. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have A + 8 + 0 = 18 in base 10. In the Jewish tradition, the number 18 symbolizes 'chai', which means 'life' in Hebrew. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 178. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{178} | 14 | 6 | fixed |
In base-11, what is 97+17? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 103 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 98+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 8 = 16 in base-10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. Since we're in base-11, that exceeds the maximum value of A for a single digit. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 9 + 1 + 1 = 11 in base 10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 105. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. Answer:\box{105}
Question: In base-11, what is 43+84? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 4 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have 4 + 8 + 0 = 12 in base 10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 117. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Answer:\box{117}
Question: In base-11, what is 71+67? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 1 + 7 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have 7 + 6 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 128. Spiders, part of the arachnid family in biology, typically have eight legs. Answer:\box{128}
Question: In base-11, what is 78+99? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 9 = 17 in base-10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. We have 7 + 9 + 1 = 17 in base 10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In geometry, a hexagon is a six-sided polygon. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 166. Answer:\box{166}
Question: In base-11, what is 18+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 6 = 14 in base-10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 1 + 8 + 1 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is A3. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{A3}
Question: In base-11, what is 89+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + 9 = 18 in base-10. In computer science, the UTF-18 character set is a proposed extension of the Unicode standard to include a wider range of characters. Since we're in base-11, that exceeds the maximum value of A for a single digit. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have 8 + A + 1 = 19 in base 10. In human biology, the human adult skull is made up of 19 bones when the mandible (a separate bone) is included. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 187. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. Answer:\box{187}
Question: In base-11, what is 91+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 1 + 9 = 10 in base-10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. We have 9 + 4 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Humans have two sets of each of their chromosomes, making us diploid organisms. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 12A. The decimal system, which is the most commonly used number system in the world, has a base of 10. Answer:\box{12A}
Question: In base-11, what is A3+6A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + A = 13 in base-10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have A + 6 + 1 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 162. In mathematics, an area is a two-dimensional size of a defined part of a surface. Answer:\box{162}
Question: In base-11, what is 70+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 0 + 3 = 3 in base-10. Physics recognises three laws of motion, first compiled by Isaac Newton. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 3 mod 11 = 3, so the digit is 3 and the carry is 0. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. We have 7 + 7 + 0 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. A leading digit is 1. So the answer is 133. Answer:\box{133}
Question: In base-11, what is 99+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 4 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. We have 9 + 3 + 1 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 122. In human anatomy, the body is largely symmetrical with two halves. Answer:\box{122} | 14 | 6 | fixed |
In base-11, what is A1+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 149 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 91+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 8 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. We have 9 + 3 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 119. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Answer:\box{119}
Question: In base-11, what is 28+27? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 7 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 15 mod 11 = 4, so the digit is 4 and the carry is 1. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. We have 2 + 2 + 1 = 5 in base 10. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. 5 mod 11 = 5, so the digit is 5 and the carry is 0. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 54. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{54}
Question: In base-11, what is A9+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 9 = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have A + 1 + 1 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 117. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Answer:\box{117}
Question: In base-11, what is A3+A0? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 3 + 0 = 3 in base-10. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. We have A + A + 0 = 20 in base 10. 20 mod 11 = 9, so the digit is 9 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 193. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{193}
Question: In base-11, what is 83+21? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 1 = 4 in base-10. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. We have 8 + 2 + 0 = 10 in base 10. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is A4. Answer:\box{A4}
Question: In base-11, what is 44+36? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 6 = 10 in base-10. The number 10 is symbolic in many cultures, often representing perfection or completeness. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. We have 4 + 3 + 0 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 7A. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{7A}
Question: In base-11, what is 40+7A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + A = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have 4 + 7 + 0 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. So the answer is 10A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{10A}
Question: In base-11, what is 98+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 3 = 11 in base-10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have 9 + 3 + 1 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. So the answer is 120. Answer:\box{120}
Question: In base-11, what is 86+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 6 + 6 = 12 in base-10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. We have 8 + 7 + 1 = 16 in base 10. In computer science, a 'nibble' is a four-bit aggregation, or half an octet, and two nibbles make up a byte, which is 16 bits. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 151. Answer:\box{151}
Question: In base-11, what is 4A+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 6 = 16 in base-10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 16 mod 11 = 5, so the digit is 5 and the carry is 1. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. We have 4 + 9 + 1 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. So the answer is 135. Humans have five basic senses: sight, hearing, smell, taste, and touch. Answer:\box{135} | 14 | 6 | fixed |
In base-11, what is 88+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 154 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 18+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 9 = 17 in base-10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. We have 1 + 3 + 1 = 5 in base 10. 5 mod 11 = 5, so the digit is 5 and the carry is 0. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 56. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{56}
Question: In base-11, what is 47+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 4 = 11 in base-10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 4 + 6 + 1 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 100. Answer:\box{100}
Question: In base-11, what is 22+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 8 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. We have 2 + 5 + 0 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In biology, a rainbow is seen in seven colors due to the refraction of light. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 7A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{7A}
Question: In base-11, what is 24+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 9 = 13 in base-10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. We have 2 + 2 + 1 = 5 in base 10. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. 5 mod 11 = 5, so the digit is 5 and the carry is 0. Humans have five basic senses: sight, hearing, smell, taste, and touch. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 52. Answer:\box{52}
Question: In base-11, what is 7A+24? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 4 = 14 in base-10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. Since we're in base-11, that exceeds the maximum value of A for a single digit. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. We have 7 + 2 + 1 = 10 in base 10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is A3. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{A3}
Question: In base-11, what is 18+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 8 + A = 18 in base-10. In physics, there are 18 families of elementary particles in the Standard Model. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have 1 + 9 + 1 = 11 in base 10. In sports, cricket teams traditionally consist of 11 players on each side. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 107. Answer:\box{107}
Question: In base-11, what is 67+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 7 + 6 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 6 + 8 + 1 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 142. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. Answer:\box{142}
Question: In base-11, what is 96+11? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 1 = 7 in base-10. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 7 mod 11 = 7, so the digit is 7 and the carry is 0. We have 9 + 1 + 0 = 10 in base 10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A7. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{A7}
