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_0889
|
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 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}"
}
] |
24
|
math
|
numbertheory_qr_sum_train_0890
|
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 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}"
}
] |
11112
|
math
|
numbertheory_qr_sum_train_0891
|
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 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}"
}
] |
88896
|
math
|
numbertheory_qr_sum_train_0892
|
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 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}"
}
] |
3
|
math
|
numbertheory_qr_sum_train_0893
|
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 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}"
}
] |
24
|
math
|
numbertheory_qr_sum_train_0894
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
10008
|
math
|
numbertheory_qr_sum_train_0895
|
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 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}"
}
] |
560
|
math
|
numbertheory_qr_sum_train_0896
|
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 5. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9995
|
math
|
numbertheory_qr_sum_train_0897
|
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 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}"
}
] |
7
|
math
|
numbertheory_qr_sum_train_0898
|
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 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}"
}
] |
9192
|
math
|
numbertheory_qr_sum_train_0899
|
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 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}"
}
] |
58
|
math
|
numbertheory_qr_sum_train_0900
|
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 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}"
}
] |
672
|
math
|
numbertheory_qr_sum_train_0901
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
99972
|
math
|
numbertheory_qr_sum_train_0902
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
11010
|
math
|
numbertheory_qr_sum_train_0903
|
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 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}"
}
] |
18
|
math
|
numbertheory_qr_sum_train_0904
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
9861
|
math
|
numbertheory_qr_sum_train_0905
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_0906
|
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 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}"
}
] |
96
|
math
|
numbertheory_qr_sum_train_0907
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
5
|
math
|
numbertheory_qr_sum_train_0908
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
99558
|
math
|
numbertheory_qr_sum_train_0909
|
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 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}"
}
] |
77784
|
math
|
numbertheory_qr_sum_train_0910
|
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 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}"
}
] |
240
|
math
|
numbertheory_qr_sum_train_0911
|
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 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}"
}
] |
8896
|
math
|
numbertheory_qr_sum_train_0912
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
3744
|
math
|
numbertheory_qr_sum_train_0913
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
6
|
math
|
numbertheory_qr_sum_train_0914
|
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 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}"
}
] |
7784
|
math
|
numbertheory_qr_sum_train_0915
|
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 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_0916
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1008
|
math
|
numbertheory_qr_sum_train_0917
|
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 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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_0918
|
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 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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_0919
|
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 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_0920
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
99909
|
math
|
numbertheory_qr_sum_train_0921
|
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 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}"
}
] |
112
|
math
|
numbertheory_qr_sum_train_0922
|
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 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}"
}
] |
9192
|
math
|
numbertheory_qr_sum_train_0923
|
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 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}"
}
] |
11112
|
math
|
numbertheory_qr_sum_train_0924
|
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 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}"
}
] |
576
|
math
|
numbertheory_qr_sum_train_0925
|
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 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}"
}
] |
78
|
math
|
numbertheory_qr_sum_train_0926
|
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 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}"
}
] |
77784
|
math
|
numbertheory_qr_sum_train_0927
|
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 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}"
}
] |
112
|
math
|
numbertheory_qr_sum_train_0928
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
16
|
math
|
numbertheory_qr_sum_train_0929
|
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 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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_0930
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
9952
|
math
|
numbertheory_qr_sum_train_0931
|
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 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}"
}
] |
57
|
math
|
numbertheory_qr_sum_train_0932
|
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 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}"
}
] |
90
|
math
|
numbertheory_qr_sum_train_0933
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
10
|
math
|
numbertheory_qr_sum_train_0934
|
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 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
945
|
math
|
numbertheory_qr_sum_train_0935
|
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 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}"
}
] |
784
|
math
|
numbertheory_qr_sum_train_0936
|
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 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}"
}
] |
3
|
math
|
numbertheory_qr_sum_train_0937
|
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 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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_0938
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_0939
|
