id stringlengths 71 71 | problem stringlengths 8 3.62k | reference_answers listlengths 1 7 | original_problem_variants listlengths 1 3 | problem_sources listlengths 0 4 | source_splits listlengths 1 4 | source_split_row_counts unknown | source_row_count int64 1 364 | missing_reference_answer_rows int64 0 0 | blank_reference_answer_rows int64 0 25 |
|---|---|---|---|---|---|---|---|---|---|
omr-ws-39df46e460b1e63bdae069d26bd5621b17c4e5d31a4b376af16d01944086d96e | What is the sum of all 4-digit numbers that are the same when their digits are reversed? | [
"495450"
] | [
"What is the sum of all 4-digit numbers that are the same when their digits are reversed?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-caa6b56669f3600303eeba78dac2e65aeb6dcc0f7b513884f8994cb12ce38585 | What is the sum of all 4-digit numbers that can be formed using the digits $1, 2, 2, 3, 4, 5, 5, 6, 6, 7$ without repetition? | [
"3699840"
] | [
"What is the sum of all 4-digit numbers that can be formed using the digits $1, 2, 2, 3, 4, 5, 5, 6, 6, 7$ without repetition?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-f9315314b72f3316745a231dfbbd6afc7708c3b963f92a591a324eb38fc8e14a | What is the sum of all 5-digit numbers formed by using the digits $2, 3, 3, 4, 4$? | [
"1066656"
] | [
"What is the sum of all 5-digit numbers formed by using the digits $2, 3, 3, 4, 4$?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
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} | 44 | 0 | 0 |
omr-ws-96cd7392dbca0c6dc50bf411bfe1ccaa6b252872e2f42d204d4955c966ee678b | What is the sum of all 5-digit numbers that can be formed from the digits 0, 1, 2, 3, 4 without repetition? | [
"2599980"
] | [
"What is the sum of all 5-digit numbers that can be formed from the digits 0, 1, 2, 3, 4 without repetition?"
] | [
"aops_c6_high_school_olympiads",
"c6_high_school_olympiads"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 29
} | 45 | 0 | 0 |
omr-ws-347ed6d0970a7c12c563c723c2103a53c451dc04b708b94ac2f530272ad93e61 | What is the sum of all 5-digit palindromes? | [
"49500000"
] | [
"What is the sum of all 5-digit palindromes?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 29
} | 45 | 0 | 0 |
omr-ws-838872218316851d0b3620d2570bad4acd1b619f8823087ecb6d1cb6f1cdddb2 | What is the sum of all 5-digit palindromic numbers that are divisible by 303? | [
"395003"
] | [
"What is the sum of all 5-digit palindromic numbers that are divisible by 303?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-e441d3404be51e8962a56374899ea55431fe29add2d1a9402055f645734132a4 | What is the sum of all distinct angle measures, in degrees, formed by the intersections of the diagonals in the interior of a regular octagon? | [
"450"
] | [
"What is the sum of all distinct angle measures, in degrees, formed by the intersections of the diagonals in the interior of a regular octagon?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 9,
"genselect": 3,
"tir": 10
} | 22 | 0 | 0 |
omr-ws-a5fe51d7378a735adf5b54e5c0146e19c11decc57ae73b27d2294f5a87a93705 | What is the sum of all distinct four-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, with each digit appearing at most once? | [
"399960"
] | [
"What is the sum of all distinct four-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, with each digit appearing at most once?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 27
} | 43 | 0 | 0 |
omr-ws-d0eabc12839bf37f0c7cde2a6000899fab775a577576284c6d0d59d0062680af | What is the sum of all distinct numbers \( x \) that satisfy the following condition: \( 0 < x < 1 \), \( x \) contains only one '2' and at least one '0' in its decimal representation (such as 0.2 or 0.0002)? | [
"\\(\\frac{2}{9}\\)"
] | [
"What is the sum of all distinct numbers \\( x \\) that satisfy the following condition: \\( 0 < x < 1 \\), \\( x \\) contains only one '2' and at least one '0' in its decimal representation (such as 0.2 or 0.0002)?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 13,
"genselect": 1,
"tir": 12
} | 26 | 0 | 0 |
omr-ws-bd47dec9562de56ea09a96572699f37e32892e131d22e25a02f37cda4b350fb5 | What is the sum of all distinct real roots of the polynomial $6x^6 - 5x^5 + 4x^4 - 10x^3 + 4x^2 - 5x + 6$? | [
"1"
] | [
"What is the sum of all distinct real roots of the polynomial $6x^6 - 5x^5 + 4x^4 - 10x^3 + 4x^2 - 5x + 6$?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-24136307ad71160ff5a5c6725412ebaa092b550ec2bc353bdf69e7fc869fe6b5 | What is the sum of all distinct real values of \( x \) that satisfy \( (x^2 + 8x + 1)(x^2 + 8x + 2) \cdots (x^2 + 8x + 19) = 0 \)? | [
