messages listlengths 1 1 | ground_truth stringclasses 135
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Given the letters {'f': 1, 'r': 3, 'x': 3, 'h': 5}, place them into 4 labeled boxes with sizes [3, 5, 1, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 490 | MATH |
[
{
"content": "Given the letters {'e': 2, 'u': 3, 'f': 3, 'o': 4}, place them into 4 indistinguishable boxes with sizes [1, 3, 5, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 409 | MATH |
[
{
"content": "Divide the letters from {'c': 3, 'f': 4, 'q': 2, 'n': 3} into 4 undistinguishable boxes with sizes [2, 3, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 715 | MATH |
[
{
"content": "Divide the letters from {'q': 2, 'c': 3, 'j': 4, 'r': 3} into 4 distinctively labeled boxes with sizes [2, 1, 5, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "You have {'u': 4, 'g': 1, 's': 5, 'e': 2} and need to distribute them into 4 identical boxes with capacities [3, 4, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 347 | MATH |
[
{
"content": "Divide the letters from {'k': 3, 'j': 4, 'y': 4, 'p': 1} into 4 undistinguishable boxes with sizes [1, 5, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 279 | MATH |
[
{
"content": "You have {'t': 2, 'q': 4, 'c': 2, 'd': 4} and need to distribute them into 4 different boxes with capacities [1, 3, 5, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 684 | MATH |
[
{
"content": "You have {'v': 2, 'u': 4, 'w': 3, 't': 3} and need to distribute them into 4 identical boxes with capacities [4, 3, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 715 | MATH |
[
{
"content": "You have {'w': 2, 'u': 2, 'j': 3, 'c': 5} and need to distribute them into 4 different boxes with capacities [3, 5, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Divide the letters from {'b': 3, 'j': 2, 'v': 1, 'k': 6} into 4 undistinguishable boxes with sizes [3, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 278 | MATH |
[
{
"content": "Given the letters {'k': 3, 'q': 3, 'i': 3, 'e': 3}, place them into 4 labeled boxes with sizes [3, 5, 1, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 928 | MATH |
[
{
"content": "Arrange the letters {'f': 4, 'm': 3, 'z': 4, 'n': 1} into 4 uniquely identified boxes that can hold [4, 2, 3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 906 | MATH |
[
{
"content": "Distribute the letters {'r': 2, 'b': 5, 'd': 3, 'c': 2} among 4 distinguishable boxes with capacities [3, 4, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1031 | MATH |
[
{
"content": "Distribute the letters {'n': 3, 'i': 4, 'v': 2, 'z': 3} among 4 identical containers that can hold [3, 3, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Divide the letters from {'p': 5, 'a': 3, 'j': 3, 'c': 1} into 4 undistinguishable boxes with sizes [4, 4, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 185 | MATH |
[
{
"content": "You have {'l': 1, 'r': 4, 'p': 3, 'i': 4} and need to distribute them into 4 different boxes with capacities [3, 2, 3, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 906 | MATH |
[
{
"content": "Divide the letters from {'f': 2, 'w': 3, 'k': 3, 'e': 4} into 4 undistinguishable boxes with sizes [5, 2, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Divide the letters from {'f': 2, 'b': 4, 'y': 3, 'g': 3} into 4 undistinguishable boxes with sizes [4, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 715 | MATH |
[
{
"content": "Arrange the letters {'j': 5, 'o': 1, 'e': 3, 'c': 3} into 4 uniquely identified boxes that can hold [5, 2, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 618 | MATH |
[
{
"content": "Arrange the letters {'y': 2, 't': 2, 'm': 4, 'x': 4} into 4 uniquely identified boxes that can hold [5, 3, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 684 | MATH |
[
{
"content": "Distribute the letters {'w': 1, 'f': 4, 'x': 3, 'q': 4} among 4 distinguishable boxes with capacities [2, 3, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 906 | MATH |
[
{
"content": "You have {'u': 1, 'c': 4, 'v': 3, 'n': 4} and need to distribute them into 4 identical boxes with capacities [3, 3, 4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 466 | MATH |
[
{
"content": "You have {'z': 5, 'u': 2, 'x': 2, 'a': 3} and need to distribute them into 4 different boxes with capacities [3, 2, 3, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1031 | MATH |
[
{
"content": "Given the letters {'y': 4, 'w': 1, 't': 4, 'g': 3}, place them into 4 labeled boxes with sizes [2, 3, 5, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 684 | MATH |
[
{
"content": "You have {'v': 3, 'r': 3, 'c': 3, 'l': 3} and need to distribute them into 4 different boxes with capacities [2, 1, 6, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 604 | MATH |