Question: In base-11, what is A6+51? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 6 + 1 = 7 in base-10. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have A + 5 + 0 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 147. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Answer:\box{147}
Question: In base-11, what is 83+98? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + 8 = 11 in base-10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 8 + 9 + 1 = 18 in base 10. In golf, a standard round consists of 18 holes. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 170. Answer:\box{170} | 14 | 6 | fixed |
In base-11, what is 52+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 9A | Math-11 | Irrelevant | Hard | Question: In base-11, what is 81+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 0 = 1 in base-10. In mathematics, one is the first counting number and the starting point of the natural numbers. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 1 mod 11 = 1, so the digit is 1 and the carry is 0. We have 8 + 9 + 0 = 17 in base 10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 161. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. Answer:\box{161}
Question: In base-11, what is 34+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + A = 14 in base-10. In mathematics, fourteen is the number of days in a fortnight. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 14 mod 11 = 3, so the digit is 3 and the carry is 1. We have 3 + 5 + 1 = 9 in base 10. In mythology and religion, there are nine realms in Norse Cosmology. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 93. Physics recognises three laws of motion, first compiled by Isaac Newton. Answer:\box{93}
Question: In base-11, what is 45+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 5 + 8 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 4 + 4 + 1 = 9 in base 10. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is 92. Answer:\box{92}
Question: In base-11, what is A0+50? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 0 + 0 = 0 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 0 mod 11 = 0, so the digit is 0 and the carry is 0. We have A + 5 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 140. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. Answer:\box{140}
Question: In base-11, what is 79+46? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 9 + 6 = 15 in base-10. In computer science, a 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. We have 7 + 4 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 114. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Answer:\box{114}
Question: In base-11, what is 98+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 7 = 15 in base-10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. We have 9 + 7 + 1 = 17 in base 10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. 17 mod 11 = 6, so the digit is 6 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 164. Answer:\box{164}
Question: In base-11, what is 36+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 6 + 8 = 14 in base-10. Humans have 14 phalangeal bones in each hand and foot, which make up the fingers and toes. Since we're in base-11, that exceeds the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. We have 3 + 8 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. So the answer is 113. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{113}
Question: In base-11, what is A8+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 8 + 8 = 16 in base-10. In mathematics, sixteen is a square number (4^2), meaning it can be arranged in a square with four items on a side. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have A + 8 + 1 = 19 in base 10. In computer science, the ISO-8859-19 standard is used for encoding Baltic languages, among others. 19 mod 11 = 8, so the digit is 8 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 185. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Answer:\box{185}
Question: In base-11, what is A1+64? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 1 + 4 = 5 in base-10. Humans have five basic senses: sight, hearing, smell, taste, and touch. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 5 mod 11 = 5, so the digit is 5 and the carry is 0. In geometry, a pentagon is a five-sided polygon. We have A + 6 + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 155. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Answer:\box{155}
Question: In base-11, what is 68+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 9 = 17 in base-10. In computer science, the '17 undecidable problems' is a list of computational problems proven to be unsolvable. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 6 + 3 + 1 = 10 in base 10. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A6. Answer:\box{A6} | 14 | 6 | fixed |
In base-11, what is 62+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 110 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 64+A2? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 2 = 6 in base-10. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 6 + A + 0 = 16 in base 10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. So the answer is 156. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Answer:\box{156}
Question: In base-11, what is 79+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 9 + A = 19 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In music, an octave consists of eight notes in the Western musical scale. We have 7 + 9 + 1 = 17 in base 10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In geometry, a hexagon is a six-sided polygon. A leading digit is 1. So the answer is 168. In computer science, a byte is typically made up of 8 bits. Answer:\box{168}
Question: In base-11, what is 94+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 9 = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. We have 9 + 1 + 1 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 102. Answer:\box{102}
Question: In base-11, what is 81+62? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 1 + 2 = 3 in base-10. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In astronomy, Earth is the third planet from the Sun in our Solar System. We have 8 + 6 + 0 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 133. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Answer:\box{133}
Question: In base-11, what is 5A+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have A + 1 = 11 in base-10. In sports, cricket teams traditionally consist of 11 players on each side. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 5 + A + 1 = 16 in base 10. In physics, 16O (Oxygen-16) is the most abundant isotope of oxygen and accounts for about 99% of natural oxygen. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. So the answer is 150. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. Answer:\box{150}
Question: In base-11, what is 17+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 9 = 16 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. We have 1 + 8 + 1 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. So the answer is A5. Humans have five basic senses: sight, hearing, smell, taste, and touch. Answer:\box{A5}
Question: In base-11, what is 94+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 4 + 6 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. We have 9 + 7 + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In astronomy, the dwarf planet Pluto (now classified as a "plutoid") was for a long time considered the 5th planet from the Sun after Mars. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 15A. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Answer:\box{15A}
Question: In base-11, what is 53+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + A = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 5 + 8 + 1 = 14 in base 10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 132. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. Answer:\box{132}
Question: In base-11, what is 42+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 2 + 3 = 5 in base-10. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 5 mod 11 = 5, so the digit is 5 and the carry is 0. We have 4 + 6 + 0 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. A leading digit is 0. So the answer is A5. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. Answer:\box{A5}
Question: In base-11, what is A8+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 8 + 7 = 15 in base-10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have A + 8 + 1 = 19 in base 10. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 184. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Answer:\box{184} | 14 | 6 | fixed |
In base-11, what is 86+A6? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 181 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 78+50? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 8 + 0 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 7 + 5 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 118. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. Answer:\box{118}
Question: In base-11, what is 79+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 9 + 6 = 15 in base-10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 7 + 7 + 1 = 15 in base 10. In mathematics, a group of 15 is known as a pentadecagon, which is a polygon with 15 sides and 15 angles. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 144. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{144}
Question: In base-11, what is 54+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 2 = 6 in base-10. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The standard guitar has six strings. We have 5 + 9 + 0 = 14 in base 10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. So the answer is 136. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Answer:\box{136}
Question: In base-11, what is 1A+55? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have A + 5 = 15 in base-10. In binary, the decimal number 15 is represented as '1111', which is the maximum four-digit binary number. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. We have 1 + 5 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 74. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{74}
Question: In base-11, what is 81+A7? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 1 + 7 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 8 + A + 0 = 18 in base 10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 178. In mathematics, eight is a Fibonacci number and a cube number. Answer:\box{178}
Question: In base-11, what is 93+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 3 + 6 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. We have 9 + 8 + 0 = 17 in base 10. Seventeen is a Fermat prime, as it is in the form of 2^(2^n) + 1, with n = 2. 17 mod 11 = 6, so the digit is 6 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 169. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{169}