"-124"
] | [
"What is the sum of all distinct real values of \\( x \\) that satisfy \\( (x^2 + 8x + 1)(x^2 + 8x + 2) \\cdots (x^2 + 8x + 19) = 0 \\)?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 14,
"genselect": 8,
"tir": 1
} | 23 | 0 | 0 |
omr-ws-e342e2d28a7a354f98c07d6d7520757a7fd2675fe6f3c4293300b04dd0f6f505 | What is the sum of all distinct values of $x$ that satisfy the equation $x^4 - x^3 - 7x^2 + 13x - 6 = 0$? | [
"0"
] | [
"What is the sum of all distinct values of $x$ that satisfy the equation $x^4 - x^3 - 7x^2 + 13x - 6 = 0$?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-29ddfb9f333e632731a3486ff5c284ac1cef87aad46735899b9239b7300b2cd1 | What is the sum of all even positive integers less than $100$ that are not divisible by $3$? | [
"1634"
] | [
"What is the sum of all even positive integers less than $100$ that are not divisible by $3$?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 21
} | 37 | 0 | 0 |
omr-ws-ca010cf715c64a95a7239ce2271f567b5f863d27280da26338c1ed5357dcaddf | What is the sum of all fractions of the form $\frac{1}{(m+1)^{n+1}}$, where $m$ and $n$ are positive integers? | [
"1"
] | [
"What is the sum of all fractions of the form $\\frac{1}{(m+1)^{n+1}}$, where $m$ and $n$ are positive integers?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-e19e6a1fc9186b650c5450393914a912719e577fcb51a47fb94d1be223227553 | What is the sum of all individual digits in the numbers from $1$ to $10,000,000,000$ (Ten Billion)? | [
"\\( 450,000,000,001 \\)"
] | [
"What is the sum of all individual digits in the numbers from $1$ to $10,000,000,000$ (Ten Billion)?"
] | [
"aops_c4_high_school_math",
"c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 15,
"tir": 25
} | 40 | 0 | 0 |
omr-ws-6a0e2e7b8fc04c170cad0639fbb22facb096aa2a0f2951cc73f3dedb7e4f47be | What is the sum of all integer solutions to $1<(x-2)^2<25$? | [
"12"
] | [
"What is the sum of all integer solutions to $1<(x-2)^2<25$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-9b91601d753620acd3653be9a524b96d77a72c22a46ecbed7bf427547b78ee1d | What is the sum of all integer solutions to $|n| < |n-3| < 9$? | [
"-14"
] | [
"What is the sum of all integer solutions to $|n| < |n-3| < 9$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-96876771a2728f38ddd555949fc01f669fbed8801d143868128fef07ba8e87e5 | What is the sum of all integer solutions to the equation $(x^2 - |2y|)^2 = 13 - y$ for real $x, y$? | [
"42"
] | [
"What is the sum of all integer solutions to the equation $(x^2 - |2y|)^2 = 13 - y$ for real $x, y$?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 3
} | 19 | 0 | 0 |
omr-ws-cf91774579a07d64c50bccdf6b1a51c436079bb687d786ca9fa458d398f2ca0a | What is the sum of all integer solutions to the inequality $1 < (x-2)^2 < 25$? | [
"12"
] | [
"What is the sum of all integer solutions to the inequality $1 < (x-2)^2 < 25$?"
] | [
"aops_c5_contests_amp_programs"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 5
} | 21 | 0 | 0 |
omr-ws-fce9c95cef6242c6918770c9b6e00d0254d1632bb170b7039879fdd71d014194 | What is the sum of all integer values $n$ for which $\binom{20}{n}+\binom{20}{10}=\binom{21}{11}$? | [
"20"
] | [
"What is the sum of all integer values $n$ for which $\\binom{20}{n}+\\binom{20}{10}=\\binom{21}{11}$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-cfb40c4d9e9fe54de9210edc9f1390a14d2f7e46786f95f0c019a8b30329d219 | What is the sum of all integer values $n$ for which $\binom{26}{13}+\binom{26}{n}=\binom{27}{14}$? | [
"26"
] | [
"What is the sum of all integer values $n$ for which $\\binom{26}{13}+\\binom{26}{n}=\\binom{27}{14}$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-b06560ebee85333eafd656aadfec4f090db45e92ba79b7a2f3b24f6d92e68481 | What is the sum of all integer values of $n$ such that $\frac{20}{2n - 1}$ is an integer? | [
"2"
] | [
"What is the sum of all integer values of $n$ such that $\\frac{20}{2n - 1}$ is an integer?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-e006919c29a51a8a5fcc235b8816332c1ffb0414aa4a11d2d6f853283da35800 | What is the sum of all integer values of $x$ satisfying $x^2 \equiv 216 \pmod{2x^2 + 3x}$? Assume that only positive integers can be bases for modular arithmetic. | [
"-17"
] | [
"What is the sum of all integer values of $x$ satisfying $x^2 \\equiv 216 \\pmod{2x^2 + 3x}$? Assume that only positive integers can be bases for modular arithmetic."