[
{
"content": "Given the letters {'u': 2, 'n': 5, 'v': 2, 'j': 3}, place them into 4 labeled boxes with sizes [2, 3, 1, 6]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Distribute the letters {'q': 2, 'v': 3, 'n': 4, 'k': 3} among 4 identical containers that can hold [4, 3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 715 | MATH |
[
{
"content": "You have {'p': 5, 'g': 2, 'z': 3, 'r': 2} and need to distribute them into 4 different boxes with capacities [3, 2, 3, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1031 | MATH |
[
{
"content": "Distribute the letters {'s': 1, 'x': 5, 'i': 2, 'a': 4} among 4 identical containers that can hold [3, 5, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 217 | MATH |
[
{
"content": "Given the letters {'d': 4, 'w': 2, 'q': 4, 'u': 2}, place them into 4 labeled boxes with sizes [2, 3, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1172 | MATH |
[
{
"content": "You have {'y': 4, 'x': 3, 'o': 3, 'n': 2} and need to distribute them into 4 different boxes with capacities [6, 1, 2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 534 | MATH |
[
{
"content": "Arrange the letters {'j': 4, 'h': 3, 'w': 4, 'p': 1} into 4 undistinguishable boxes with capacities [5, 2, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 367 | MATH |
[
{
"content": "You have {'i': 3, 'n': 4, 'm': 3, 'y': 2} and need to distribute them into 4 identical boxes with capacities [3, 4, 1, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 458 | MATH |
[
{
"content": "Distribute the letters {'d': 2, 'i': 3, 'b': 3, 'y': 4} among 4 distinguishable boxes with capacities [6, 2, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 690 | MATH |
[
{
"content": "Divide the letters from {'p': 3, 'x': 2, 'g': 4, 'o': 3} into 4 undistinguishable boxes with sizes [3, 5, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 551 | MATH |
[
{
"content": "Arrange the letters {'e': 2, 'n': 2, 'p': 2, 'h': 6} into 4 uniquely identified boxes that can hold [3, 3, 2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 690 | MATH |
[
{
"content": "Arrange the letters {'t': 3, 'k': 2, 'l': 3, 'x': 4} into 4 undistinguishable boxes with capacities [2, 4, 2, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 316 | MATH |
[
{
"content": "Arrange the letters {'u': 3, 'v': 3, 'r': 5, 'o': 1} into 4 uniquely identified boxes that can hold [6, 4, 1, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 236 | MATH |
[
{
"content": "Divide the letters from {'p': 3, 'f': 3, 'r': 3, 'y': 3} into 4 undistinguishable boxes with sizes [4, 3, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 532 | MATH |
[
{
"content": "Given the letters {'a': 3, 'x': 3, 'g': 3, 'k': 3}, place them into 4 indistinguishable boxes with sizes [3, 3, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | MATH |
[
{
"content": "Given the letters {'e': 3, 't': 4, 'z': 3, 'u': 2}, place them into 4 labeled boxes with sizes [3, 4, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1395 | MATH |
[
{
"content": "Given the letters {'t': 2, 'z': 4, 'm': 2, 'g': 4}, place them into 4 indistinguishable boxes with sizes [2, 4, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 277 | MATH |
[
{
"content": "Divide the letters from {'h': 4, 'z': 1, 'b': 3, 'w': 4} into 4 undistinguishable boxes with sizes [4, 1, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 311 | MATH |
[
{
"content": "Distribute the letters {'s': 2, 'o': 4, 'q': 5, 'g': 1} among 4 distinguishable boxes with capacities [1, 3, 7, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 164 | MATH |
[
{
"content": "Divide the letters from {'s': 3, 'm': 2, 'c': 4, 'k': 3} into 4 distinctively labeled boxes with sizes [2, 5, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Distribute the letters {'u': 2, 'g': 2, 'l': 4, 'z': 4} among 4 identical containers that can hold [5, 1, 1, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "Given the letters {'z': 3, 'e': 2, 'v': 4, 'n': 3}, place them into 4 labeled boxes with sizes [3, 3, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1395 | MATH |
[
{
"content": "You have {'v': 4, 'z': 3, 'l': 3, 'j': 2} and need to distribute them into 4 different boxes with capacities [3, 4, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1395 | MATH |
[
{
"content": "Distribute the letters {'o': 3, 'b': 1, 'm': 3, 'w': 5} among 4 identical containers that can hold [4, 3, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 409 | MATH |
[
{
"content": "Distribute the letters {'x': 5, 'v': 4, 'j': 1, 'f': 2} among 4 identical containers that can hold [2, 3, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 347 | MATH |
[
{