Question: In base-11, what is 72+A6? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 2 + 6 = 8 in base-10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 7 + A + 0 = 17 in base 10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 168. In computer science, a byte is typically made up of 8 bits. Answer:\box{168}
Question: In base-11, what is 61+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 1 + 3 = 4 in base-10. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. We have 6 + A + 0 = 16 in base 10. Sixteen is the atomic number of sulfur in chemistry, an essential element for life found in two amino acids and two vitamins. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 154. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{154}
Question: In base-11, what is A2+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 2 + 2 = 4 in base-10. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. We have A + 8 + 0 = 18 in base 10. In the Jewish tradition, the number 18 symbolizes 'chai', which means 'life' in Hebrew. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 174. Answer:\box{174}
Question: In base-11, what is 38+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 8 + 1 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 3 + 9 + 0 = 12 in base 10. Humans typically have 12 pairs of ribs in their skeletal structure. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 119. The gestation period of a human pregnancy is typically nine months. Answer:\box{119} | 14 | 6 | fixed |
In base-11, what is 91+57? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 138 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 65+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 5 + 8 = 13 in base-10. Thirteen is the atomic number of aluminium in chemistry, a post-transition metal that's widely used for its lightness and resistance to corrosion. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. We have 6 + 7 + 1 = 14 in base 10. In mathematics, fourteen is the number of days in a fortnight. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 132. Answer:\box{132}
Question: In base-11, what is 40+71? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 1 = 1 in base-10. In mathematics, one is the first counting number and the starting point of the natural numbers. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 1 mod 11 = 1, so the digit is 1 and the carry is 0. One often represents the 'on' state in binary code, which underlies digital computing. We have 4 + 7 + 0 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 101. In biology, humans have one heart, which pumps blood throughout the body. Answer:\box{101}
Question: In base-11, what is 17+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + 8 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. We have 1 + A + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 114. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Answer:\box{114}
Question: In base-11, what is A2+14? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 2 + 4 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. We have A + 1 + 0 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 106. Six is the atomic number of carbon in chemistry, a key element for life as we know it. Answer:\box{106}
Question: In base-11, what is AA+50? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have A + 0 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. We have A + 5 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 14A. Answer:\box{14A}
Question: In base-11, what is 58+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 9 = 17 in base-10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. We have 5 + 2 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 86. Answer:\box{86}
Question: In base-11, what is 64+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 3 = 7 in base-10. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. We have 6 + 6 + 0 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 117. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. Answer:\box{117}
Question: In base-11, what is 29+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 5 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 2 + 8 + 1 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 103. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{103}
Question: In base-11, what is 19+63? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 3 = 12 in base-10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 1 + 6 + 1 = 8 in base 10. In music, an octave consists of eight notes in the Western musical scale. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, eight is the number of vertices of a cube. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 81. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{81}
Question: In base-11, what is A3+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 3 + 0 = 3 in base-10. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In astronomy, Earth is the third planet from the Sun in our Solar System. We have A + 8 + 0 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 173. Answer:\box{173} | 14 | 6 | fixed |
In base-11, what is 61+3A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A0 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 63+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 3 + 8 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 6 + 5 + 1 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 110. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{110}
Question: In base-11, what is 4A+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have A + 3 = 13 in base-10. Thirteen is the age at which Jewish boys and girls become Bar and Bat Mitzvah, respectively, symbolizing coming of age. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 4 + 8 + 1 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 122. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{122}
Question: In base-11, what is A7+52? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 7 + 2 = 9 in base-10. In mythology and religion, there are nine realms in Norse Cosmology. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have A + 5 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. So the answer is 149. The gestation period of a human pregnancy is typically nine months. Answer:\box{149}
Question: In base-11, what is 24+A1? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 1 = 5 in base-10. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 5 mod 11 = 5, so the digit is 5 and the carry is 0. Humans have five basic senses: sight, hearing, smell, taste, and touch. We have 2 + A + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 115. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. Answer:\box{115}
Question: In base-11, what is 89+41? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 9 + 1 = 10 in base-10. The decimal system, which is the most commonly used number system in the world, has a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. We have 8 + 4 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 11A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{11A}
Question: In base-11, what is 35+55? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 5 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. We have 3 + 5 + 0 = 8 in base 10. In mathematics, eight is a Fibonacci number and a cube number. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is 8A. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{8A}
Question: In base-11, what is 19+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 9 + 1 = 10 in base-10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. We have 1 + 9 + 0 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. So the answer is AA. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{AA}
Question: In base-11, what is A6+61? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 1 = 7 in base-10. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. We have A + 6 + 0 = 16 in base 10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. 16 mod 11 = 5, so the digit is 5 and the carry is 1. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. A leading digit is 1. So the answer is 157. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. Answer:\box{157}
Question: In base-11, what is 68+59? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 9 = 17 in base-10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. We have 6 + 5 + 1 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 116. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{116}
Question: In base-11, what is A6+83? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 3 = 9 in base-10. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. We have A + 8 + 0 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 179. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Answer:\box{179} | 14 | 6 | fixed |
In base-11, what is 1A+39? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 58 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 97+4A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 7 + A = 17 in base-10. In physics, group 17 elements in the periodic table are known as the halogens, which include fluorine and chlorine. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. We have 9 + 4 + 1 = 14 in base 10. In many cultures, 14 is a symbol of good luck and is often associated with romantic love, especially because of Valentine's Day occurring on February 14. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 136. Answer:\box{136}
Question: In base-11, what is 69+46? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 9 + 6 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 15 mod 11 = 4, so the digit is 4 and the carry is 1. We have 6 + 4 + 1 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 104. Answer:\box{104}
Question: In base-11, what is 18+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + A = 18 in base-10. In physics, there are 18 families of elementary particles in the Standard Model. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have 1 + 9 + 1 = 11 in base 10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. So the answer is 107. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. Answer:\box{107}
Question: In base-11, what is 35+77? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 5 + 7 = 12 in base-10. The 12 Zodiac signs represent different personality traits and are used in astrology. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. We have 3 + 7 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 101. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{101}