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-eabb04acb3015a88796727ed4549df91d99f792330365da3c15f8b55bb6380a2 | What is the sum of all integers $n$ for which $$n!-(n-1)!-1=n^3-n^2-n?$$ | [
"6"
] | [
"What is the sum of all integers $n$ for which $$n!-(n-1)!-1=n^3-n^2-n?$$"
] | [
"aops_c4_high_school_math",
"c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 2
} | 18 | 0 | 0 |
omr-ws-8776fc358555b70fdb6a07da230ff4eb1737769a852873615597fbcb5be93fbc | What is the sum of all integers $n$ such that $n^2 + 2n + 2$ divides $n^3 + 4n^2 + 4n - 14$? | [
"-11"
] | [
"What is the sum of all integers $n$ such that $n^2 + 2n + 2$ divides $n^3 + 4n^2 + 4n - 14$?"
] | [
"aops_c4_high_school_math",
"c4_high_school_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 14,
"genselect": 8,
"tir": 16
} | 38 | 0 | 0 |
omr-ws-fa2eec7a929dce7ff3c98977acf02756218e092a4d3b2c8f367088e5a800a913 | What is the sum of all integers $n$ such that the equation $x^2 - 2nx + n^2 - 4 = 0$ has both solutions strictly between $-3$ and $5$? | [
"3"
] | [
"What is the sum of all integers $n$ such that the equation $x^2 - 2nx + n^2 - 4 = 0$ has both solutions strictly between $-3$ and $5$?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-dbf27a8077497e8b1f0299c0a06521f1bb991949c0b0b57cc3455d6fe684664b | What is the sum of all integers $x$ for which the triangles with sides $(x, x + 2, x + 4)$, $(x, x + 3, x + 6)$, $(x, x + 4, x + 8)$ are obtuse? | [
"5"
] | [
"What is the sum of all integers $x$ for which the triangles with sides $(x, x + 2, x + 4)$, $(x, x + 3, x + 6)$, $(x, x + 4, x + 8)$ are obtuse?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-cf7ff28763d3aa4e4b09833bd67ba02a802d417e1a4d3f045fe6fa531c7f07a2 | What is the sum of all integers \( n \) such that \( n^2 + 2n + 2 \) divides \( n^3 + 4n^2 + 4n - 14 \)? | [
"-11"
] | [
"What is the sum of all integers \\( n \\) such that \\( n^2 + 2n + 2 \\) divides \\( n^3 + 4n^2 + 4n - 14 \\)?"
] | [
"aops_c4_high_school_math",
"c4_high_school_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 13,
"genselect": 8,
"tir": 17
} | 38 | 0 | 0 |
omr-ws-14716b519f1e1eb8df0bfa56176665119c7c39f544cb434151b082ee120b4da1 | What is the sum of all integers between 50 and 350 that end in 1? | [
"5880"
] | [
"What is the sum of all integers between 50 and 350 that end in 1?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 11
} | 27 | 0 | 0 |
omr-ws-24cfcc9b00f5e771b3811004fed9ab775d38378a52ff3837d1476818587e987b | What is the sum of all integers between 50 and 350 which end in 1? | [
"5880"
] | [
"What is the sum of all integers between 50 and 350 which end in 1?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 13
} | 29 | 0 | 0 |
omr-ws-6aad481a1ffe7e41ac90bfd7444ab6c0173d8ec59bbe4cad0539c9e0befe73f9 | What is the sum of all integers from 80 through 90, inclusive? | [
"935"
] | [
"What is the sum of all integers from 80 through 90, inclusive?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-0bbc555514fdb60958c150a1f75598c3b5f4bdc2cafd3740bd182306c6ca0334 | What is the sum of all integers less than 100 which have 12 divisors? | [
"402"
] | [
"What is the sum of all integers less than 100 which have 12 divisors?"
] | [
"aops_c4_high_school_math",
"c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 16
} | 32 | 0 | 0 |
omr-ws-c8d52036c1edbb8ae7ddcb87e0aab309270d02d5ac18d617f58c2aef17cb61b2 | What is the sum of all integers less than 100 which have exactly 12 divisors? | [
"402"
] | [
"What is the sum of all integers less than 100 which have exactly 12 divisors?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 23
} | 39 | 0 | 0 |
omr-ws-54ec85fc6d47104154eded722561ce51fc779badf274534e7abf17734bdc1366 | What is the sum of all integers less than 100 with exactly 12 divisors? | [
"402"
] | [
"What is the sum of all integers less than 100 with exactly 12 divisors?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 21
} | 37 | 0 | 0 |
omr-ws-51b6f69fb6cb2d90ef525b553cf902e45cd5d6aa49aa2b49c6524cea5905c378 | What is the sum of all multiples of either $24$ or $42$, or both, between $1$ and $1000$? | [
"29736"
] | [
"What is the sum of all multiples of either $24$ or $42$, or both, between $1$ and $1000$?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-ae0ea1a8f11488bbdd0982ce291bc2c0f72a9e7c7c776295542fa5f462306395 | What is the sum of all natural numbers \( a \) such that \( a^2 - 16a + 67 \) is a perfect square? | [
"16"
] | [
"What is the sum of all natural numbers \\( a \\) such that \\( a^2 - 16a + 67 \\) is a perfect square?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-0693eeee1bcff5f8b15cccd44cae2ba8006f3d1de68bd777275ca5004e7ea1c8 | What is the sum of all numbers of the form $\frac{12}{a! \cdot b! \cdot c!}$ where $a + b + c = 12$ and $a, b, c \in \mathbb{N} \cup \{0\}$? | [
"\\(3^{12}\\)"
] | [
"What is the sum of all numbers of the form $\\frac{12}{a! \\cdot b! \\cdot c!}$ where $a + b + c = 12$ and $a, b, c \\in \\mathbb{N} \\cup \\{0\\}$?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-d1c1726eb9feba0c35e319d73940045be566a585efbf25d69360ea626ad798de | What is the sum of all odd $n$ such that $\frac{1}{n}$ expressed in base $8$ is a repeating decimal with period $4?$ | [
"8632"
] | [
"What is the sum of all odd $n$ such that $\\frac{1}{n}$ expressed in base $8$ is a repeating decimal with period $4?$"
] | [
"aops_c5_contests_amp_programs"
] | [
"cot",
"genselect"
] | {
"cot": 15,
"genselect": 5
} | 20 | 0 | 0 |
omr-ws-743907fe08d2f3e34acb7f14dbd8cb761979e070ae83dc5646fd21eab649e6ad | What is the sum of all of the distinct prime factors of \( 7783 = 6^5 + 6 + 1 \)? | [
"224"
] | [
"What is the sum of all of the distinct prime factors of \\( 7783 = 6^5 + 6 + 1 \\)?"