"content": "Divide the letters from {'k': 1, 'l': 2, 'g': 4, 'r': 5} into 4 distinctively labeled boxes with sizes [6, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 382 | MATH |
[
{
"content": "Arrange the letters {'o': 3, 'n': 3, 'm': 4, 't': 2} into 4 undistinguishable boxes with capacities [3, 5, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 409 | MATH |
[
{
"content": "Divide the letters from {'x': 1, 'i': 3, 'c': 5, 'y': 3} into 4 distinctively labeled boxes with sizes [3, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 928 | MATH |
[
{
"content": "Divide the letters from {'u': 2, 'n': 3, 'v': 2, 'p': 5} into 4 undistinguishable boxes with sizes [1, 2, 4, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 528 | MATH |
[
{
"content": "Given the letters {'g': 4, 'd': 2, 'z': 4, 'v': 2}, place them into 4 indistinguishable boxes with sizes [3, 5, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 476 | MATH |
[
{
"content": "You have {'m': 2, 'h': 2, 'j': 5, 'e': 3} and need to distribute them into 4 identical boxes with capacities [1, 3, 1, 7]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 137 | MATH |
[
{
"content": "Arrange the letters {'j': 3, 'r': 4, 'i': 3, 'f': 2} into 4 undistinguishable boxes with capacities [2, 1, 5, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Divide the letters from {'e': 1, 'n': 5, 'b': 4, 'j': 2} into 4 distinctively labeled boxes with sizes [3, 5, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 528 | MATH |
[
{
"content": "Arrange the letters {'e': 4, 'h': 3, 'w': 4, 'b': 1} into 4 undistinguishable boxes with capacities [3, 2, 2, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 367 | MATH |
[
{
"content": "Arrange the letters {'w': 2, 'u': 2, 'h': 3, 'm': 5} into 4 undistinguishable boxes with capacities [4, 1, 2, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 528 | MATH |
[
{
"content": "Divide the letters from {'k': 4, 'v': 2, 'd': 3, 'm': 3} into 4 undistinguishable boxes with sizes [2, 2, 3, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 551 | MATH |
[
{
"content": "Given the letters {'h': 2, 'j': 4, 'b': 2, 'f': 4}, place them into 4 indistinguishable boxes with sizes [4, 3, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 607 | MATH |
[
{
"content": "Given the letters {'c': 2, 'j': 4, 'k': 4, 'b': 2}, place them into 4 indistinguishable boxes with sizes [1, 3, 3, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 354 | MATH |
[
{
"content": "You have {'j': 3, 'i': 1, 'z': 5, 'p': 3} and need to distribute them into 4 identical boxes with capacities [2, 5, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 331 | MATH |
[
{
"content": "Distribute the letters {'m': 2, 'j': 1, 'k': 5, 's': 4} among 4 distinguishable boxes with capacities [4, 2, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "You have {'b': 4, 'p': 3, 'm': 1, 'w': 4} and need to distribute them into 4 identical boxes with capacities [1, 2, 4, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 464 | MATH |
[
{
"content": "Arrange the letters {'f': 4, 'q': 4, 'u': 3, 's': 1} into 4 uniquely identified boxes that can hold [2, 4, 4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 774 | MATH |
[
{
"content": "Arrange the letters {'f': 3, 'u': 2, 'p': 2, 'd': 5} into 4 undistinguishable boxes with capacities [2, 2, 4, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 241 | MATH |
[
{
"content": "Given the letters {'m': 1, 'v': 5, 't': 3, 'b': 3}, place them into 4 labeled boxes with sizes [5, 3, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 618 | MATH |
[
{
"content": "You have {'y': 2, 'u': 4, 's': 2, 'j': 4} and need to distribute them into 4 different boxes with capacities [2, 4, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1172 | MATH |
[
{
"content": "Distribute the letters {'h': 3, 'i': 3, 'f': 1, 'x': 5} among 4 distinguishable boxes with capacities [3, 5, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 490 | MATH |
[
{
"content": "Divide the letters from {'z': 4, 'i': 3, 'u': 2, 'g': 3} into 4 distinctively labeled boxes with sizes [1, 2, 5, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Arrange the letters {'c': 3, 'z': 4, 't': 1, 'r': 4} into 4 undistinguishable boxes with capacities [5, 2, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 367 | MATH |
[
{
"content": "Arrange the letters {'q': 1, 'o': 2, 'a': 4, 'p': 5} into 4 undistinguishable boxes with capacities [2, 2, 3, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 286 | MATH |
[
{
"content": "Distribute the letters {'c': 4, 'l': 1, 'v': 3, 'o': 4} among 4 identical containers that can hold [2, 4, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 210 | MATH |
[
{
