Dataset Viewer
id
stringlengths 35
35
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringclasses 26
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
combinatory_distribution_train_0000
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'w': 3, 'r': 1} into 2 undistinguishable boxes with capacities [2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
combinatory_distribution_train_0001
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'n': 4, 't': 2} among 2 distinguishable boxes with capacities [3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0002
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'s': 2, 'a': 4} into 2 undistinguishable boxes with sizes [5, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0003
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'k': 2, 'm': 3} among 2 distinguishable boxes with capacities [1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0004
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'b': 4, 'x': 2} and need to distribute them into 2 different boxes with capacities [3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0005
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'k': 3, 'o': 3}, place them into 2 indistinguishable boxes with sizes [4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0006
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'f': 3, 'p': 3} among 2 identical containers that can hold [2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0007
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'f': 3, 'p': 3} into 2 uniquely identified boxes that can hold [3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
combinatory_distribution_train_0008
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'o': 2, 'w': 3} into 2 undistinguishable boxes with capacities [3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0009
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'s': 1, 'v': 4} and need to distribute them into 2 identical boxes with capacities [3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0010
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'w': 4, 'v': 2} into 2 uniquely identified boxes that can hold [4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0011
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'y': 3, 'u': 2}, place them into 2 labeled boxes with sizes [3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0012
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'d': 5, 'h': 1} into 2 undistinguishable boxes with capacities [4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0013
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'w': 2, 'k': 4} and need to distribute them into 2 different boxes with capacities [3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0014
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'w': 3, 'z': 1}, place them into 2 indistinguishable boxes with sizes [1, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0015
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'n': 2, 'v': 3} and need to distribute them into 2 different boxes with capacities [1, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0016
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'q': 4, 'p': 2}, place them into 2 indistinguishable boxes with sizes [4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0017
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'q': 2, 'v': 3} into 2 uniquely identified boxes that can hold [2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0018
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'i': 3, 'z': 1} among 2 distinguishable boxes with capacities [2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0019
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'w': 3, 'o': 3}, place them into 2 indistinguishable boxes with sizes [2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0020
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'r': 4, 'j': 2}, place them into 2 labeled boxes with sizes [4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0021
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'i': 2, 's': 4}, place them into 2 indistinguishable boxes with sizes [4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0022
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'d': 2, 'k': 4} into 2 undistinguishable boxes with sizes [3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0023
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'g': 1, 'a': 3} into 2 uniquely identified boxes that can hold [2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0024
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'l': 1, 'd': 4} among 2 distinguishable boxes with capacities [2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0025
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'v': 3, 'n': 3} among 2 distinguishable boxes with capacities [1, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0026
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'z': 1, 'a': 3} into 2 undistinguishable boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0027
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'z': 1, 'e': 4} into 2 undistinguishable boxes with sizes [1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0028
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'w': 3, 'y': 3} into 2 undistinguishable boxes with capacities [3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0029
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'u': 4, 'n': 2} into 2 undistinguishable boxes with sizes [3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0030
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'a': 2, 'k': 2} and need to distribute them into 2 identical boxes with capacities [2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0031
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'n': 2, 'q': 3} into 2 undistinguishable boxes with capacities [1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0032
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'g': 1, 'o': 3} into 2 uniquely identified boxes that can hold [1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0033
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'c': 4, 'l': 1} and need to distribute them into 2 identical boxes with capacities [4, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0034
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'b': 2, 'h': 3} into 2 undistinguishable boxes with sizes [3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0035
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'i': 1, 'f': 3} into 2 undistinguishable boxes with capacities [2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
combinatory_distribution_train_0036
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'y': 3, 'e': 1} and need to distribute them into 2 identical boxes with capacities [2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
combinatory_distribution_train_0037
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'f': 3, 'q': 1}, place them into 2 labeled boxes with sizes [2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0038
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'u': 2, 'r': 3} and need to distribute them into 2 different boxes with capacities [1, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0039
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'x': 2, 's': 2} among 2 distinguishable boxes with capacities [2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0040
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'t': 2, 'o': 3}, place them into 2 labeled boxes with sizes [3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0041
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'l': 2, 'n': 3} into 2 undistinguishable boxes with capacities [2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0042
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'k': 1, 'c': 3} and need to distribute them into 2 identical boxes with capacities [2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
combinatory_distribution_train_0043
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'c': 2, 's': 4} among 2 distinguishable boxes with capacities [5, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0044
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'b': 2, 'a': 4}, place them into 2 labeled boxes with sizes [2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0045
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'x': 3, 't': 2} among 2 identical containers that can hold [2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0046
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'v': 1, 'k': 4} and need to distribute them into 2 different boxes with capacities [3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0047
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'n': 3, 'm': 2} among 2 identical containers that can hold [3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0048
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'o': 5, 'f': 1} among 2 identical containers that can hold [3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
combinatory_distribution_train_0049