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 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}"
}
] |
77784
|
math
|
numbertheory_qr_sum_train_0940
|
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 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}"
}
] |
108
|
math
|
numbertheory_qr_sum_train_0941
|
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 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_0942
|
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 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}"
}
] |
1607
|
math
|
numbertheory_qr_sum_train_0943
|
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 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}"
}
] |
84
|
math
|
numbertheory_qr_sum_train_0944
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1078
|
math
|
numbertheory_qr_sum_train_0945
|
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 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}"
}
] |
22
|
math
|
numbertheory_qr_sum_train_0946
|
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 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}"
}
] |
11112
|
math
|
numbertheory_qr_sum_train_0947
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
9880
|
math
|
numbertheory_qr_sum_train_0948
|
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 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}"
}
] |
448
|
math
|
numbertheory_qr_sum_train_0949
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
9
|
math
|
numbertheory_qr_sum_train_0950
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
12
|
math
|
numbertheory_qr_sum_train_0951
|
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 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}"
}
] |
11112
|
math
|
numbertheory_qr_sum_train_0952
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
10089
|
math
|
numbertheory_qr_sum_train_0953
|
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 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}"
}
] |
16
|
math
|
numbertheory_qr_sum_train_0954
|
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 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}"
}
] |
5356
|
math
|
numbertheory_qr_sum_train_0955
|
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 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}"
}
] |
22224
|
math
|
numbertheory_qr_sum_train_0956
|
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 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}"
}
] |
4958
|
math
|
numbertheory_qr_sum_train_0957
|
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 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}"
}
] |
108
|
math
|
numbertheory_qr_sum_train_0958
|
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 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}"
}
] |
33336
|
math
|
numbertheory_qr_sum_train_0959
|
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 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}"
}
] |
68
|
math
|
numbertheory_qr_sum_train_0960
|
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 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}"
}
] |
224
|
math
|
numbertheory_qr_sum_train_0961
|
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 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}"
}
] |
88896
|
math
|
numbertheory_qr_sum_train_0962
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
1
|
math
|
numbertheory_qr_sum_train_0963
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
80
|
math
|
numbertheory_qr_sum_train_0964
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
99999
|
math
|
numbertheory_qr_sum_train_0965
|
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 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}"
}
] |
74
|
math
|
numbertheory_qr_sum_train_0966
|
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 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}"
}
] |
18
|
math
|
numbertheory_qr_sum_train_0967
|
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 6. Find N mod 10000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9996
|
math
|
numbertheory_qr_sum_train_0968
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
9930
|
math
|
numbertheory_qr_sum_train_0969
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
25
|
math
|
numbertheory_qr_sum_train_0970
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
6
|
math
|
numbertheory_qr_sum_train_0971
|
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 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}"
}
] |
5701
|
math
|
numbertheory_qr_sum_train_0972
|
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 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}"
}
] |
3548
|
math
|
numbertheory_qr_sum_train_0973
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
99900
|
math
|
numbertheory_qr_sum_train_0974
|
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 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_0975
|
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 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}"
}
] |
11
|
math
|
numbertheory_qr_sum_train_0976
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
84
|
math
|
numbertheory_qr_sum_train_0977
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
999
|
math
|
numbertheory_qr_sum_train_0978
|
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 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}"
}
] |
18
|
math
|
numbertheory_qr_sum_train_0979
|
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 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}"
}
] |
11
|
math
|
numbertheory_qr_sum_train_0980
|
numbertheory_qr_sum
| null |
[
{
"role": "user",
"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}"
}
] |
9
|
math
|
numbertheory_qr_sum_train_0981
|
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 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}"
}
] |
3
|
math
|
numbertheory_qr_sum_train_0982
|
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 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}"
}
] |
1106
|
math
|
numbertheory_qr_sum_train_0983
|
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 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}"
}
] |
3
|
math
|
numbertheory_qr_sum_train_0984
|
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 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}"
}
] |
2224
|
math
|
numbertheory_qr_sum_train_0985
|
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 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}"
}
] |
79
|
math
|
numbertheory_qr_sum_train_0986
|
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 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}"
}
] |
14
|
math
|
numbertheory_qr_sum_train_0987
|
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 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}"
}
] |
224
|
math
|
numbertheory_qr_sum_train_0988
|
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 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}"
}
] |
1002
|
math
|
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