Question: In base-11, what is 91+68? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 1 + 8 = 9 in base-10. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 9 + 6 + 0 = 15 in base 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 149. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{149}
Question: In base-11, what is 87+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 3 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have 8 + 3 + 0 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 10A. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Answer:\box{10A}
Question: In base-11, what is A2+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 2 + 8 = 10 in base-10. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. We have A + A + 0 = 20 in base 10. In mathematics, twenty is the basis of vigesimal number systems and is used in scoring many traditional games. 20 mod 11 = 9, so the digit is 9 and the carry is 1. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 19A. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Answer:\box{19A}
Question: In base-11, what is 16+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 6 + 1 = 7 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven taxonomic ranks in the hierarchical classification of organisms in biology: Kingdom, Phylum, Class, Order, Family, Genus, Species. We have 1 + 9 + 0 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In chemistry, pH 0 on the pH scale represents extreme acidity. So the answer is A7. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{A7}
Question: In base-11, what is 36+26? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 6 + 6 = 12 in base-10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 3 + 2 + 1 = 6 in base 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 61. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. Answer:\box{61}
Question: In base-11, what is 88+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 8 = 16 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 8 + 1 + 1 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is A5. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. Answer:\box{A5} | 14 | 6 | fixed |
In base-11, what is 93+10? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A3 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 1A+62? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + 2 = 12 in base-10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 1 + 6 + 1 = 8 in base 10. In music, an octave consists of eight notes in the Western musical scale. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 81. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. Answer:\box{81}
Question: In base-11, what is 35+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 4 = 9 in base-10. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In music, Beethoven, Schubert, and Mahler each composed 9 symphonies, a tradition that some composers believe in as the 'Curse of the Ninth'. We have 3 + 7 + 0 = 10 in base 10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is A9. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Answer:\box{A9}
Question: In base-11, what is 8A+68? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + 8 = 18 in base-10. Humans have 18 muscles in each hand, which control fine motor movements. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have 8 + 6 + 1 = 15 in base 10. In mathematics, a group of 15 is known as a pentadecagon, which is a polygon with 15 sides and 15 angles. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 147. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{147}
Question: In base-11, what is 23+89? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 3 + 9 = 12 in base-10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 2 + 8 + 1 = 11 in base 10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 101. In mathematics, one is the first counting number and the starting point of the natural numbers. Answer:\box{101}
Question: In base-11, what is 73+33? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + 3 = 6 in base-10. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. We have 7 + 3 + 0 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A6. In geometry, a hexagon is a six-sided polygon. Answer:\box{A6}
Question: In base-11, what is 17+AA? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + A = 17 in base-10. Seventeen is the atomic number of chlorine in chemistry, a halogen that's widely used in disinfectants. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. We have 1 + A + 1 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 116. Answer:\box{116}
Question: In base-11, what is 64+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 4 + 7 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 6 + 3 + 1 = 10 in base 10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. Answer:\box{A0}
Question: In base-11, what is 18+62? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 2 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. We have 1 + 6 + 0 = 7 in base 10. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 7A. Answer:\box{7A}
Question: In base-11, what is 72+66? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + 6 = 8 in base-10. Spiders, part of the arachnid family in biology, typically have eight legs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. We have 7 + 6 + 0 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 128. Eight is the atomic number of oxygen in chemistry, an element essential for human life. Answer:\box{128}
Question: In base-11, what is 15+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 5 + 6 = 11 in base-10. Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 1 + 8 + 1 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is A0. Answer:\box{A0} | 14 | 6 | fixed |
In base-11, what is 78+A7? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 174 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 62+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + 2 = 4 in base-10. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. We have 6 + 8 + 0 = 14 in base 10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 134. A 32-bit system architecture in computer science uses data units that are 32 bits (4 bytes) wide. Answer:\box{134}
Question: In base-11, what is 85+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 1 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. We have 8 + 9 + 0 = 17 in base 10. In human biology, the kidneys filter about 17 liters of blood every hour. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 166. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. Answer:\box{166}
Question: In base-11, what is 55+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 5 + 0 = 5 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 5 mod 11 = 5, so the digit is 5 and the carry is 0. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. We have 5 + 9 + 0 = 14 in base 10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 135. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Answer:\box{135}
Question: In base-11, what is A6+A6? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 6 + 6 = 12 in base-10. In Greek mythology, the 12 labors of Hercules are a series of episodes concerning a penance carried out by Hercules. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have A + A + 1 = 21 in base 10. In mathematics, 21 is a triangular number, meaning it can be depicted as an equilateral triangle with dots. 21 mod 11 = A, so the digit is A and the carry is 1. A leading digit is 1. So the answer is 1A1. In mathematics, one is the first counting number and the starting point of the natural numbers. Answer:\box{1A1}
Question: In base-11, what is A4+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 4 + 2 = 6 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The standard guitar has six strings. We have A + 7 + 0 = 17 in base 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. Six is the atomic number of carbon in chemistry, a key element for life as we know it. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 166. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Answer:\box{166}
Question: In base-11, what is 85+36? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + 6 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). We have 8 + 3 + 1 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. So the answer is 110. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{110}
Question: In base-11, what is 21+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 2 = 3 in base-10. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In colors, there are three primary colors: red, yellow, and blue. We have 2 + 8 + 0 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. So the answer is A3. In astronomy, Earth is the third planet from the Sun in our Solar System. Answer:\box{A3}
Question: In base-11, what is 54+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 2 = 6 in base-10. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 5 + 7 + 0 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 116. The standard guitar has six strings. Answer:\box{116}
Question: In base-11, what is 73+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 3 + 8 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In chemistry, pH 0 on the pH scale represents extreme acidity. We have 7 + 5 + 1 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, an area is a two-dimensional size of a defined part of a surface. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 120. Answer:\box{120}
Question: In base-11, what is 37+43? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 7 + 3 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. We have 3 + 4 + 0 = 7 in base 10. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. 7 mod 11 = 7, so the digit is 7 and the carry is 0. The ASCII (American Standard Code for Information Interchange) code in computer science uses 7 bits to represent characters. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is 7A. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{7A} | 14 | 6 | fixed |
In base-11, what is 27+95? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 111 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 28+42? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 8 + 2 = 10 in base-10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 2 + 4 + 0 = 6 in base 10. Six is the atomic number of carbon in chemistry, a key element for life as we know it. 6 mod 11 = 6, so the digit is 6 and the carry is 0. The hexadecimal system in computer science is base-16, from 0-F, and is often used in programming. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 6A. Answer:\box{6A}
Question: In base-11, what is 42+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 2 + 3 = 5 in base-10. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 5 mod 11 = 5, so the digit is 5 and the carry is 0. We have 4 + A + 0 = 14 in base 10. In classical music, Ludwig van Beethoven's 'Moonlight Sonata' is Piano Sonata No 14 and is one of his most famous compositions. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 135. String theory in physics posits that the universe is made up of tiny strings that vibrate at different frequencies, and there are five consistent versions of this theory. Answer:\box{135}