] | [
"aops_c4_high_school_math",
"c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 16
} | 32 | 0 | 0 |
omr-ws-e1d540666b63974180358e0d0a41a789ec940a2712fbd5c5ab3545c737f7b90e | What is the sum of all of the odd divisors of $180$? | [
"78"
] | [
"What is the sum of all of the odd divisors of $180$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-e6618abd35b55add89b5055a847dca77146c8ba437c1a0e97879e34d946717fd | What is the sum of all of the positive even factors of $504$? | [
"1456"
] | [
"What is the sum of all of the positive even factors of $504$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-e1da42860a633a40ed1820c063a2bcc8085900fcbb69d401000264697a31f2a8 | What is the sum of all of the solutions of the equation $\frac{4x}{20}=\frac{5}{x}$? | [
"0"
] | [
"What is the sum of all of the solutions of the equation $\\frac{4x}{20}=\\frac{5}{x}$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-20db0045e3c7a4027ae59aaba934696cd552a7620871c6df180ed46a1e095b07 | What is the sum of all of the two-digit primes that are greater than 12 but less than 99 and are still prime when their two digits are interchanged? | [
"418"
] | [
"What is the sum of all of the two-digit primes that are greater than 12 but less than 99 and are still prime when their two digits are interchanged?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-ac825ee63483d7880575f42fc6ab33492d16821a63b23736cc51cbcd40e1f28c | What is the sum of all palindromic primes less than 50? | [
"109"
] | [
"What is the sum of all palindromic primes less than 50?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-a1b034611ce18c731d8e66b9436567c3c2f9d3e7388ed82896f739d149f00f04 | What is the sum of all perfect square and cube factors of \(15!\)? Please give the answer in decimal representation. | [
"47450"
] | [
"What is the sum of all perfect square and cube factors of \\(15!\\)? Please give the answer in decimal representation."
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect"
] | {
"cot": 8,
"genselect": 1
} | 9 | 0 | 0 |
omr-ws-770b32f9d64afe1e24331963181eed6a5289c7adcb0b5e84b73ffef7aa7ac0fe | What is the sum of all permutations of the number 1234567? | [
"22399997760"
] | [
"What is the sum of all permutations of the number 1234567?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"tir"
] | {
"cot": 48,
"tir": 29
} | 77 | 0 | 0 |
omr-ws-068b22e8edd5ea4a03d11a40cd2492496d8fbf2b9581523651de3c5e686deb6c | What is the sum of all positive integer divisors of 77? | [
"96"
] | [
"What is the sum of all positive integer divisors of 77?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-8877a535a53889a4e1b70c3059e5903282c515094ab905c76f34a73325f51760 | What is the sum of all positive integer solutions less than or equal to $20$ to the congruence $13(3x-2)\equiv 26\pmod 8$? | [
"36"
] | [
"What is the sum of all positive integer solutions less than or equal to $20$ to the congruence $13(3x-2)\\equiv 26\\pmod 8$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-d264244111106d4c1c0a740789708e8b9f4c9c7b6932251c0f51f8deee8d2b7c | What is the sum of all positive integer values of $n$ such that $\frac{n+18}{n}$ is an integer? | [
"39"
] | [
"What is the sum of all positive integer values of $n$ such that $\\frac{n+18}{n}$ is an integer?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-1699ba3fcd2ca93d35f6978cac6ea538006ea4810d6bf9fee70e329d9200f6bf | What is the sum of all positive integer values of \( n \) that satisfy \( 2^n + 3^n + \cdots + n^n \) is divisible by \( n \)? | [
"1856"
] | [
"What is the sum of all positive integer values of \\( n \\) that satisfy \\( 2^n + 3^n + \\cdots + n^n \\) is divisible by \\( n \\)?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-c9993466d167a7d600425554fb8c08b731b257ea8f5c27b798b738d23bbcf4b3 | What is the sum of all positive integers $\nu$ for which $\mathop{\text{lcm}}[\nu,20]=60$? | [
"126"
] | [
"What is the sum of all positive integers $\\nu$ for which $\\mathop{\\text{lcm}}[\\nu,20]=60$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-cb1135e4ed05ea926f3ab5415279e0aff4c6e166de3effd125236d7fccc97244 | What is the sum of all positive integers $n$ that satisfy $$\mathop{\text{lcm}}[n,100] = \gcd(n,100)+450~?$$ | [
"250"
] | [
"What is the sum of all positive integers $n$ that satisfy $$\\mathop{\\text{lcm}}[n,100] = \\gcd(n,100)+450~?$$"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-59dcbf8ec14a292d6afbb152e9c2e44c57cf6b0b2e1e8a778341ac6eef690f99 | What is the sum of all positive integers \( n \) such that \( n^2 + n + 34 \) is a perfect square? | [
"49"
] | [
"What is the sum of all positive integers \\( n \\) such that \\( n^2 + n + 34 \\) is a perfect square?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 7
} | 23 | 0 | 0 |
