messages listlengths 1 1 | ground_truth stringclasses 93 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "You have {'h': 3, 's': 2, 'c': 3, 'a': 3} and need to distribute them into 4 different boxes with capacities [2, 2, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 894 | MATH |
[
{
"content": "Divide the letters from {'u': 3, 'i': 3, 'd': 3, 'b': 2} into 4 undistinguishable boxes with sizes [1, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 349 | MATH |
[
{
"content": "Distribute the letters {'l': 4, 'm': 2, 'd': 2, 'c': 3} among 4 identical containers that can hold [4, 3, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
[
{
"content": "Given the letters {'f': 1, 'j': 4, 'q': 2, 'r': 4}, place them into 4 indistinguishable boxes with sizes [1, 3, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 199 | MATH |
[
{
"content": "Given the letters {'j': 3, 'q': 2, 'm': 3, 'n': 3}, place them into 4 labeled boxes with sizes [5, 3, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 495 | MATH |
[
{
"content": "Arrange the letters {'g': 4, 'c': 2, 'w': 2, 'n': 3} into 4 uniquely identified boxes that can hold [3, 5, 2, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 431 | MATH |
[
{
"content": "You have {'s': 3, 'd': 3, 'v': 3, 'y': 2} and need to distribute them into 4 identical boxes with capacities [4, 2, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 474 | MATH |
[
{
"content": "Divide the letters from {'w': 3, 'o': 2, 'l': 2, 'c': 4} into 4 undistinguishable boxes with sizes [3, 3, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 298 | MATH |
[
{
"content": "Arrange the letters {'a': 3, 'h': 3, 'm': 2, 'x': 3} into 4 undistinguishable boxes with capacities [3, 4, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 474 | MATH |
[
{
"content": "Distribute the letters {'h': 3, 'o': 3, 'v': 2, 'c': 3} among 4 identical containers that can hold [1, 2, 4, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 285 | MATH |
[
{
"content": "You have {'l': 3, 'k': 2, 't': 3, 'c': 3} and need to distribute them into 4 identical boxes with capacities [3, 3, 1, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 349 | MATH |
[
{
"content": "You have {'i': 2, 'j': 3, 'v': 4, 'u': 2} and need to distribute them into 4 different boxes with capacities [2, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 894 | MATH |
[
{
"content": "Divide the letters from {'z': 2, 'i': 5, 'v': 2, 'k': 2} into 4 undistinguishable boxes with sizes [2, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 304 | MATH |
[
{
"content": "You have {'m': 2, 'q': 4, 'g': 4, 'y': 1} and need to distribute them into 4 identical boxes with capacities [2, 3, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 263 | MATH |
[
{
"content": "Given the letters {'w': 1, 'e': 4, 'c': 5, 'j': 1}, place them into 4 labeled boxes with sizes [3, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 315 | MATH |
[
{
"content": "Divide the letters from {'q': 7, 'z': 1, 'd': 1, 'i': 2} into 4 undistinguishable boxes with sizes [4, 2, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "Arrange the letters {'h': 1, 'z': 2, 'p': 5, 'i': 3} into 4 uniquely identified boxes that can hold [4, 3, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 431 | MATH |
[
{
"content": "Arrange the letters {'j': 3, 'g': 2, 'm': 3, 't': 3} into 4 undistinguishable boxes with capacities [4, 1, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 285 | MATH |
[
{
"content": "Divide the letters from {'u': 2, 'f': 4, 'd': 2, 'q': 3} into 4 distinctively labeled boxes with sizes [2, 2, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 562 | MATH |
[
{
"content": "Given the letters {'s': 3, 'n': 1, 'q': 4, 'x': 3}, place them into 4 labeled boxes with sizes [2, 4, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 579 | MATH |
[
{
"content": "Given the letters {'f': 2, 'b': 4, 'm': 4, 'g': 1}, place them into 4 indistinguishable boxes with sizes [3, 1, 2, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 295 | MATH |
[
{
"content": "Arrange the letters {'a': 4, 'k': 3, 'o': 3, 'x': 1} into 4 uniquely identified boxes that can hold [2, 2, 2, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Divide the letters from {'c': 4, 'x': 2, 'r': 3, 'j': 2} into 4 distinctively labeled boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 755 | MATH |
[
{
"content": "Divide the letters from {'r': 4, 'l': 3, 'y': 3, 't': 1} into 4 distinctively labeled boxes with sizes [4, 1, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 456 | MATH |