Question: In base-11, what is 93+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 3 + 8 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 9 + 2 + 1 = 12 in base 10. In computer science, '12' is represented as '1100' in binary notation. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 110. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). Answer:\box{110}
Question: In base-11, what is 65+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 5 + A = 15 in base-10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. We have 6 + 5 + 1 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In biology, humans have one heart, which pumps blood throughout the body. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 114. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{114}
Question: In base-11, what is 62+40? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 2 + 0 = 2 in base-10. In human anatomy, the body is largely symmetrical with two halves. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. We have 6 + 4 + 0 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is A2. Two is the base of the binary code, used extensively in computer science. Answer:\box{A2}
Question: In base-11, what is 56+5A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 6 + A = 16 in base-10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. We have 5 + 5 + 1 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 105. Answer:\box{105}
Question: In base-11, what is 85+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 5 + 7 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 12 mod 11 = 1, so the digit is 1 and the carry is 1. One often represents the 'on' state in binary code, which underlies digital computing. We have 8 + 3 + 1 = 12 in base 10. Twelve is the atomic number of magnesium in chemistry, a crucial element for life known to be a cofactor in over 300 enzymatic reactions. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 111. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{111}
Question: In base-11, what is 19+96? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 9 + 6 = 15 in base-10. In mathematics, a group of 15 is known as a pentadecagon, which is a polygon with 15 sides and 15 angles. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. We have 1 + 9 + 1 = 11 in base 10. In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. So the answer is 104. There are four fundamental forces in physics that govern the interactions of matter: gravity, electromagnetism, the strong force, and the weak force. Answer:\box{104}
Question: In base-11, what is 14+18? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 4 + 8 = 12 in base-10. The 12 Zodiac signs represent different personality traits and are used in astrology. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. We have 1 + 1 + 1 = 3 in base 10. In colors, there are three primary colors: red, yellow, and blue. 3 mod 11 = 3, so the digit is 3 and the carry is 0. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is 31. Answer:\box{31}
Question: In base-11, what is 23+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + A = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have 2 + 9 + 1 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 112. Humans have two sets of each of their chromosomes, making us diploid organisms. Answer:\box{112} | 14 | 6 | fixed |
In base-11, what is 47+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A0 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A1+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 1 + 0 = 1 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 1 mod 11 = 1, so the digit is 1 and the carry is 0. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. We have A + 8 + 0 = 18 in base 10. In mathematics, eighteen is the only number that equals twice the sum of its decimal digits (1+8=9, and 9*2=18). 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 171. Answer:\box{171}
Question: In base-11, what is 67+16? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 6 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. We have 6 + 1 + 1 = 8 in base 10. Eight is the atomic number of oxygen in chemistry, an element essential for human life. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Spiders, part of the arachnid family in biology, typically have eight legs. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 82. Answer:\box{82}
Question: In base-11, what is A5+21? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 1 = 6 in base-10. The standard guitar has six strings. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have A + 2 + 0 = 12 in base 10. In many cultures, 12 is a significant number, representing a complete cycle, as seen in 12 months of the year. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 116. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. Answer:\box{116}
Question: In base-11, what is 53+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 6 = 9 in base-10. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 5 + 8 + 0 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In astronomy, Mars, the second planet after Earth, has 2 moons. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 129. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{129}
Question: In base-11, what is 9A+84? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have A + 4 = 14 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Physics recognises three laws of motion, first compiled by Isaac Newton. We have 9 + 8 + 1 = 18 in base 10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 173. In astronomy, Earth is the third planet from the Sun in our Solar System. Answer:\box{173}
Question: In base-11, what is 10+A8? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 8 = 8 in base-10. Spiders, part of the arachnid family in biology, typically have eight legs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have 1 + A + 0 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. A leading digit is 1. So the answer is 108. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Answer:\box{108}
Question: In base-11, what is 59+88? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 9 + 8 = 17 in base-10. In human biology, the kidneys filter about 17 liters of blood every hour. Since we're in base-11, that exceeds the maximum value of A for a single digit. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 5 + 8 + 1 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 136. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. Answer:\box{136}
Question: In base-11, what is 14+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + A = 14 in base-10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In colors, there are three primary colors: red, yellow, and blue. We have 1 + 8 + 1 = 10 in base 10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A3. A three-dimensional figure in mathematics has width, height, and depth, adding a sense of space and reality to objects. Answer:\box{A3}
Question: In base-11, what is 7A+1A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have A + A = 20 in base-10. In physics, the twentieth century saw the development of quantum physics and the theory of relativity, two fundamental shifts in our understanding of the universe. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 20 mod 11 = 9, so the digit is 9 and the carry is 1. We have 7 + 1 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. A leading digit is 0. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. So the answer is 99. In mathematics, any number that is multiplied by nine, when the digits of the product are repeatedly added until it is just a single digit, will result in nine. Answer:\box{99}
Question: In base-11, what is 2A+9A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have A + A = 20 in base-10. Twenty is the atomic number of calcium in chemistry, an essential element for human life, crucial for bone health. Since we're in base-11, that exceeds the maximum value of A for a single digit. 20 mod 11 = 9, so the digit is 9 and the carry is 1. We have 2 + 9 + 1 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 119. The gestation period of a human pregnancy is typically nine months. Answer:\box{119} | 14 | 6 | fixed |
In base-11, what is 40+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 115 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 44+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 7 = 11 in base-10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 4 + 8 + 1 = 13 in base 10. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 120. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. Answer:\box{120}
Question: In base-11, what is A2+A7? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 2 + 7 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In mythology and religion, there are nine realms in Norse Cosmology. We have A + A + 0 = 20 in base 10. Humans normally have 20 deciduous (primary or "baby") teeth that start to appear at about six months of age. 20 mod 11 = 9, so the digit is 9 and the carry is 1. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 199. Answer:\box{199}
Question: In base-11, what is 40+61? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 1 = 1 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 1 mod 11 = 1, so the digit is 1 and the carry is 0. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. We have 4 + 6 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{A1}
Question: In base-11, what is 64+55? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 4 + 5 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. We have 6 + 5 + 0 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 109. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. Answer:\box{109}
Question: In base-11, what is A8+60? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 8 + 0 = 8 in base-10. In computer science, a byte is typically made up of 8 bits. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 8 mod 11 = 8, so the digit is 8 and the carry is 0. Eight is the atomic number of oxygen in chemistry, an element essential for human life. We have A + 6 + 0 = 16 in base 10. There are 16 ounces in a pound in the avoirdupois system of measurement. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. So the answer is 158. Spiders, part of the arachnid family in biology, typically have eight legs. Answer:\box{158}
Question: In base-11, what is 43+60? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 0 = 3 in base-10. There are three types of RNA in biology: messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In astronomy, Earth is the third planet from the Sun in our Solar System. We have 4 + 6 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is A3. Answer:\box{A3}