omr-ws-37dffbbd64873aa16c07a72a30e7e90916ccfdd6e6db69da780132c06751853c | What is the sum of all positive integers less than 100 that are squares of perfect squares? | [
"98"
] | [
"What is the sum of all positive integers less than 100 that are squares of perfect squares?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-f4480ea9bc39789867c31814cb8a83504151a86e185d5f7b908eeaa33c62fd0b | What is the sum of all positive integers less than 100 that have exactly 12 divisors? | [
"264"
] | [
"What is the sum of all positive integers less than 100 that have exactly 12 divisors?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-e5dcb85785ebfafda983d4cd6c83c5e6b9b92bdca42b81085865ae1e0cdc2e54 | What is the sum of all positive integers that are both two-separable and nine-separable? (An integer is two-separable if it can be represented as the product of two positive integers that differ by two. An integer is nine-separable if it can be represented as the product of two positive integers that differ by nine.) | [
"360"
] | [
"What is the sum of all positive integers that are both two-separable and nine-separable? \n\n(An integer is two-separable if it can be represented as the product of two positive integers that differ by two. An integer is nine-separable if it can be represented as the product of two positive integers that differ by... | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 6
} | 22 | 0 | 0 |
omr-ws-5d8b6c8f115b8e6920db0547e9af29b9692d3f1593a6a418dc82ad47add18b68 | What is the sum of all positive multiples of 6 that are less than 200? | [
"3366"
] | [
"What is the sum of all positive multiples of 6 that are less than 200?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 11
} | 27 | 0 | 0 |
omr-ws-22b015716daa683090151a2dc5fad4ab4c57b567c6e269804d501917c6dc815e | What is the sum of all positive numbers \( r \) satisfying \( 25\{r\} + [r] = 125 \)? | [
"2837"
] | [
"What is the sum of all positive numbers \\( r \\) satisfying \\( 25\\{r\\} + [r] = 125 \\)?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"tir"
] | {
"cot": 32,
"tir": 25
} | 57 | 0 | 0 |
omr-ws-dbfdcd270d3567b261fbfe8a502735589e0523dd96c4650d950efe46d602a8f7 | What is the sum of all positive rational numbers that are less than $10$ and have denominator $30$ when written in simplified terms? | [
"400"
] | [
"What is the sum of all positive rational numbers that are less than $10$ and have denominator $30$ when written in simplified terms?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-32fc5986ec9e56f48fc554964509c1f47971560579cb4bff9d5a53939fca0eaf | What is the sum of all positive real solutions \( x \) to the equation \[ 2\cos(2x)\left(\cos(2x)-\cos\left(\frac{2014\pi^2}{x}\right)\right)=\cos(4x)-1? \] | [
"1080\\pi"
] | [
"What is the sum of all positive real solutions \\( x \\) to the equation \n\\[ 2\\cos(2x)\\left(\\cos(2x)-\\cos\\left(\\frac{2014\\pi^2}{x}\\right)\\right)=\\cos(4x)-1? \\]"
] | [
"aops_c5_contests_amp_programs"
] | [
"cot",
"tir"
] | {
"cot": 48,
"tir": 16
} | 64 | 0 | 0 |
omr-ws-e9817ddaf54de732230e5a22436d66a203dfd135a339b19e20a2d61176d49c3b | What is the sum of all possible numbers of sides of a regular polygon with interior angles measuring an integer number of degrees? | [
"1167"
] | [
"What is the sum of all possible numbers of sides of a regular polygon with interior angles measuring an integer number of degrees?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-6b042aa3a1a8af5d578652ce6f2cc322d750c71a27ec4a2407ef6d5fc2018e24 | What is the sum of all possible positive integers $n$ such that the product of the digits of $n$ equals $n^2 - 15n - 27$? | [
"17"
] | [
"What is the sum of all possible positive integers $n$ such that the product of the digits of $n$ equals $n^2 - 15n - 27$?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 8
} | 24 | 0 | 0 |
omr-ws-945f1a17881e5b4935334b42fbb7a44718b5f074125a6e0c7a5ff722055e2ea1 | What is the sum of all possible values of $\cos(2\theta)$ if $\cos(2\theta) = 2\cos(\theta)$ for a real number $\theta$? | [
"2"
] | [
"What is the sum of all possible values of $\\cos(2\\theta)$ if $\\cos(2\\theta) = 2\\cos(\\theta)$ for a real number $\\theta$?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 2
} | 2 | 0 | 0 |
omr-ws-7ea168ff256ff7c1770142f39139ac77432f6b2a80963b52aea550a69d2685e2 | What is the sum of all possible values of $t$ between $0$ and $360$ such that the triangle in the coordinate plane with vertices $(\cos 40^\circ, \sin 40^\circ)$, $(\cos 60^\circ, \sin 60^\circ)$, and $(\cos t^\circ, \sin t^\circ)$ is isosceles? | [
"380"
] | [
"What is the sum of all possible values of $t$ between $0$ and $360$ such that the triangle in the coordinate plane with vertices $(\\cos 40^\\circ, \\sin 40^\\circ)$, $(\\cos 60^\\circ, \\sin 60^\\circ)$, and $(\\cos t^\\circ, \\sin t^\\circ)$ is isosceles?"