[
{
"content": "Distribute the letters {'t': 2, 'i': 2, 'k': 6, 'e': 1} among 4 identical containers that can hold [1, 2, 3, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 198 | MATH |
[
{
"content": "Arrange the letters {'t': 2, 'd': 2, 'g': 2, 'u': 5} into 4 uniquely identified boxes that can hold [3, 3, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 645 | MATH |
[
{
"content": "You have {'j': 3, 's': 1, 'a': 2, 'w': 5} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 175 | MATH |
[
{
"content": "Given the letters {'y': 4, 's': 2, 'e': 3, 'u': 2}, place them into 4 labeled boxes with sizes [1, 3, 5, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 431 | MATH |
[
{
"content": "Divide the letters from {'m': 3, 'r': 3, 'f': 2, 'd': 3} into 4 undistinguishable boxes with sizes [4, 3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 349 | MATH |
[
{
"content": "Distribute the letters {'o': 5, 'b': 2, 'n': 3, 'u': 1} among 4 identical containers that can hold [4, 3, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 175 | MATH |
[
{
"content": "You have {'g': 3, 'h': 5, 'q': 2, 'z': 1} and need to distribute them into 4 different boxes with capacities [1, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
[
{
"content": "Distribute the letters {'r': 2, 'n': 4, 'd': 1, 'q': 4} among 4 identical containers that can hold [4, 2, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 263 | MATH |
[
{
"content": "Arrange the letters {'s': 1, 'i': 4, 'd': 1, 'r': 5} into 4 undistinguishable boxes with capacities [3, 1, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "Given the letters {'h': 3, 'x': 6, 'v': 1, 'c': 1}, place them into 4 labeled boxes with sizes [2, 2, 6, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "Arrange the letters {'g': 3, 's': 6, 'h': 1, 'f': 1} into 4 uniquely identified boxes that can hold [4, 2, 1, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 163 | MATH |
[
{
"content": "Divide the letters from {'t': 2, 'j': 3, 'k': 3, 'd': 3} into 4 undistinguishable boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 190 | MATH |
[
{
"content": "You have {'d': 2, 'r': 3, 'q': 3, 'g': 3} and need to distribute them into 4 different boxes with capacities [3, 1, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 685 | MATH |
[
{
"content": "Arrange the letters {'g': 2, 'b': 2, 'n': 3, 'k': 4} into 4 undistinguishable boxes with capacities [1, 3, 5, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 431 | MATH |
[
{
"content": "Divide the letters from {'x': 3, 'r': 2, 'k': 3, 'f': 3} into 4 undistinguishable boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 190 | MATH |
[
{
"content": "Given the letters {'m': 5, 'h': 2, 'z': 3, 'l': 1}, place them into 4 indistinguishable boxes with sizes [4, 1, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 175 | MATH |
[
{
"content": "Given the letters {'m': 3, 'h': 3, 'v': 2, 'c': 3}, place them into 4 indistinguishable boxes with sizes [1, 2, 5, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 495 | MATH |
[
{
"content": "Given the letters {'l': 4, 'd': 3, 'e': 2, 'j': 2}, place them into 4 labeled boxes with sizes [2, 3, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 755 | MATH |
[
{
"content": "Arrange the letters {'l': 2, 't': 2, 'x': 1, 's': 6} into 4 undistinguishable boxes with capacities [3, 2, 5, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 198 | MATH |
[
{
"content": "You have {'i': 2, 'n': 5, 'x': 2, 'd': 2} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "You have {'w': 4, 'm': 3, 'x': 2, 'i': 2} and need to distribute them into 4 different boxes with capacities [3, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 894 | MATH |
[
{
"content": "You have {'g': 2, 'x': 4, 'v': 4, 'l': 1} and need to distribute them into 4 different boxes with capacities [1, 4, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 385 | MATH |
[
{
"content": "Divide the letters from {'r': 3, 'v': 2, 'c': 3, 's': 3} into 4 distinctively labeled boxes with sizes [2, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 894 | MATH |
[
{
"content": "Divide the letters from {'a': 2, 'c': 1, 'f': 6, 'v': 2} into 4 distinctively labeled boxes with sizes [3, 3, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 231 | MATH |
[
{
"content": "Distribute the letters {'q': 2, 'a': 3, 'j': 2, 's': 4} among 4 identical containers that can hold [4, 2, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
[
{
