prompt stringlengths 39 2.68k | completion stringlengths 1 286 | category stringclasses 8
values | answer stringlengths 0 7 | meta stringlengths 0 553 |
|---|---|---|---|---|
The integer 2431 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 15.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{56} | aime_bench | 56 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 462, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{66} | aime_bench | 66 | |
Find the smallest positive integer x with x mod 8 = 1 and x mod 7 = 5. The answer is a positive integer less than 56.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response wit... | \boxed{33} | aime_bench | 33 | |
Compute the value of ((4^13) * 8) mod 103, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 103.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{98} | aime_bench | 98 | |
Two positive integers x and y satisfy x + y = 20 and x * y = 96, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{208} | aime_bench | 208 | |
The integer 165 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 25.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your re... | \boxed{44} | aime_bench | 44 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 161, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{17} | aime_bench | 17 | |
Find the smallest positive integer x with x mod 14 = 3 and x mod 11 = 6. The answer is a positive integer less than 154.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response ... | \boxed{17} | aime_bench | 17 | |
Compute the value of ((2^11) * 3) mod 107, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 107.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{45} | aime_bench | 45 | |
Two positive integers x and y satisfy x + y = 20 and x * y = 100, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '... | \boxed{200} | aime_bench | 200 | |
The integer 285 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 8.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your res... | \boxed{35} | aime_bench | 35 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 141, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{87} | aime_bench | 87 | |
Find the smallest positive integer x with x mod 8 = 0 and x mod 11 = 9. The answer is a positive integer less than 88.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response wi... | \boxed{64} | aime_bench | 64 | |
Compute the value of ((6^12) * 7) mod 107, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 107.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{5} | aime_bench | 5 | |
Two positive integers x and y satisfy x + y = 23 and x * y = 130, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '... | \boxed{269} | aime_bench | 269 | |
The integer 1615 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 32.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{73} | aime_bench | 73 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 64, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' where... | \boxed{73} | aime_bench | 73 | |
Find the smallest positive integer x with x mod 14 = 9 and x mod 13 = 1. The answer is a positive integer less than 182.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response ... | \boxed{79} | aime_bench | 79 | |
Compute the value of ((5^19) * 3) mod 101, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 101.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{10} | aime_bench | 10 | |
Two positive integers x and y satisfy x + y = 21 and x * y = 110, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '... | \boxed{221} | aime_bench | 221 | |
The integer 1105 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 11.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{46} | aime_bench | 46 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 465, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{87} | aime_bench | 87 | |
Find the smallest positive integer x with x mod 12 = 0 and x mod 13 = 12. The answer is a positive integer less than 156.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response... | \boxed{12} | aime_bench | 12 | |
Compute the value of ((9^17) * 6) mod 97, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 97.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and ... | \boxed{47} | aime_bench | 47 | |
Two positive integers x and y satisfy x + y = 22 and x * y = 120, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '... | \boxed{244} | aime_bench | 244 | |
The integer 1729 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 19.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{58} | aime_bench | 58 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 258, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{87} | aime_bench | 87 | |
Find the smallest positive integer x with x mod 8 = 4 and x mod 13 = 12. The answer is a positive integer less than 104.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response ... | \boxed{12} | aime_bench | 12 | |
Compute the value of ((6^14) * 6) mod 107, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 107.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{32} | aime_bench | 32 | |
Two positive integers x and y satisfy x + y = 13 and x * y = 40, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{89} | aime_bench | 89 | |
The integer 2431 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 11.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{52} | aime_bench | 52 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 424, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{73} | aime_bench | 73 | |
Find the smallest positive integer x with x mod 12 = 9 and x mod 13 = 10. The answer is a positive integer less than 156.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response... | \boxed{153} | aime_bench | 153 | |
Compute the value of ((7^10) * 4) mod 103, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 103.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{60} | aime_bench | 60 | |