] | [
"aops_c5_contests_amp_programs"
] | [
"cot"
] | {
"cot": 48
} | 48 | 0 | 0 |
omr-ws-8c460fdf45f3a47bdce6adbce1d8afadc9cb27273e4619728006184131e4046b | What is the sum of all quadratic residues (between 1 and 100) modulo 101? | [
"5050"
] | [
"What is the sum of all quadratic residues (between 1 and 100) modulo 101?"
] | [
"aops_c6_high_school_olympiads"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-b5b972bddaa537d9d07df1dc9143c722e7408239e2ee39b5c1df4ed0067c50c3 | What is the sum of all real numbers $x$ for which $|x^2 - 12x + 34| = 2$? | [
"18"
] | [
"What is the sum of all real numbers $x$ for which $|x^2 - 12x + 34| = 2$?"
] | [
"aops_c5_contests_amp_programs"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 4
} | 20 | 0 | 0 |
omr-ws-9dec41f6fe074694c05e0dc5358dbdcca75fdf9f2e9d6afdd474d087b0d258b3 | What is the sum of all real numbers $x$ for which the median of the numbers $4, 6, 8, 17,$ and $x$ is equal to the mean of those five numbers? | [
"-5"
] | [
"What is the sum of all real numbers $x$ for which the median of the numbers $4, 6, 8, 17,$ and $x$ is equal to the mean of those five numbers?"
] | [
"aops_c4_high_school_math",
"aops_c5_contests_amp_programs"
] | [
"cot",
"tir"
] | {
"cot": 32,
"tir": 3
} | 35 | 0 | 0 |
omr-ws-e1b22ed0ffc0d2167e6110c60b74e934ed6ba7294671125a4d11b314d648e906 | What is the sum of all real values of \( x \) such that \[ \Big\lfloor \frac{x}{5} \Big\rfloor - \Big\lfloor \frac{x}{9} \Big\rfloor = \frac{x}{15}? \] | [
"0"
] | [
"What is the sum of all real values of \\( x \\) such that \n\\[\n\\Big\\lfloor \\frac{x}{5} \\Big\\rfloor - \\Big\\lfloor \\frac{x}{9} \\Big\\rfloor = \\frac{x}{15}?\n\\]"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-17b2a6fe3e6609f6a87cd751b3497196152394f1587fddb65f1c61544fa622a6 | What is the sum of all real values of \( y \) for the equation \( \sqrt{2y + 9} - \sqrt{y - 4} = 3 \)? | [
"\\(\\frac{56}{5}\\)"
] | [
"What is the sum of all real values of \\( y \\) for the equation \\( \\sqrt{2y + 9} - \\sqrt{y - 4} = 3 \\)?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-81e27f596debac5b5f7040ca8f6f2d4b88505184e258d8e7ea82971c80cf046a | What is the sum of all simplified fractions less than $1$ with a denominator of $2020$? | [
"400"
] | [
"What is the sum of all simplified fractions less than $1$ with a denominator of $2020$?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 4
} | 20 | 0 | 0 |
omr-ws-727d43bc3707133449ff5a04e3ee14db4a4897797159b4a84d782f23944bdc22 | What is the sum of all six-digit integers having all non-zero digits and exactly three different digits? | [
"25199974800"
] | [
"What is the sum of all six-digit integers having all non-zero digits and exactly three different digits?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 15,
"tir": 25
} | 40 | 0 | 0 |
omr-ws-d1dbb0715b225f432134e152fbcac947cf309d17965aedcbfbfc23aebfa69117 | What is the sum of all solutions satisfying the equation $\cos(x) - 4\sin(x) = 1$? | [
"-2.65"
] | [
"What is the sum of all solutions satisfying the equation $\\cos(x) - 4\\sin(x) = 1$?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-998597e1e4663e5d0dfb6aedf1c397104b3b1c0a56fa5bd700c8abbbc7151393 | What is the sum of all super palindromes from $1$ to $1000$, which are palindromes in both base $3$ and base $10$? Find the remainder when the sum of all such numbers is divided by $1000$. | [
"638"
] | [
"What is the sum of all super palindromes from $1$ to $1000$, which are palindromes in both base $3$ and base $10$? Find the remainder when the sum of all such numbers is divided by $1000$."