"content": "You have {'x': 2, 'q': 4, 'e': 4, 'n': 2} and need to distribute them into 4 identical boxes with capacities [1, 3, 3, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 354 | MATH |
[
{
"content": "Given the letters {'z': 3, 'd': 2, 'g': 4, 'h': 3}, place them into 4 indistinguishable boxes with sizes [3, 4, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 715 | MATH |
[
{
"content": "Arrange the letters {'m': 4, 'y': 2, 't': 1, 'r': 5} into 4 uniquely identified boxes that can hold [2, 4, 3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Arrange the letters {'b': 4, 'f': 3, 'c': 4, 'h': 1} into 4 uniquely identified boxes that can hold [2, 2, 6, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 471 | MATH |
[
{
"content": "Given the letters {'m': 6, 'g': 1, 'i': 1, 'e': 4}, place them into 4 indistinguishable boxes with sizes [2, 2, 2, 6]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Divide the letters from {'l': 3, 't': 2, 'm': 5, 'v': 2} into 4 distinctively labeled boxes with sizes [4, 3, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 684 | MATH |
[
{
"content": "Given the letters {'y': 1, 'e': 5, 'r': 3, 'l': 3}, place them into 4 indistinguishable boxes with sizes [4, 2, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 185 | MATH |
[
{
"content": "Given the letters {'j': 2, 't': 5, 'v': 2, 'n': 3}, place them into 4 labeled boxes with sizes [2, 4, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1031 | MATH |
[
{
"content": "Divide the letters from {'l': 5, 'o': 3, 'h': 1, 'w': 3} into 4 distinctively labeled boxes with sizes [4, 2, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 684 | MATH |
[
{
"content": "You have {'y': 1, 'w': 4, 'k': 3, 'x': 4} and need to distribute them into 4 identical boxes with capacities [2, 4, 4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 210 | MATH |
[
{
"content": "Distribute the letters {'d': 3, 'm': 2, 'y': 6, 'o': 1} among 4 distinguishable boxes with capacities [1, 6, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | MATH |
[
{
"content": "Distribute the letters {'j': 2, 'c': 4, 'v': 4, 'w': 2} among 4 identical containers that can hold [3, 3, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 607 | MATH |
[
{
"content": "Arrange the letters {'c': 1, 'p': 1, 'm': 7, 'q': 3} into 4 undistinguishable boxes with capacities [3, 3, 2, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 135 | MATH |
[
{
"content": "Divide the letters from {'e': 3, 'w': 3, 'v': 3, 'q': 3} into 4 distinctively labeled boxes with sizes [4, 4, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1060 | MATH |
[
{
"content": "You have {'h': 4, 't': 2, 'k': 2, 'b': 4} and need to distribute them into 4 identical boxes with capacities [2, 2, 3, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 476 | MATH |
[
{
"content": "You have {'b': 2, 't': 2, 'o': 6, 'q': 2} and need to distribute them into 4 different boxes with capacities [3, 3, 1, 5]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 441 | MATH |
[
{
"content": "Arrange the letters {'g': 1, 'p': 2, 'x': 5, 'l': 4} into 4 uniquely identified boxes that can hold [3, 3, 1, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 419 | MATH |
[
{
"content": "Arrange the letters {'g': 3, 'h': 3, 'c': 4, 'k': 2} into 4 undistinguishable boxes with capacities [5, 3, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 551 | MATH |
[
{
"content": "Arrange the letters {'w': 4, 'n': 4, 'd': 2, 'l': 2} into 4 uniquely identified boxes that can hold [4, 3, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1172 | MATH |
[
{
"content": "Distribute the letters {'p': 2, 'w': 3, 'a': 3, 'd': 4} among 4 identical containers that can hold [4, 2, 1, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Divide the letters from {'m': 2, 'p': 3, 'x': 4, 'h': 3} into 4 distinctively labeled boxes with sizes [1, 6, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 534 | MATH |
[
{
"content": "Given the letters {'a': 2, 'm': 4, 'l': 3, 'o': 3}, place them into 4 labeled boxes with sizes [2, 3, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1395 | MATH |
[
{
"content": "You have {'f': 2, 'o': 4, 'c': 4, 'p': 2} and need to distribute them into 4 identical boxes with capacities [3, 4, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 607 | MATH |
[
{
"content": "You have {'o': 2, 'k': 5, 'c': 4, 'x': 1} and need to distribute them into 4 different boxes with capacities [4, 3, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 670 | MATH |
[
{
"content": "Divide the letters from {'m': 3, 'k': 1, 'o': 4, 's': 4} into 4 undistinguishable boxes with sizes [4, 1, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 464 | MATH |
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