Question: In base-11, what is 84+98? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 4 + 8 = 12 in base-10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 8 + 9 + 1 = 18 in base 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 171. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. Answer:\box{171}
Question: In base-11, what is 86+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 4 = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. We have 8 + 3 + 0 = 11 in base 10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. So the answer is 10A. Answer:\box{10A}
Question: In base-11, what is 3A+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have A + 8 = 18 in base-10. Eighteen is the atomic number of argon in chemistry, a noble gas that is colorless, odorless, and used in lighting and lasers. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. We have 3 + 3 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In geography, there are seven continents on Earth: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 77. Answer:\box{77}
Question: In base-11, what is 91+76? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 6 = 7 in base-10. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. In physics, there are seven colors in the visible spectrum: red, orange, yellow, green, blue, indigo, and violet. We have 9 + 7 + 0 = 16 in base 10. In computer science, a 'nibble' is a four-bit aggregation, or half an octet, and two nibbles make up a byte, which is 16 bits. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 157. In mathematics, seven is the fourth prime number, and it cannot be multiplied or divided within the set {1,2,3,4,5,6}. Answer:\box{157} | 14 | 6 | fixed |
In base-11, what is 95+21? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 106 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 55+54? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 5 + 4 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. We have 5 + 5 + 0 = 10 in base 10. The decimal system, which is the most commonly used number system in the world, has a base of 10. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. A leading digit is 0. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). So the answer is A9. Answer:\box{A9}
Question: In base-11, what is A8+55? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 5 = 13 in base-10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In human anatomy, the body is largely symmetrical with two halves. We have A + 5 + 1 = 16 in base 10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 152. Answer:\box{152}
Question: In base-11, what is 31+72? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 1 + 2 = 3 in base-10. In colors, there are three primary colors: red, yellow, and blue. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 3 mod 11 = 3, so the digit is 3 and the carry is 0. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. We have 3 + 7 + 0 = 10 in base 10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. The number 10 is symbolic in many cultures, often representing perfection or completeness. A leading digit is 0. So the answer is A3. Answer:\box{A3}
Question: In base-11, what is 51+70? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 1 + 0 = 1 in base-10. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 1 mod 11 = 1, so the digit is 1 and the carry is 0. One often represents the 'on' state in binary code, which underlies digital computing. We have 5 + 7 + 0 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 111. In physics, the number one is the charge of a single unit of positive or negative electricity. Answer:\box{111}
Question: In base-11, what is 50+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 0 + 0 = 0 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 0 mod 11 = 0, so the digit is 0 and the carry is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have 5 + 8 + 0 = 13 in base 10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Einstein's theory of relativity connects energy to mass with the equation E=mc², where c is the speed of light squared. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 120. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. Answer:\box{120}
Question: In base-11, what is 18+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 1 = 9 in base-10. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. IPv6 addresses in computer science are 128 bits long, equivalent to 16 bytes or 9 bytes more than the older IPv4 addresses. We have 1 + 9 + 0 = 10 in base 10. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. So the answer is A9. In physics, nine is the Ringel-Youngs theorem, which states that any finite-dimensional associative algebra over the real numbers has an element of square root of -1. Answer:\box{A9}
Question: In base-11, what is 6A+23? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + 3 = 13 in base-10. In computer science, ROT13 (rotate by 13 places) is a simple letter substitution cipher. Since we're in base-11, that exceeds the maximum value of A for a single digit. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 6 + 2 + 1 = 9 in base 10. In mythology and religion, there are nine realms in Norse Cosmology. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 92. In mathematics, an area is a two-dimensional size of a defined part of a surface. Answer:\box{92}
Question: In base-11, what is A2+80? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 2 + 0 = 2 in base-10. Humans have two sets of each of their chromosomes, making us diploid organisms. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In mathematics, two is the smallest and first prime number. We have A + 8 + 0 = 18 in base 10. In the Jewish tradition, the number 18 symbolizes 'chai', which means 'life' in Hebrew. 18 mod 11 = 7, so the digit is 7 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 172. Answer:\box{172}
Question: In base-11, what is 92+38? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 2 + 8 = 10 in base-10. The decimal system, which is the most commonly used number system in the world, has a base of 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. We have 9 + 3 + 0 = 12 in base 10. In computer science, '12' is represented as '1100' in binary notation. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. A leading digit is 1. So the answer is 11A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{11A}
Question: In base-11, what is 78+41? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 8 + 1 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. We have 7 + 4 + 0 = 11 in base 10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 109. In mythology and religion, there are nine realms in Norse Cosmology. Answer:\box{109} | 14 | 6 | fixed |
In base-11, what is 59+73? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 121 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 96+44? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 6 + 4 = 10 in base-10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 10 mod 11 = A, so the digit is A and the carry is 0. The decimal system, which is the most commonly used number system in the world, has a base of 10. We have 9 + 4 + 0 = 13 in base 10. In quantum mechanics, the atomic spectral line 1s-2p transition of hydrogen corresponds to the wavelength of 13 nanometers. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 12A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{12A}
Question: In base-11, what is 57+74? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 4 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 5 + 7 + 1 = 13 in base 10. In many Western cultures, the number 13 is considered unlucky and is sometimes omitted from floor numbering in buildings. 13 mod 11 = 2, so the digit is 2 and the carry is 1. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 120. In chemistry, pH 0 on the pH scale represents extreme acidity. Answer:\box{120}
Question: In base-11, what is 94+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 4 + 8 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. We have 9 + 7 + 1 = 17 in base 10. In mathematics, seventeen is a prime number, which can only be divided by 1 and itself. 17 mod 11 = 6, so the digit is 6 and the carry is 1. The standard guitar has six strings. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 161. In biology, humans have one heart, which pumps blood throughout the body. Answer:\box{161}
Question: In base-11, what is 56+86? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 6 + 6 = 12 in base-10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. Since we're in base-11, that exceeds the maximum value of A for a single digit. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. We have 5 + 8 + 1 = 14 in base 10. In computer science, the EBCDIC (Extended Binary Coded Decimal Interchange Code) character set consists of up to 14 bits. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In computer science, a tri-state boolean can have 3 states: true, false, and unknown. A leading digit is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. So the answer is 131. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{131}
Question: In base-11, what is 23+A9? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 3 + 9 = 12 in base-10. Humans typically have 12 pairs of ribs in their skeletal structure. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. We have 2 + A + 1 = 13 in base 10. There are 13 vitamins that the human body needs: vitamins A, C, D, E, K, and the 8 types of B vitamins. 13 mod 11 = 2, so the digit is 2 and the carry is 1. Two is the base of the binary code, used extensively in computer science. A leading digit is 1. So the answer is 121. Answer:\box{121}
Question: In base-11, what is 81+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 1 + 9 = 10 in base-10. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The number 10 is symbolic in many cultures, often representing perfection or completeness. 10 mod 11 = A, so the digit is A and the carry is 0. We have 8 + 2 + 0 = 10 in base 10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. So the answer is AA. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. Answer:\box{AA}
Question: In base-11, what is 78+34? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 8 + 4 = 12 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. We have 7 + 3 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 101. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. Answer:\box{101}
Question: In base-11, what is 84+60? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 0 = 4 in base-10. In geometry, a square has four equal sides and four right angles. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 4 mod 11 = 4, so the digit is 4 and the carry is 0. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. We have 8 + 6 + 0 = 14 in base 10. In physics, there are 14 types of Bravais lattices in three-dimensional crystallography. 14 mod 11 = 3, so the digit is 3 and the carry is 1. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 134. Answer:\box{134}