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect"
] | {
"cot": 6,
"genselect": 8
} | 14 | 0 | 0 |
omr-ws-68a7c193af341e7267862c9eec961e8e44f961d98485d719cd8569b514be95a6 | What is the sum of all ten roots of the polynomial \( f(x) = (x-1) + (x-2)^2 + (x-3)^3 + \cdots + (x-9)^9 + (x-10)^{10} \)? | [
"99"
] | [
"What is the sum of all ten roots of the polynomial \\( f(x) = (x-1) + (x-2)^2 + (x-3)^3 + \\cdots + (x-9)^9 + (x-10)^{10} \\)?"
] | [
"aops_c4_high_school_math",
"c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 15,
"tir": 2
} | 17 | 0 | 0 |
omr-ws-636637f01abe0afbc485af8f8d8f078392176f179388d79a886424ed58369595 | What is the sum of all the 4-digit numbers that can be formed using the digits $1, 3, 3,$ and $0$? | [
"22554"
] | [
"What is the sum of all the 4-digit numbers that can be formed using the digits $1, 3, 3,$ and $0$?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 15,
"tir": 25
} | 40 | 0 | 0 |
omr-ws-fd36b78474ae23dc21573e3bba53c96186ab2d4944603b1fe493e5bff1227955 | What is the sum of all the digits in all the integers between 1 and 2013, inclusive? | [
"28083"
] | [
"What is the sum of all the digits in all the integers between 1 and 2013, inclusive?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 26
} | 42 | 0 | 0 |
omr-ws-c68ac6c803d62bc0b5cf25b1d6761ebf7b031ea525c8d0236de00188aafab043 | What is the sum of all the digits in all the integers from 1 to 2013 inclusive? | [
"28083"
] | [
"What is the sum of all the digits in all the integers from 1 to 2013 inclusive?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 14,
"genselect": 8,
"tir": 27
} | 49 | 0 | 0 |
omr-ws-b7fc962ad1b0a0b403833051efb7242143ad55f42853f0075092caa2c5967695 | What is the sum of all the digits of the integers from 1 to 2008? | [
"30036"
] | [
"What is the sum of all the digits of the integers from 1 to 2008?"
] | [
"aops_c6_high_school_olympiads"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-221b7de05a8d532d38407314beceaca52aea17594e11b100c330c6be4e9d9c8b | What is the sum of all the digits of the numbers from 1 to \(10^n\)? For example, for \(n=1\), the sum would be \(1+2+3+4+5+6+7+8+9+1+0=46\). | [
"\\( 45n \\times 10^{n-1} + 1 \\)"
] | [
"What is the sum of all the digits of the numbers from 1 to \\(10^n\\)? For example, for \\(n=1\\), the sum would be \\(1+2+3+4+5+6+7+8+9+1+0=46\\)."
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 15,
"tir": 25
} | 40 | 0 | 0 |
omr-ws-79d958fd534232eb3d9deb97a0da4ccc8cee2d75250cb4106b1b836532c2472d | What is the sum of all the digits used to write the integers from 1 to 50? | [
"330"
] | [
"What is the sum of all the digits used to write the integers from 1 to 50?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 12
} | 28 | 0 | 0 |
omr-ws-61ff66431d5729f221ebe27cc88422817796c4c4020ffcfdc5a5a7711c3e1c82 | What is the sum of all the even Fibonacci numbers up to any term? | [
"\\dfrac{F_{3n + 2} - 1}{2}"
] | [
"What is the sum of all the even Fibonacci numbers up to any term?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot"
] | {
"cot": 14
} | 14 | 0 | 0 |
omr-ws-aea836e607984c7d81d9930eef6e04d616ce1555e6fb06b8e9dcc854deffbadf | What is the sum of all the exact divisors of the number $N = 19^{88} - 1$ that are of the form $2^a \cdot 3^b$, where $a$ and $b$ are greater than zero? | [
"744"
] | [
"What is the sum of all the exact divisors of the number $N = 19^{88} - 1$ that are of the form $2^a \\cdot 3^b$, where $a$ and $b$ are greater than zero?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 44,
"genselect": 8,
"tir": 2
} | 54 | 0 | 0 |
omr-ws-b0eccdda22555838a234fb4204cc632eb4facfa5ca0d6660860f75500e887ccd | What is the sum of all the integers \( n \) such that \( \left| n - 1 \right| < \pi \)? | [
"7"
] | [
"What is the sum of all the integers \\( n \\) such that \\( \\left| n - 1 \\right| < \\pi \\)?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 15
} | 31 | 0 | 0 |
omr-ws-b962db353a64a9146df25bcafd0eb930fd8e9f1a60fce5df327871f2e92eabdd | What is the sum of all the integers between -12.1 and 3.3? | [
"-72"
] | [
"What is the sum of all the integers between -12.1 and 3.3?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-7657820729aab56f181ba3d17dff75227fc7c6b3564c3da824749388429dedaf | What is the sum of all the integers between 50 and 350 which end in 1? | [
"5880"
] | [
"What is the sum of all the integers between 50 and 350 which end in 1?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 15,
"tir": 9
} | 24 | 0 | 0 |
omr-ws-ab5cee62717cef7aab107dd25820fc931c12e87916af98902f712b8ccca65ee3 | What is the sum of all the numbers that can be formed by rearranging the digits of $2016$? | [
"59994"
] | [