Two positive integers x and y satisfy x + y = 11 and x * y = 24, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{73} | aime_bench | 73 | |
The integer 385 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 30.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your re... | \boxed{53} | aime_bench | 53 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 380, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{101} | aime_bench | 101 | |
Find the smallest positive integer x with x mod 14 = 8 and x mod 19 = 7. The answer is a positive integer less than 266.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response ... | \boxed{64} | aime_bench | 64 | |
Compute the value of ((8^19) * 8) mod 107, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 107.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{86} | aime_bench | 86 | |
Two positive integers x and y satisfy x + y = 9 and x * y = 14, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\b... | \boxed{53} | aime_bench | 53 | |
The integer 399 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your res... | \boxed{31} | aime_bench | 31 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 87, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' where... | \boxed{87} | aime_bench | 87 | |
Find the smallest positive integer x with x mod 10 = 3 and x mod 11 = 8. The answer is a positive integer less than 110.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response ... | \boxed{63} | aime_bench | 63 | |
Compute the value of ((7^18) * 4) mod 107, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 107.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{9} | aime_bench | 9 | |
Two positive integers x and y satisfy x + y = 10 and x * y = 24, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{52} | aime_bench | 52 | |
The integer 105 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 32.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your re... | \boxed{47} | aime_bench | 47 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 82, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' where... | \boxed{73} | aime_bench | 73 | |
Find the smallest positive integer x with x mod 14 = 9 and x mod 17 = 11. The answer is a positive integer less than 238.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response... | \boxed{79} | aime_bench | 79 | |
Compute the value of ((4^12) * 2) mod 97, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 97.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and ... | \boxed{95} | aime_bench | 95 | |
The integer 1729 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 46.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{85} | aime_bench | 85 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 436, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{94} | aime_bench | 94 | |
Find the smallest positive integer x with x mod 15 = 12 and x mod 7 = 0. The answer is a positive integer less than 105.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response ... | \boxed{42} | aime_bench | 42 | |
Compute the value of ((9^12) * 2) mod 113, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 113.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{8} | aime_bench | 8 | |
Two positive integers x and y satisfy x + y = 12 and x * y = 32, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{80} | aime_bench | 80 | |
The integer 429 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 19.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your re... | \boxed{46} | aime_bench | 46 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 499, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{94} | aime_bench | 94 | |
Find the smallest positive integer x with x mod 14 = 12 and x mod 11 = 2. The answer is a positive integer less than 154.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response... | \boxed{68} | aime_bench | 68 | |
Compute the value of ((6^14) * 2) mod 97, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 97.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and ... | \boxed{72} | aime_bench | 72 | |
Two positive integers x and y satisfy x + y = 15 and x * y = 50, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{125} | aime_bench | 125 | |
The integer 741 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 40.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your re... | \boxed{75} | aime_bench | 75 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 60, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' where... | \boxed{87} | aime_bench | 87 | |
Find the smallest positive integer x with x mod 6 = 3 and x mod 11 = 9. The answer is a positive integer less than 66.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response wi... | \boxed{9} | aime_bench | 9 | |
Compute the value of ((4^7) * 2) mod 97, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 97.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and e... | \boxed{79} | aime_bench | 79 | |
The integer 1547 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 7.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your re... | \boxed{44} | aime_bench | 44 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 105, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{87} | aime_bench | 87 | |
Find the smallest positive integer x with x mod 6 = 4 and x mod 7 = 6. The answer is a positive integer less than 42.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response wit... | \boxed{34} | aime_bench | 34 | |
Compute the value of ((7^12) * 2) mod 107, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 107.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{66} | aime_bench | 66 | |
Two positive integers x and y satisfy x + y = 15 and x * y = 54, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{117} | aime_bench | 117 | |