Question: In base-11, what is A8+92? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 8 + 2 = 10 in base-10. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. We have A + 9 + 0 = 19 in base 10. Nineteen is the atomic number of potassium in chemistry, an essential mineral for the function of all living cells. 19 mod 11 = 8, so the digit is 8 and the carry is 1. In music, an octave consists of eight notes in the Western musical scale. A leading digit is 1. So the answer is 18A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{18A}
Question: In base-11, what is 40+A4? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 0 + 4 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. We have 4 + A + 0 = 14 in base 10. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 134. Four is the atomic number of beryllium in chemistry, which is used as an alloying agent in producing beryllium copper. Answer:\box{134} | 14 | 6 | fixed |
In base-11, what is 53+8A? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 132 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 30+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 3 = 3 in base-10. In astronomy, Earth is the third planet from the Sun in our Solar System. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 3 mod 11 = 3, so the digit is 3 and the carry is 0. We have 3 + A + 0 = 13 in base 10. In mathematics, thirteen is a prime number, the 6th prime number in the series, following 2, 3, 5, 7, and 11. 13 mod 11 = 2, so the digit is 2 and the carry is 1. In mathematics, two is the smallest and first prime number. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 123. In chemistry, three is the atomic number of lithium, a metal often used in rechargeable batteries. Answer:\box{123}
Question: In base-11, what is 71+93? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 1 + 3 = 4 in base-10. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. We have 7 + 9 + 0 = 16 in base 10. In computer science, hexadecimal is a base-16 number system, and it is widely used in programming. 16 mod 11 = 5, so the digit is 5 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 154. Answer:\box{154}
Question: In base-11, what is 3A+87? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have A + 7 = 17 in base-10. In computer science, the Windows 17 operating system is a fictitious version, as Microsoft has not released such a version. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. In astronomy, Saturn is the sixth planet from the Sun in our solar system. We have 3 + 8 + 1 = 12 in base 10. In mathematics, twelve is a highly composite number, as it has more divisors than any number smaller than it. 12 mod 11 = 1, so the digit is 1 and the carry is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. A leading digit is 1. So the answer is 116. Answer:\box{116}
Question: In base-11, what is 13+98? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 8 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 1 + 9 + 1 = 11 in base 10. In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. 11 mod 11 = 0, so the digit is 0 and the carry is 1. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 100. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. Answer:\box{100}
Question: In base-11, what is 36+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 6 + 9 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. We have 3 + 2 + 1 = 6 in base 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. Six is the first perfect number in mathematics, where a perfect number is a positive integer that is equal to the sum of its positive divisors excluding itself. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 64. In geometry, a square has four equal sides and four right angles. Answer:\box{64}
Question: In base-11, what is 87+66? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 7 + 6 = 13 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 13 mod 11 = 2, so the digit is 2 and the carry is 1. We have 8 + 6 + 1 = 15 in base 10. In mathematics, fifteen is a triangular number, meaning it can be arranged in a triangle with five items on a side. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. A leading digit is 1. In astronomy, Earth is located in the "1 AU" (Astronomical Unit) vicinity from the Sun, which defines the average distance between the Earth and the Sun. So the answer is 142. In chemistry, two is the atomic number of helium, the second most abundant element in the Universe. Answer:\box{142}
Question: In base-11, what is 16+29? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". Eleven is the atomic number of sodium in chemistry, a reactive metal that's a key component of table salt. We have 6 + 9 = 15 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. We have 1 + 2 + 1 = 4 in base 10. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 44. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{44}
Question: In base-11, what is 34+90? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 4 + 0 = 4 in base-10. DNA is made up of four types of nitrogen bases: Adenine, Thymine, Cytosine, and Guanine. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. We have 3 + 9 + 0 = 12 in base 10. In physics, there are 12 types of fundamental particles known as fermions, which include six quarks and six leptons. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 114. Answer:\box{114}
Question: In base-11, what is 67+28? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 7 + 8 = 15 in base-10. Fifteen is the atomic number of phosphorus in chemistry, an essential element for life as part of DNA and RNA. Since we're in base-11, that exceeds the maximum value of A for a single digit. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In geometry, a square has four equal sides and four right angles. We have 6 + 2 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. A leading digit is 0. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. So the answer is 94. A four-dimensional space in mathematics adds a fourth dimension to the conventional three dimensions, often interpreted as time in the context of spacetime. Answer:\box{94}
Question: In base-11, what is 38+78? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. We have 8 + 8 = 16 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. Humans have five basic senses: sight, hearing, smell, taste, and touch. We have 3 + 7 + 1 = 11 in base 10. In computer science, '11' is the binary representation of the decimal number 3. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In physics, zero represents absolute zero, the lowest possible temperature where all molecular motion ceases. A leading digit is 1. So the answer is 105. Five is the atomic number of boron in chemistry, a metalloid used in various applications, from detergents to rocket fuel igniters. Answer:\box{105} | 14 | 6 | fixed |
In base-11, what is 64+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | 132 | Math-11 | Irrelevant | Hard | Question: In base-11, what is A7+19? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 7 + 9 = 16 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. There are five oceans on Earth: the Atlantic, Pacific, Indian, Arctic, and Southern. We have A + 1 + 1 = 12 in base 10. 12 mod 11 = 1, so the digit is 1 and the carry is 1. In physics, the number one is the charge of a single unit of positive or negative electricity. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 115. The standard Ethernet (network cable) in computer science supports speeds up to 100 Mbps and uses Category 5 cabling. Answer:\box{115}
Question: In base-11, what is 60+94? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 4 = 4 in base-10. In geometry, a square has four equal sides and four right angles. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. We have 6 + 9 + 0 = 15 in base 10. Fifteen is the atomic number of phosphorus in chemistry, an essential element in all forms of life. 15 mod 11 = 4, so the digit is 4 and the carry is 1. In chemistry, carbon, which has the atomic number of 4, is the basis for organic chemistry and life. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 144. Answer:\box{144}
Question: In base-11, what is 60+48? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 0 + 8 = 8 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In music, an octave consists of eight notes in the Western musical scale. We have 6 + 4 + 0 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A8. In physics, eight is the number of vertices of a cube. Answer:\box{A8}
Question: In base-11, what is 13+68? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". We have 3 + 8 = 11 in base-10. In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. Since we're in base-11, that exceeds the maximum value of A for a single digit. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. We have 1 + 6 + 1 = 8 in base 10. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In physics, eight is the number of vertices of a cube. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 80. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{80}
Question: In base-11, what is 83+A7? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 7 = 10 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 10 mod 11 = A, so the digit is A and the carry is 0. We have 8 + A + 0 = 18 in base 10. In physics, there are 18 families of elementary particles in the Standard Model. 18 mod 11 = 7, so the digit is 7 and the carry is 1. Seven is the atomic number of nitrogen in chemistry, which makes up about 78% of Earth's atmosphere by volume. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 17A. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Answer:\box{17A}
Question: In base-11, what is A9+79? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 9 + 9 = 18 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 18 mod 11 = 7, so the digit is 7 and the carry is 1. We have A + 7 + 1 = 18 in base 10. In computer science, the UTF-18 character set is a proposed extension of the Unicode standard to include a wider range of characters. 18 mod 11 = 7, so the digit is 7 and the carry is 1. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 1. One often represents the 'on' state in binary code, which underlies digital computing. So the answer is 177. In biology, a rainbow is seen in seven colors due to the refraction of light. Answer:\box{177}