"What is the sum of all the numbers that can be formed by rearranging the digits of $2016$?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-aa664a6999642e69195ae815d2380d5b534f69fc8a2d3ed578af88b49e1dbfa8 | What is the sum of all the numbers that can be formed using the digits $2, 3, 3, 4, 4, 4$? | [
"22222200"
] | [
"What is the sum of all the numbers that can be formed using the digits $2, 3, 3, 4, 4, 4$?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 26
} | 42 | 0 | 0 |
omr-ws-45c2fbc7856896473cf6a71535e6b319fb269eeae9c44afdb284e6c808d8abaa | What is the sum of all the numbers that can be obtained by rearranging the digits of $2016$? | [
"58000"
] | [
"What is the sum of all the numbers that can be obtained by rearranging the digits of $2016$?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-f372f559e33e2991d44f4a3cfacc17b3a86a65aea887bba78a93186c63d1f923 | What is the sum of all the odd integers between $300$ and $500$? | [
"40000"
] | [
"What is the sum of all the odd integers between $300$ and $500$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-bd06e1c47bc9b6108e7a65e525b685d104bdc1538b3d55d01b5d9b26751bd9a5 | What is the sum of all the positive divisors of 91? | [
"112"
] | [
"What is the sum of all the positive divisors of 91?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-c6a7893e7f49b44b29d35547502c37e2ba5d6fe149d7cefbd7a2ca99a69b679a | What is the sum of all the positive two-digit integers divisible by both the sum and product of their digits? | [
"72"
] | [
"What is the sum of all the positive two-digit integers divisible by both the sum and product of their digits?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-87ebe3419da437e97b2482b92c6a51d5be194eac9098dd13fd98cbe1fc992869 | What is the sum of all the prime numbers between 1 and 10? | [
"17"
] | [
"What is the sum of all the prime numbers between 1 and 10?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-b739271d8ac9506fbeed3abfd7864ec6033385ba7de175eaf448320a20c76d0a | What is the sum of all the real solutions of \( x \) if \( \left| x + \sqrt{4 - x} \right| - 4x = 0 \)? | [
"\\(\\frac{-1 + \\sqrt{145}}{18}\\)"
] | [
"What is the sum of all the real solutions of \\( x \\) if \\( \\left| x + \\sqrt{4 - x} \\right| - 4x = 0 \\)?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 27
} | 43 | 0 | 0 |
omr-ws-ab47e5e1941cbc3e9b4347ef2300ac0ec24ff051fcbc341f2332ca09c9c81f6c | What is the sum of all the reciprocals of all positive integers? | [
"positive infinity"
] | [
"What is the sum of all the reciprocals of all positive integers?"
] | [
"c4_high_school_math"
] | [
"tir"
] | {
"tir": 1
} | 1 | 0 | 0 |
omr-ws-8aad08dbc06adc78a41792a6041cca8c91f320ab51400deb2d2ab7ae2490d3f3 | What is the sum of all the solutions of $x = \left|2x-|60-2x|\right|$? | [
"92"
] | [
"What is the sum of all the solutions of $x = \\left|2x-|60-2x|\\right|$?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-47a1ba945528c02024269914afddcd7bc3fb8d906268823e5fe0b269b66da53f | What is the sum of all the solutions of the equation \( x = |2x - |60 - 2x|| \)? | [
"92"
] | [
"What is the sum of all the solutions of the equation \\( x = |2x - |60 - 2x|| \\)?"
] | [
"aops_c5_contests_amp_programs"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-d3c7c8cf12f26fd77bb40851a3e201ff1d304ea64b01bd819e06537cb838c174 | What is the sum of all the three-digit positive integers? | [
"494550"
] | [
"What is the sum of all the three-digit positive integers?"
] | [
"MATH_training_set"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-8ad384bf9741319395a7d0b8f907ec62ca42981f4d939e4abaa25f50668587e2 | What is the sum of all three-digit even numbers divisible by $17$? | [
"14688"
] | [
"What is the sum of all three-digit even numbers divisible by $17$?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 27
} | 43 | 0 | 0 |
omr-ws-fb591c6eac6211d15384b1bcf61a0e180856437683a495b62e03066a5d2846a9 | What is the sum of all three-digit integers that only use the digits $0, 4$, and $8$? Leading zeroes are not allowed. | [
"2532"
] | [
"What is the sum of all three-digit integers that only use the digits $0, 4$, and $8$? Leading zeroes are not allowed."
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-d3e5c778891b8e6de96ae1e0221e70a15b3234dca01c2a39616923aba95863f3 | What is the sum of all three-digit numbers where the middle digit is a perfect square, and the digits are formed using the numbers 1 to 9? | [
"134055"
] | [
"What is the sum of all three-digit numbers where the middle digit is a perfect square, and the digits are formed using the numbers 1 to 9?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
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