"content": "Distribute the letters {'e': 2, 'r': 3, 'a': 2, 'k': 4} among 4 distinguishable boxes with capacities [1, 4, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 489 | MATH |
[
{
"content": "Arrange the letters {'f': 2, 'g': 5, 'c': 1, 'u': 3} into 4 undistinguishable boxes with capacities [2, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Given the letters {'w': 1, 'a': 2, 'u': 4, 'p': 4}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | MATH |
[
{
"content": "You have {'i': 5, 'v': 3, 'k': 2, 'o': 1} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 175 | MATH |
[
{
"content": "Divide the letters from {'l': 3, 'u': 3, 'd': 2, 'm': 3} into 4 distinctively labeled boxes with sizes [1, 4, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 567 | MATH |
[
{
"content": "Divide the letters from {'e': 2, 'k': 2, 'd': 2, 't': 5} into 4 distinctively labeled boxes with sizes [4, 2, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 562 | MATH |
[
{
"content": "Given the letters {'o': 2, 'i': 3, 'w': 4, 'n': 2}, place them into 4 indistinguishable boxes with sizes [3, 4, 3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 298 | MATH |
[
{
"content": "Distribute the letters {'i': 1, 's': 2, 'f': 4, 'o': 4} among 4 identical containers that can hold [3, 1, 5, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 295 | MATH |
[
{
"content": "Distribute the letters {'s': 2, 'n': 3, 'q': 5, 'c': 1} among 4 distinguishable boxes with capacities [3, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 431 | MATH |
[
{
"content": "Distribute the letters {'n': 3, 'd': 5, 'z': 2, 'k': 1} among 4 distinguishable boxes with capacities [4, 2, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 431 | MATH |
[
{
"content": "Given the letters {'r': 2, 'm': 1, 't': 5, 's': 3}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Arrange the letters {'g': 3, 'x': 4, 'u': 2, 'e': 2} into 4 uniquely identified boxes that can hold [2, 2, 4, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 755 | MATH |
[
{
"content": "Arrange the letters {'o': 2, 'z': 2, 'r': 3, 'y': 4} into 4 uniquely identified boxes that can hold [4, 2, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 755 | MATH |
[
{
"content": "Distribute the letters {'t': 3, 'v': 1, 'x': 3, 'a': 4} among 4 identical containers that can hold [2, 5, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
[
{
"content": "Given the letters {'j': 1, 'r': 4, 'c': 4, 'g': 2}, place them into 4 indistinguishable boxes with sizes [3, 2, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 263 | MATH |
[
{
"content": "You have {'v': 2, 'c': 2, 'p': 5, 'm': 2} and need to distribute them into 4 different boxes with capacities [4, 1, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Distribute the letters {'t': 5, 'z': 1, 'd': 2, 'f': 3} among 4 identical containers that can hold [2, 3, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Arrange the letters {'v': 4, 'w': 3, 'n': 2, 'c': 2} into 4 undistinguishable boxes with capacities [2, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162 | MATH |
[
{
"content": "Given the letters {'k': 4, 'h': 4, 'f': 2, 't': 1}, place them into 4 indistinguishable boxes with sizes [3, 3, 4, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 199 | MATH |
[
{
"content": "You have {'e': 3, 'n': 3, 'a': 4, 'l': 1} and need to distribute them into 4 identical boxes with capacities [4, 3, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 308 | MATH |
[
{
"content": "Given the letters {'q': 2, 'n': 3, 'k': 5, 't': 1}, place them into 4 indistinguishable boxes with sizes [2, 3, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "You have {'n': 4, 'a': 1, 'i': 3, 'r': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 5, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | MATH |
[
{
"content": "Distribute the letters {'b': 2, 'd': 3, 'w': 3, 'j': 3} among 4 distinguishable boxes with capacities [5, 1, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 315 | MATH |
[
{
"content": "Given the letters {'k': 1, 'h': 3, 'd': 3, 'p': 4}, place them into 4 indistinguishable boxes with sizes [4, 2, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 308 | MATH |
[
{
"content": "Given the letters {'c': 4, 'a': 1, 'r': 3, 'y': 3}, place them into 4 labeled boxes with sizes [3, 5, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
[
{
"content": "Arrange the letters {'o': 4, 'k': 4, 'a': 2, 'd': 1} into 4 uniquely identified boxes that can hold [2, 1, 3, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 295 | MATH |
