id
stringlengths 21
60
| setting_key
stringclasses 55
values | setting_name
stringclasses 7
values | messages
listlengths 1
1
| ground_truth
stringlengths 1
3.09k
| dataset
stringclasses 1
value |
|---|---|---|---|---|---|
numbertheory_qr_sum_train_0989
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
784
|
math
|
numbertheory_qr_sum_train_0990
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
2
|
math
|
numbertheory_qr_sum_train_0991
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
10008
|
math
|
numbertheory_qr_sum_train_0992
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
77
|
math
|
numbertheory_qr_sum_train_0993
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
12
|
math
|
numbertheory_qr_sum_train_0994
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
14
|
math
|
numbertheory_qr_sum_train_0995
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
9999
|
math
|
numbertheory_qr_sum_train_0996
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
99
|
math
|
numbertheory_qr_sum_train_0997
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
18
|
math
|
numbertheory_qr_sum_train_0998
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
55560
|
math
|
numbertheory_qr_sum_train_0999
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
77784
|
math
|
numbertheory_qr_sum_train_1000
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
24
|
math
|
numbertheory_qr_sum_train_1001
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
90
|
math
|
numbertheory_qr_sum_train_1002
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
895
|
math
|
numbertheory_qr_sum_train_1003
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1008
|
math
|
numbertheory_qr_sum_train_1004
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
10020
|
math
|
numbertheory_qr_sum_train_1005
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
10
|
math
|
numbertheory_qr_sum_train_1006
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
932
|
math
|
numbertheory_qr_sum_train_1007
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
36
|
math
|
numbertheory_qr_sum_train_1008
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_1009
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
4243
|
math
|
numbertheory_qr_sum_train_1010
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
2
|
math
|
numbertheory_qr_sum_train_1011
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
96
|
math
|
numbertheory_qr_sum_train_1012
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1008
|
math
|
numbertheory_qr_sum_train_1013
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
3
|
math
|
numbertheory_qr_sum_train_1014
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
77784
|
math
|
numbertheory_qr_sum_train_1015
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
3
|
math
|
numbertheory_qr_sum_train_1016
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_1017
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1135
|
math
|
numbertheory_qr_sum_train_1018
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
108
|
math
|
numbertheory_qr_sum_train_1019
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
10008
|
math
|
numbertheory_qr_sum_train_1020
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
96
|
math
|
numbertheory_qr_sum_train_1021
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
66
|
math
|
numbertheory_qr_sum_train_1022
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
22224
|
math
|
numbertheory_qr_sum_train_1023
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
9
|
math
|
numbertheory_qr_sum_train_1024
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1004
|
math
|
numbertheory_qr_sum_train_1025
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
10
|
math
|
numbertheory_qr_sum_train_1026
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
105
|
math
|
numbertheory_qr_sum_train_1027
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_1028
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
18
|
math
|
numbertheory_qr_sum_train_1029
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
22224
|
math
|
numbertheory_qr_sum_train_1030
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_1031
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
78
|
math
|
numbertheory_qr_sum_train_1032
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
22224
|
math
|
numbertheory_qr_sum_train_1033
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
30
|
math
|
numbertheory_qr_sum_train_1034
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_1035
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
11145
|
math
|
numbertheory_qr_sum_train_1036
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_1037
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_1038
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1008
|
math
|
numbertheory_qr_sum_train_1039
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
22224
|
math
|
numbertheory_qr_sum_train_1040
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
60
|
math
|
numbertheory_qr_sum_train_1041
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
94
|
math
|
numbertheory_qr_sum_train_1042
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_1043
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
336
|
math
|
numbertheory_qr_sum_train_1044
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_1045
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
897
|
math
|
numbertheory_qr_sum_train_1046
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
66672
|
math
|
numbertheory_qr_sum_train_1047
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
16
|
math
|
numbertheory_qr_sum_train_1048
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
3
|
math
|
numbertheory_qr_sum_train_1049
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
8896
|
math
|
numbertheory_qr_sum_train_1050
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
77781
|
math
|
numbertheory_qr_sum_train_1051
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
84
|
math
|
numbertheory_qr_sum_train_1052
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
7
|
math
|
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