{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 17. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "471", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1472", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 11. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4384", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 14. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4943", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6672", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99918", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6107", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4958", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9972", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "699", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7784", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89000", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 2-digit positive integer with the property that the sum of the digits of n is divisible by 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99997", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5356", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8904", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99999", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10078", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10090", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9804", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9990", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3336", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9897", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99997", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6672", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10067", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1200", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1212", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3336", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9990", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98808", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8896", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99990", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2853", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99993", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 2-digit positive integer with the property that the sum of the digits of n is divisible by 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1112", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9897", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 19. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9208", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9942", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 3-digit positive integer with the property that the sum of the digits of n is divisible by 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99935", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10080", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 4-digit positive integer with the property that the sum of the digits of n is divisible by 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1029", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10045", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 2-digit positive integer with the property that the sum of the digits of n is divisible by 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 15. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9990", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1020", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 3-digit positive integer with the property that the sum of the digits of n is divisible by 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "189", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 17. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 7. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99999", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 13. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3438", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9960", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6396", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99963", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5866", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10200", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "629", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "990", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7781", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99999", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5207", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99981", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 15. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 7. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10128", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11115", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9998", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10005", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "781", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9905", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 17. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "750", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "963", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99999", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 11. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6876", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99923", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1145", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7784", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 11. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 7. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 2-digit positive integer with the property that the sum of the digits of n is divisible by 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 2-digit positive integer with the property that the sum of the digits of n is divisible by 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 14. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2122", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1026", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2122", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4448", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3336", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 14. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99897", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8904", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9000", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 9. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 9. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 9. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 12. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9990", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 19. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99960", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 12. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 4-digit positive integer with the property that the sum of the digits of n is divisible by 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1038", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 15. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 7. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1607", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10004", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10026", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 12. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5631", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "430", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 15. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9998", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 13. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90000", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 19. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1604", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1002", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9997", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1004", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9983", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 12. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7784", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7988", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 2-digit positive integer with the property that the sum of the digits of n is divisible by 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 17. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "897", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1520", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2224", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1115", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11145", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 4-digit positive integer with the property that the sum of the digits of n is divisible by 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1089", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 4-digit positive integer with the property that the sum of the digits of n is divisible by 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1045", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4448", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "862", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 15. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22230", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 3-digit positive integer with the property that the sum of the digits of n is divisible by 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "951", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1622", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "751", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5701", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 9. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10000", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3438", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 13. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 3-digit positive integer with the property that the sum of the digits of n is divisible by 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "228", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1000", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9997", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7781", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9797", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 3-digit positive integer with the property that the sum of the digits of n is divisible by 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "972", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 7. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2224", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1112", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6877", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "638", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11002", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10029", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90004", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 19. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "711", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9902", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8488", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 3-digit positive integer with the property that the sum of the digits of n is divisible by 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2507", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 12. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1050", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3484", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9584", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 7. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1112", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 4-digit positive integer with the property that the sum of the digits of n is divisible by 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1128", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8794", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "946", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10109", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 3-digit positive integer with the property that the sum of the digits of n is divisible by 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "901", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99999", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70070", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 12. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99999", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 2-digit positive integer with the property that the sum of the digits of n is divisible by 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2224", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 9. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99999", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "707", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1112", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4307", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1112", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1115", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 4-digit positive integer with the property that the sum of the digits of n is divisible by 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1109", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8896", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4307", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10050", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4384", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9924", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "781", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "473", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "992", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77781", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 4-digit positive integer with the property that the sum of the digits of n is divisible by 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1090", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8794", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99899", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99905", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "303", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 14. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2224", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1520", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8896", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "904", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1112", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 3-digit positive integer with the property that the sum of the digits of n is divisible by 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 3-digit positive integer with the property that the sum of the digits of n is divisible by 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5631", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9999", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99897", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1112", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4244", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5984", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 12. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9993", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8677", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 11. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99999", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5560", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5560", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "395", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10080", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99997", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9918", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99700", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9960", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 3-digit positive integer with the property that the sum of the digits of n is divisible by 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "925", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9981", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1112", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99880", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 3-digit positive integer with the property that the sum of the digits of n is divisible by 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "961", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3555", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9997", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7784", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 3-digit positive integer with the property that the sum of the digits of n is divisible by 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "167", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 13. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "576", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3548", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1005", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5866", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99804", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99945", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99903", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "700", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "318", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 15. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "990", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9004", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "699", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1112", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 11. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "230", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 11. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "569", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 14. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9897", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99960", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2160", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 2-digit positive integer with the property that the sum of the digits of n is divisible by 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 9. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1622", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 17. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 13. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11115", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 2-digit positive integer with the property that the sum of the digits of n is divisible by 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77751", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7988", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "629", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8472", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99997", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3407", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 3-digit positive integer with the property that the sum of the digits of n is divisible by 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9284", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89000", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 13. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9914", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 3-digit positive integer with the property that the sum of the digits of n is divisible by 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10004", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 19. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3555", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 2-digit positive integer with the property that the sum of the digits of n is divisible by 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 2-digit positive integer with the property that the sum of the digits of n is divisible by 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 15. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 15. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99990", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 3-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9999", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10038", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9997", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8488", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 17. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9408", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44448", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10002", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "853", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6876", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7751", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 12. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9995", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9192", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 13. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99972", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11010", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9861", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 17. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99558", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3744", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 7. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7784", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99909", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9192", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "576", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 17. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 5. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9952", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 11. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 3-digit positive integer with the property that the sum of the digits of n is divisible by 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "945", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1607", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 4-digit positive integer with the property that the sum of the digits of n is divisible by 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1078", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 14. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9880", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 11. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11112", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10089", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5356", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4958", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33336", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88896", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 12. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99999", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9996", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9930", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5701", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3548", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 14. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99900", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the third greatest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1106", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1002", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 5-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 9. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9999", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 9. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55560", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "let N be the largest 3-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 3-digit positive integer with the property that the sum of the digits of n is divisible by 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10020", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth greatest 3-digit positive integer with the property that the sum of the digits of n is divisible by 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "932", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4243", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77784", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 19. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1135", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10008", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "let N be the tenth smallest 2-digit positive integer with the property that the sum of the digits of n is divisible by 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1004", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 4. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 19. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11145", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the minimum 2-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 7. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22224", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 4-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "897", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66672", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 7, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8896", "dataset": "MATH"}
{"messages": [{"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77781", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 1, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}