[
{
"content": "Divide the letters from {'h': 4, 'x': 3, 'i': 2, 'r': 2} into 4 distinctively labeled boxes with sizes [3, 4, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 755 | MATH |
[
{
"content": "You have {'f': 2, 'q': 2, 'v': 2, 'j': 5} and need to distribute them into 4 different boxes with capacities [4, 5, 1, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 223 | MATH |
[
{
"content": "Divide the letters from {'p': 1, 'f': 3, 'g': 4, 'a': 3} into 4 distinctively labeled boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 685 | MATH |
[
{
"content": "Distribute the letters {'w': 2, 'i': 3, 'c': 4, 'a': 2} among 4 distinguishable boxes with capacities [2, 2, 2, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 562 | MATH |
[
{
"content": "Divide the letters from {'s': 2, 'k': 2, 'b': 4, 'd': 3} into 4 distinctively labeled boxes with sizes [1, 3, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 579 | MATH |
[
{
"content": "Distribute the letters {'j': 3, 'k': 2, 'g': 5, 'v': 1} among 4 identical containers that can hold [3, 3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Distribute the letters {'m': 3, 'o': 2, 'x': 3, 'r': 3} among 4 distinguishable boxes with capacities [2, 2, 2, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 645 | MATH |
[
{
"content": "Given the letters {'z': 3, 'y': 3, 'k': 4, 'd': 1}, place them into 4 indistinguishable boxes with sizes [2, 2, 6, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123 | MATH |
[
{
"content": "You have {'g': 3, 'e': 3, 'u': 2, 'p': 3} and need to distribute them into 4 different boxes with capacities [2, 4, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 894 | MATH |
[
{
"content": "Distribute the letters {'k': 3, 'v': 2, 'o': 5, 'j': 1} among 4 identical containers that can hold [2, 3, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "You have {'j': 2, 'e': 5, 'n': 2, 'i': 2} and need to distribute them into 4 different boxes with capacities [1, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Distribute the letters {'v': 2, 'r': 3, 'q': 3, 'o': 3} among 4 identical containers that can hold [1, 4, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 349 | MATH |
[
{
"content": "Given the letters {'y': 1, 'u': 3, 'p': 3, 't': 4}, place them into 4 labeled boxes with sizes [4, 2, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 579 | MATH |
[
{
"content": "Distribute the letters {'m': 4, 'b': 3, 'x': 2, 'w': 2} among 4 distinguishable boxes with capacities [3, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 755 | MATH |
[
{
"content": "You have {'m': 1, 'c': 6, 's': 2, 'e': 2} and need to distribute them into 4 identical boxes with capacities [4, 2, 1, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "Given the letters {'a': 5, 'k': 1, 'c': 2, 'h': 3}, place them into 4 indistinguishable boxes with sizes [3, 1, 2, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 270 | MATH |
[
{
"content": "Divide the letters from {'h': 4, 't': 3, 'r': 2, 's': 2} into 4 undistinguishable boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162 | MATH |
[
{
"content": "Arrange the letters {'x': 4, 'g': 2, 'w': 1, 'f': 4} into 4 undistinguishable boxes with capacities [3, 4, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 263 | MATH |
[
{
"content": "You have {'v': 2, 'h': 2, 'a': 3, 'e': 4} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162 | MATH |
[
{
"content": "Given the letters {'f': 4, 'h': 3, 'c': 2, 'x': 2}, place them into 4 labeled boxes with sizes [3, 2, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 894 | MATH |
[
{
"content": "You have {'k': 2, 'i': 2, 'q': 4, 'e': 3} and need to distribute them into 4 different boxes with capacities [3, 4, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 755 | MATH |
[
{
"content": "You have {'k': 3, 'a': 2, 'y': 2, 'd': 4} and need to distribute them into 4 identical boxes with capacities [1, 2, 2, 6]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "Arrange the letters {'f': 5, 'v': 1, 'd': 2, 'n': 3} into 4 undistinguishable boxes with capacities [4, 4, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 149 | MATH |
[
{
"content": "Arrange the letters {'s': 3, 't': 2, 'c': 4, 'a': 2} into 4 undistinguishable boxes with capacities [2, 6, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "Divide the letters from {'u': 4, 'b': 3, 'e': 3, 'd': 1} into 4 distinctively labeled boxes with sizes [2, 1, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.