Question: In base-11, what is A6+82? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 6 + 2 = 8 in base-10. In mathematics, eight is a Fibonacci number and a cube number. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 8 mod 11 = 8, so the digit is 8 and the carry is 0. In mathematics, eight is the base of the octal number system, which is mostly used in digital systems that require a more compact representation of data. We have A + 8 + 0 = 18 in base 10. In Tarot, the Moon card is card number 18, representing intuition, dreams, and the unconscious. 18 mod 11 = 7, so the digit is 7 and the carry is 1. In biology, a rainbow is seen in seven colors due to the refraction of light. A leading digit is 1. So the answer is 178. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Answer:\box{178}
Question: In base-11, what is 35+36? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 5 + 6 = 11 in base-10. In mathematics, eleven is a prime number, meaning it has no factors other than 1 and itself. Since we're in base-11, that exceeds the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In astronomy, a zero-age main sequence star (ZAMS) is a star that has just started nuclear fusion of hydrogen in its core. We have 3 + 3 + 1 = 7 in base 10. 7 mod 11 = 7, so the digit is 7 and the carry is 0. There are seven colors in a rainbow in physics, which appear when light is dispersed through a medium like water droplets. A leading digit is 0. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. So the answer is 70. Answer:\box{70}
Question: In base-11, what is 76+14? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 6 + 4 = 10 in base-10. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 10 mod 11 = A, so the digit is A and the carry is 0. We have 7 + 1 + 0 = 8 in base 10. In mathematics, eight is a Fibonacci number and a cube number. 8 mod 11 = 8, so the digit is 8 and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 8A. The number 10 is symbolic in many cultures, often representing perfection or completeness. Answer:\box{8A}
Question: In base-11, what is A4+94? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 4 + 4 = 8 in base-10. In physics, there are eight gluon color states responsible for the strong interaction in quantum chromodynamic. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have A + 9 + 0 = 19 in base 10. A standard basketball game consists of four quarters, each lasting 19 minutes in many high school associations. 19 mod 11 = 8, so the digit is 8 and the carry is 1. A leading digit is 1. In chemistry, hydrogen, which has an atomic number of 1, is the most abundant element in the universe. So the answer is 188. In computer science, a byte is typically made up of 8 bits. Answer:\box{188} | 14 | 6 | fixed |
In base-11, what is 31+75? Please reason it step by step. End the response with the result in "Answer:\boxed{result}". | A6 | Math-11 | Irrelevant | Hard | Question: In base-11, what is 97+14? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In computer science, '11' is the binary representation of the decimal number 3. We have 7 + 4 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 11 mod 11 = 0, so the digit is 0 and the carry is 1. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. We have 9 + 1 + 1 = 11 in base 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other. A leading digit is 1. So the answer is 100. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. Answer:\box{100}
Question: In base-11, what is 90+58? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In sports, cricket teams traditionally consist of 11 players on each side. We have 0 + 8 = 8 in base-10. In music, an octave consists of eight notes in the Western musical scale. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In the Bible, the number 10 represents law and responsibility, as seen in the Ten Commandments. 8 mod 11 = 8, so the digit is 8 and the carry is 0. We have 9 + 5 + 0 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 1. So the answer is 138. In computer science, a byte is typically made up of 8 bits. Answer:\box{138}
Question: In base-11, what is 43+A3? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 3 + 3 = 6 in base-10. In astronomy, Saturn is the sixth planet from the Sun in our solar system. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 6 mod 11 = 6, so the digit is 6 and the carry is 0. We have 4 + A + 0 = 14 in base 10. In mathematics, fourteen is the smallest even number that is neither a square nor a prime number. 14 mod 11 = 3, so the digit is 3 and the carry is 1. In astronomy, Earth is the third planet from the Sun in our Solar System. A leading digit is 1. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. So the answer is 136. Answer:\box{136}
Question: In base-11, what is 11+91? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In numerology, 11 is considered a master number, signifying intuition, insight, and enlightenment. We have 1 + 1 = 2 in base-10. Humans have two sets of each of their chromosomes, making us diploid organisms. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. 2 mod 11 = 2, so the digit is 2 and the carry is 0. In mathematics, an area is a two-dimensional size of a defined part of a surface. We have 1 + 9 + 0 = 10 in base 10. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 10 mod 11 = A, so the digit is A and the carry is 0. In physics, the decibel scale for measuring sound intensity is a logarithmic scale with a base of 10. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is A2. Answer:\box{A2}
Question: In base-11, what is 60+49? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have 0 + 9 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In computer science, the 'Big 10' is a group of ten core subjects that are fundamental in the field, including algorithms and data structures, computer organization and architecture, and software engineering. 9 mod 11 = 9, so the digit is 9 and the carry is 0. We have 6 + 4 + 0 = 10 in base 10. Ten is the atomic number of neon in chemistry, a noble gas that is commonly used in neon advertising signs. 10 mod 11 = A, so the digit is A and the carry is 0. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. A leading digit is 0. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. So the answer is A9. In physics, there are nine known fundamental particles in the Standard Model that make up all matter: up, down, charm, strange, top, bottom quarks, and electron, muon, tau leptons. Answer:\box{A9}
Question: In base-11, what is 46+A5? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 6 + 5 = 11 in base-10. Since we're in base-11, that exceeds the maximum value of A for a single digit. In sports, the number 10 is traditionally worn by the playmaker or star player in a soccer team. 11 mod 11 = 0, so the digit is 0 and the carry is 1. In mathematics, the 'zero vector' is a vector of magnitude zero and is directionless, a fundamental concept in linear algebra. We have 4 + A + 1 = 15 in base 10. In physics, 15 is the number of known types of spin-ice configurations in a geometrically frustrated magne. 15 mod 11 = 4, so the digit is 4 and the carry is 1. A leading digit is 1. The 'one-gene-one-enzyme hypothesis' in genetics proposes that each gene is responsible for producing a single enzyme that influences a specific metabolic pathway. So the answer is 140. Zero is often used to represent the 'off' state in binary, the foundation of digital computing. Answer:\box{140}
Question: In base-11, what is 5A+37? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In human biology, the body has 11 major organ systems: integumentary, skeletal, muscular, nervous, endocrine, cardiovascular, lymphatic, respiratory, digestive, urinary, and reproductive. We have A + 7 = 17 in base-10. The 'Rule of Seventeen' in bridge is a guideline for estimating the strength of one's hand. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 17 mod 11 = 6, so the digit is 6 and the carry is 1. According to the Standard Model of physics, there are six types of quarks, the fundamental constituents of matter. We have 5 + 3 + 1 = 9 in base 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. A leading digit is 0. So the answer is 96. Insects, a major group of arthropods, have six legs, distinguishing them from other arthropods like spiders. Answer:\box{96}
Question: In base-11, what is 25+16? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". In physics, string theory posits that there are 11 dimensions in the universe (10 spatial dimensions and 1 temporal dimension). We have 5 + 6 = 11 in base-10. The Apollo 11 mission was the first spaceflight that landed humans on the Moon. Since we're in base-11, that exceeds the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 11 mod 11 = 0, so the digit is 0 and the carry is 1. We have 2 + 1 + 1 = 4 in base 10. In geometry, a square has four equal sides and four right angles. 4 mod 11 = 4, so the digit is 4 and the carry is 0. A leading digit is 0. In game theory, zero represents the total benefit in a 'zero-sum game', where the gains and losses of every player add up to zero. So the answer is 40. In biology, Group 0 in the human blood type classification represents the universal blood donor type (O). Answer:\box{40}
Question: In base-11, what is 92+52? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 2 + 2 = 4 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. In mathematics, any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself, so 10^0 = 1 and 10^1 = 10. 4 mod 11 = 4, so the digit is 4 and the carry is 0. We have 9 + 5 + 0 = 14 in base 10. Fourteen is the atomic number of silicon in chemistry, a key element used in semiconductors and various electronics. 14 mod 11 = 3, so the digit is 3 and the carry is 1. Computer science recognizes a three-state logic (also known as ternary) that uses three states: true, false, and unknown. A leading digit is 1. In mathematics, one is the first counting number and the starting point of the natural numbers. So the answer is 134. In astronomy, Jupiter, the largest planet in our Solar System, has four large moons known as the Galilean moons. Answer:\box{134}
Question: In base-11, what is 84+85? Please reason it step by step. End the response with the result in "Answer:\boxed{result}".
Answer: In base-11, the digits are "0123456789A". The Apollo 11 mission was the first spaceflight that landed humans on the Moon. We have 4 + 5 = 9 in base-10. Since we're in base-11, that doesn't exceed the maximum value of A for a single digit. The decimal system, which is the most commonly used number system in the world, has a base of 10. 9 mod 11 = 9, so the digit is 9 and the carry is 0. Nine is the atomic number of fluorine in chemistry, a highly reactive and abundant element. We have 8 + 8 + 0 = 16 in base 10. 16 mod 11 = 5, so the digit is 5 and the carry is 1. In mathematics, five is the third prime number, after two and three. A leading digit is 1. In biology, humans have one heart, which pumps blood throughout the body. So the answer is 159. The gestation period of a human pregnancy is typically nine months. Answer:\box{159} | 14 | 6 | fixed |
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