The integer 165 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 29.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your re... | \boxed{48} | aime_bench | 48 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 51, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' where... | \boxed{87} | aime_bench | 87 | |
Find the smallest positive integer x with x mod 6 = 5 and x mod 13 = 6. The answer is a positive integer less than 78.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response wi... | \boxed{71} | aime_bench | 71 | |
Compute the value of ((6^9) * 9) mod 107, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 107.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and... | \boxed{72} | aime_bench | 72 | |
Two positive integers x and y satisfy x + y = 15 and x * y = 26, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{173} | aime_bench | 173 | |
The integer 1309 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 20.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{55} | aime_bench | 55 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 486, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{108} | aime_bench | 108 | |
Find the smallest positive integer x with x mod 8 = 7 and x mod 9 = 5. The answer is a positive integer less than 72.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response wit... | \boxed{23} | aime_bench | 23 | |
Compute the value of ((6^9) * 7) mod 101, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 101.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and... | \boxed{18} | aime_bench | 18 | |
Two positive integers x and y satisfy x + y = 8 and x * y = 16, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\b... | \boxed{32} | aime_bench | 32 | |
The integer 1729 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 38.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{77} | aime_bench | 77 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 256, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{94} | aime_bench | 94 | |
Find the smallest positive integer x with x mod 6 = 0 and x mod 11 = 7. The answer is a positive integer less than 66.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response wi... | \boxed{18} | aime_bench | 18 | |
Compute the value of ((4^8) * 4) mod 113, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 113.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and... | \boxed{97} | aime_bench | 97 | |
Two positive integers x and y satisfy x + y = 24 and x * y = 143, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '... | \boxed{290} | aime_bench | 290 | |
The integer 1615 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 14.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{55} | aime_bench | 55 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 359, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{80} | aime_bench | 80 | |
Find the smallest positive integer x with x mod 8 = 6 and x mod 11 = 1. The answer is a positive integer less than 88.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response wi... | \boxed{78} | aime_bench | 78 | |
Compute the value of ((3^16) * 8) mod 97, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 97.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and ... | \boxed{3} | aime_bench | 3 | |
Two positive integers x and y satisfy x + y = 13 and x * y = 30, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{109} | aime_bench | 109 | |
The integer 595 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 9.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your res... | \boxed{38} | aime_bench | 38 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 255, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{66} | aime_bench | 66 | |
Find the smallest positive integer x with x mod 10 = 9 and x mod 7 = 2. The answer is a positive integer less than 70.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response wi... | \boxed{9} | aime_bench | 9 | |
Compute the value of ((3^7) * 8) mod 103, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 103.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and... | \boxed{89} | aime_bench | 89 | |
Two positive integers x and y satisfy x + y = 19 and x * y = 88, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\... | \boxed{185} | aime_bench | 185 | |
The integer 105 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 19.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your re... | \boxed{34} | aime_bench | 34 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 288, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{108} | aime_bench | 108 | |
Find the smallest positive integer x with x mod 14 = 2 and x mod 9 = 6. The answer is a positive integer less than 126.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response w... | \boxed{114} | aime_bench | 114 | |
Compute the value of ((5^19) * 6) mod 103, where ^ denotes integer exponentiation. The final answer is a non-negative integer less than 103.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step an... | \boxed{1} | aime_bench | 1 | |
Two positive integers x and y satisfy x + y = 7 and x * y = 10, with 2 <= x <= y. Compute the integer x^2 + y^2.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\b... | \boxed{29} | aime_bench | 29 | |
The integer 1463 factors uniquely as a product of three distinct primes. Let s be the sum of those three primes. Compute s + 44.
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your r... | \boxed{81} | aime_bench | 81 | |
Define f(n) = 7 * (sum of digits of n) + 3. Starting at n_0 = 110, compute n_3 = f(f(f(n_0))).
Solve carefully and end with '#### N' where N is the final integer answer.
This is an AIME problem. The answer is an integer between 0 and 999. Solve the problem step by step and end your response with '\boxed{ANSWER}' wher... | \boxed{101} | aime_bench | 101 |
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