messages listlengths 1 1 | ground_truth stringclasses 3 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Arrange the letters {'f': 3, 'n': 1} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'u': 3, 'm': 1} into 2 undistinguishable boxes with capacities [3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'f': 3, 'l': 1} into 2 uniquely identified boxes that can hold [3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'w': 2, 'l': 2} into 2 distinctively labeled boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'o': 1, 'c': 3} into 2 undistinguishable boxes with sizes [3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'r': 1, 'y': 3} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'n': 2, 'd': 2} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'w': 3, 'z': 1} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "You have {'s': 2, 'u': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'o': 3, 'm': 1} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'p': 3, 'l': 1}, place them into 2 labeled boxes with sizes [1, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'j': 1, 'n': 3} among 2 identical containers that can hold [1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'p': 2, 'd': 2}, 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}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Given the letters {'f': 2, 'h': 2}, 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}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Arrange the letters {'n': 2, 't': 2} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'v': 1, 'l': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'j': 3, 'l': 1} among 2 identical containers that can hold [1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'u': 1, 'h': 3}, 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'w': 3, 'y': 1} and need to distribute them into 2 identical boxes with capacities [3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'t': 3, 'j': 1} 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Arrange the letters {'g': 3, 'y': 1} into 2 undistinguishable boxes with capacities [3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'n': 3, 'h': 1} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'r': 3, 'o': 1}, 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Distribute the letters {'i': 3, 'x': 1} among 2 distinguishable boxes with capacities [3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'k': 2, 'a': 2} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Arrange the letters {'e': 3, 'l': 1} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'a': 2, 's': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'y': 2, 'a': 2} 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}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Divide the letters from {'q': 2, 's': 2} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Arrange the letters {'f': 2, 'k': 2} 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}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Arrange the letters {'v': 3, 's': 1} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'s': 1, 't': 3} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'q': 2, 'c': 2} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'f': 2, 'j': 2}, 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'b': 2, 'v': 2}, 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}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Given the letters {'l': 2, 'y': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'s': 2, 'u': 2} into 2 distinctively labeled boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'s': 1, 'n': 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Divide the letters from {'z': 1, 'x': 3} into 2 undistinguishable boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'y': 3, 'j': 1} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'f': 2, 'p': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'t': 2, 'l': 2} among 2 distinguishable boxes with capacities [2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Arrange the letters {'t': 2, 'w': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'g': 1, 'n': 3}, 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Distribute the letters {'h': 2, 's': 2} among 2 distinguishable boxes with capacities [1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'o': 3, 'g': 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Distribute the letters {'w': 2, 'n': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'m': 1, 'u': 3} into 2 distinctively labeled boxes with sizes [3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'d': 2, 'y': 2}, place them into 2 indistinguishable boxes with sizes [3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'u': 1, 'b': 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Distribute the letters {'u': 2, 'e': 2} among 2 distinguishable boxes with capacities [2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "You have {'d': 2, 'q': 2} and need to distribute them into 2 different boxes with capacities [3, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'t': 3, 'm': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'i': 1, 'k': 3} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Arrange the letters {'t': 2, 'a': 2} into 2 undistinguishable boxes with capacities [3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'j': 2, 'd': 2} and need to distribute them into 2 identical boxes with capacities [3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'b': 3, 'o': 1} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'j': 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}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Arrange the letters {'i': 2, 'q': 2} into 2 uniquely identified boxes that can hold [3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'z': 2, 'e': 2} among 2 identical containers that can hold [1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'o': 1, 'p': 3} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'n': 2, 'x': 2} into 2 undistinguishable boxes with capacities [3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'l': 3, 'v': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'p': 1, 'x': 3} and need to distribute them into 2 identical boxes with capacities [1, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'n': 2, 'o': 2} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'b': 2, 'k': 2} into 2 undistinguishable boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'p': 3, 'h': 1} into 2 undistinguishable boxes with sizes [3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'b': 1, 'q': 3} among 2 identical containers that can hold [1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'p': 2, 'v': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'h': 2, 'z': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'i': 2, 'c': 2} and need to distribute them into 2 different boxes with capacities [3, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'n': 1, 'd': 3} among 2 distinguishable boxes with capacities [2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'b': 3, 'm': 1} into 2 undistinguishable boxes with capacities [3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'e': 3, 'x': 1} among 2 identical containers that can hold [1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'d': 2, 'k': 2} into 2 distinctively labeled boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'y': 2, 't': 2} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'v': 3, 'j': 1}, 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Given the letters {'o': 3, 'f': 1}, place them into 2 indistinguishable boxes with sizes [3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'s': 2, 'b': 2}, place them into 2 indistinguishable boxes with sizes [3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'l': 2, 's': 2} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Given the letters {'d': 3, 'm': 1}, 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Arrange the letters {'h': 1, 'd': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'k': 3, 'j': 1} into 2 distinctively labeled boxes with sizes [3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'p': 1, 'y': 3} 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Divide the letters from {'a': 2, 'b': 2} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Arrange the letters {'d': 2, 'n': 2} into 2 undistinguishable boxes with capacities [3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'y': 3, 's': 1} among 2 distinguishable boxes with capacities [1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'a': 3, 'h': 1} into 2 uniquely identified boxes that can hold [3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'s': 2, 'v': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'f': 2, 'x': 2} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Given the letters {'b': 1, 'm': 3}, 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}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Divide the letters from {'i': 3, 'l': 1} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'l': 2, 'u': 2} into 2 undistinguishable boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'m': 2, 'j': 2} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "You have {'s': 2, 'j': 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'b': 1, 'f': 3} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'k': 1, 'j': 3} 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}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'d': 3, 'z': 1} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Arrange the letters {'z': 2, 'w': 2} into 2 undistinguishable boxes with capacities [3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'b': 3, 'k': 1} 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}",
"role": "user"
}
] | 2 | MATH |
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