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'w': 2, 'p': 3} into 2 distinctively labeled boxes with sizes [3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0050
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'p': 2, 'c': 3} into 2 undistinguishable boxes with sizes [1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0051
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'u': 2, 'n': 3} into 2 undistinguishable boxes with capacities [3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0052
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'h': 2, 'f': 2} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0053
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'d': 3, 'g': 3} into 2 distinctively labeled boxes with sizes [2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0054
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'j': 3, 'r': 2} into 2 uniquely identified boxes that can hold [4, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0055
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'e': 3, 'g': 3} into 2 undistinguishable boxes with sizes [2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0056
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'b': 2, 'l': 2} and need to distribute them into 2 different boxes with capacities [2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0057
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'f': 2, 'w': 4} among 2 distinguishable boxes with capacities [2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0058
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'x': 4, 'o': 2} into 2 uniquely identified boxes that can hold [3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0059
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'h': 2, 'd': 3} into 2 uniquely identified boxes that can hold [3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0060
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'g': 2, 'd': 3} into 2 undistinguishable boxes with capacities [2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0061
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'l': 2, 'p': 2} into 2 distinctively labeled boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0062
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'i': 2, 'r': 3} among 2 distinguishable boxes with capacities [2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0063
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'x': 3, 'r': 2}, place them into 2 labeled boxes with sizes [4, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0064
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'q': 4, 's': 2} into 2 distinctively labeled boxes with sizes [2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0065
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'p': 3, 'o': 3} among 2 identical containers that can hold [3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0066
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'h': 2, 'e': 3}, place them into 2 labeled boxes with sizes [1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0067
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'b': 3, 'o': 2} and need to distribute them into 2 different boxes with capacities [3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0068
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'s': 2, 'u': 3} and need to distribute them into 2 identical boxes with capacities [1, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0069
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'v': 2, 's': 3} into 2 uniquely identified boxes that can hold [3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0070
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'h': 4, 'l': 2} among 2 identical containers that can hold [3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0071
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'c': 2, 'b': 2}, place them into 2 labeled boxes with sizes [3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0072
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'h': 2, 'l': 2} among 2 identical containers that can hold [2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0073
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'w': 4, 'p': 2} and need to distribute them into 2 different boxes with capacities [3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0074
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'m': 2, 'a': 2} among 2 identical containers that can hold [3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0075
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'n': 2, 'e': 2} among 2 distinguishable boxes with capacities [1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0076
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'s': 4, 'f': 2} into 2 undistinguishable boxes with sizes [1, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0077
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'k': 3, 'n': 1} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
combinatory_distribution_train_0078
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'x': 4, 'f': 2} and need to distribute them into 2 different boxes with capacities [3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0079
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'q': 2, 'v': 4} and need to distribute them into 2 different boxes with capacities [2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0080
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'i': 3, 'j': 2} and need to distribute them into 2 identical boxes with capacities [4, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0081
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'v': 2, 'j': 3}, place them into 2 labeled boxes with sizes [1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0082
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'j': 3, 'r': 2}, place them into 2 indistinguishable boxes with sizes [4, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0083
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'u': 5, 'f': 1}, place them into 2 indistinguishable boxes with sizes [1, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0084
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'v': 3, 'y': 3} and need to distribute them into 2 identical boxes with capacities [3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0085
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'j': 2, 'v': 4} and need to distribute them into 2 different boxes with capacities [2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0086
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'y': 2, 'n': 2} among 2 distinguishable boxes with capacities [2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0087
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'w': 2, 'g': 4} into 2 undistinguishable boxes with sizes [4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0088
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'k': 1, 'b': 3}, place them into 2 labeled boxes with sizes [3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0089
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'c': 2, 'b': 2}, place them into 2 indistinguishable boxes with sizes [2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0090
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'k': 4, 'q': 1} and need to distribute them into 2 different boxes with capacities [4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0091
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Given the letters {'x': 3, 'v': 2}, place them into 2 labeled boxes with sizes [4, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0092
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'o': 3, 't': 3} into 2 undistinguishable boxes with sizes [3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0093
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'k': 2, 'a': 2} among 2 identical containers that can hold [2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0094
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'p': 1, 'h': 4} into 2 distinctively labeled boxes with sizes [3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0095
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'a': 3, 'd': 1} among 2 distinguishable boxes with capacities [1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0096
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "You have {'i': 3, 'w': 1} and need to distribute them into 2 different boxes with capacities [1, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0097
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Arrange the letters {'q': 2, 'x': 2} into 2 undistinguishable boxes with capacities [2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
combinatory_distribution_train_0098
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Distribute the letters {'n': 2, 'm': 3} among 2 identical containers that can hold [3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
combinatory_distribution_train_0099
|
combinatory_distribution
| null |
[
{
"role": "user",
"content": "Divide the letters from {'w': 2, 'q': 4} into 2 distinctively labeled boxes with sizes [2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
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