{"messages": [{"content": "You have {'z': 3, 'l': 4, 'k': 1, 'w': 4} and need to distribute them into 4 identical boxes with capacities [2, 3, 2, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'm': 3, 'o': 4, 'v': 2}, place them into 4 labeled boxes with sizes [3, 2, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 2, 'j': 1, 'i': 3, 'z': 6}, place them into 4 indistinguishable boxes with sizes [3, 1, 1, 7]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 2, 'r': 4, 'i': 2, 'c': 4}, place them into 4 indistinguishable boxes with sizes [4, 1, 2, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 3, 'k': 2, 'o': 2, 'm': 5} and need to distribute them into 4 different boxes with capacities [2, 1, 5, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 1, 'l': 4, 'z': 4, 'y': 3} and need to distribute them into 4 identical boxes with capacities [3, 4, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 4, 'u': 1, 'z': 2, 'o': 5} and need to distribute them into 4 different boxes with capacities [1, 4, 5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 2, 'b': 3, 'm': 3, 'k': 4} into 4 distinctively labeled boxes with sizes [3, 2, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 1, 'p': 3, 'q': 2, 'c': 6} and need to distribute them into 4 identical boxes with capacities [4, 2, 5, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 4, 'b': 3, 'v': 4, 'z': 1}, place them into 4 indistinguishable boxes with sizes [1, 4, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 2, 'w': 3, 'v': 6, 'a': 1} among 4 identical containers that can hold [2, 4, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 3, 'i': 5, 'w': 1, 'y': 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"}], "ground_truth": "331", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'a': 3, 'y': 4, 'i': 4, 'p': 1} into 4 undistinguishable boxes with sizes [4, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 2, 't': 5, 's': 3, 'y': 2} and need to distribute them into 4 identical boxes with capacities [4, 2, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 3, 'e': 4, 'j': 3, 'c': 2} among 4 distinguishable boxes with capacities [5, 2, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 3, 'u': 1, 'b': 3, 'm': 5} and need to distribute them into 4 identical boxes with capacities [2, 2, 5, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "331", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 3, 'x': 6, 's': 1, 'b': 2}, place them into 4 indistinguishable boxes with sizes [3, 2, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 5, 'v': 3, 'g': 3, 't': 1} into 4 undistinguishable boxes with sizes [4, 2, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 1, 'w': 3, 'r': 3, 'u': 5} among 4 distinguishable boxes with capacities [1, 3, 5, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 3, 'q': 1, 'b': 4, 'r': 4} into 4 uniquely identified boxes that can hold [4, 2, 2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 4, 'p': 3, 'g': 2, 'b': 3} into 4 uniquely identified boxes that can hold [2, 6, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 4, 't': 3, 'x': 3, 'n': 2}, place them into 4 labeled boxes with sizes [4, 4, 1, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'm': 2, 'g': 4, 'e': 4} and need to distribute them into 4 identical boxes with capacities [2, 3, 5, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 2, 'w': 4, 'b': 2, 'p': 4} among 4 identical containers that can hold [4, 3, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "394", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 2, 'j': 4, 'x': 2, 'b': 4} into 4 undistinguishable boxes with sizes [3, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 3, 'l': 1, 'y': 4, 'z': 4} among 4 identical containers that can hold [3, 4, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 4, 'h': 2, 'n': 4, 'k': 2} into 4 uniquely identified boxes that can hold [3, 3, 4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 3, 'q': 3, 'y': 3, 'm': 3} and need to distribute them into 4 different boxes with capacities [4, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 3, 't': 2, 'p': 4, 'a': 3} into 4 undistinguishable boxes with sizes [4, 2, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 3, 'v': 2, 'j': 4, 'p': 3} among 4 identical containers that can hold [4, 1, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'m': 3, 'n': 4, 'v': 2, 'h': 3} 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"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 3, 'l': 3, 'v': 1, 'u': 5} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 2, 'z': 3, 'o': 3, 'q': 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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 2, 'm': 2, 'o': 5, 'd': 3} among 4 identical containers that can hold [6, 2, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 3, 'i': 3, 'm': 3, 'h': 3} among 4 distinguishable boxes with capacities [4, 3, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1060", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 4, 's': 2, 'l': 3, 'y': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 4, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 'l': 4, 'a': 3, 'o': 2} and need to distribute them into 4 different boxes with capacities [4, 2, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 3, 'd': 1, 'n': 3, 'i': 5} and need to distribute them into 4 different boxes with capacities [3, 6, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 5, 'n': 2, 't': 2, 'd': 3} 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"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 2, 'p': 4, 'b': 4, 'm': 2} among 4 distinguishable boxes with capacities [2, 3, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 3, 'x': 2, 'g': 4, 'c': 3} among 4 identical containers that can hold [3, 3, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 4, 'a': 4, 'v': 2, 'u': 2} into 4 distinctively labeled boxes with sizes [4, 1, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 1, 'd': 4, 'z': 5, 'y': 2} into 4 uniquely identified boxes that can hold [3, 3, 4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 2, 'p': 5, 'g': 2, 'w': 3} into 4 undistinguishable boxes with sizes [5, 4, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 5, 'i': 2, 'w': 2, 'r': 3} and need to distribute them into 4 identical boxes with capacities [4, 2, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 3, 'o': 4, 'c': 1, 'y': 4} into 4 distinctively labeled boxes with sizes [5, 3, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 3, 'k': 2, 'v': 4, 'j': 3}, place them into 4 indistinguishable boxes with sizes [2, 5, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 5, 'd': 3, 'm': 3, 'c': 1} 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"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'m': 3, 'b': 3, 'f': 2, 'v': 4} into 4 undistinguishable boxes with capacities [2, 4, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'v': 3, 'u': 2, 'x': 2, 'e': 5} into 4 undistinguishable boxes with sizes [5, 1, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 2, 'u': 2, 'r': 5, 'p': 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"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 3, 'l': 3, 'q': 3, 'r': 3} into 4 undistinguishable boxes with sizes [2, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 4, 'b': 4, 'z': 3, 't': 1} and need to distribute them into 4 identical boxes with capacities [3, 3, 5, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'r': 3, 'a': 3, 'y': 3} into 4 uniquely identified boxes that can hold [2, 6, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 5, 't': 2, 'g': 3, 'w': 2} among 4 distinguishable boxes with capacities [4, 4, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 3, 'l': 4, 'z': 2, 'm': 3}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 2, 'z': 4, 'j': 3, 'f': 3} and need to distribute them into 4 different boxes with capacities [4, 4, 1, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 4, 'x': 2, 'k': 3, 'n': 3} into 4 distinctively labeled boxes with sizes [3, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 3, 'j': 5, 'c': 3, 'i': 1} 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"}], "ground_truth": "273", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'm': 3, 'h': 5, 'b': 2} 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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 3, 'z': 3, 'x': 4, 'u': 2} into 4 distinctively labeled boxes with sizes [2, 2, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 3, 'm': 3, 'a': 3, 'u': 3}, place them into 4 labeled boxes with sizes [4, 2, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 1, 'm': 4, 'h': 5, 'b': 2} and need to distribute them into 4 identical boxes with capacities [1, 7, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 2, 'y': 3, 'q': 2, 's': 5} into 4 undistinguishable boxes with capacities [1, 5, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 3, 'd': 5, 'h': 1, 'y': 3} into 4 distinctively labeled boxes with sizes [2, 2, 4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 3, 'c': 2, 'v': 3, 'x': 4} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'm': 3, 'w': 4, 'p': 2} into 4 undistinguishable boxes with capacities [3, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 1, 'a': 5, 'p': 3, 'n': 3} among 4 distinguishable boxes with capacities [5, 4, 2, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 5, 'f': 2, 's': 1, 'k': 4} 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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 2, 'j': 3, 'l': 3, 'c': 4}, place them into 4 indistinguishable boxes with sizes [4, 6, 1, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 2, 'm': 4, 't': 2, 'v': 4} and need to distribute them into 4 identical boxes with capacities [3, 1, 3, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 4, 'r': 4, 'u': 2, 'q': 2} and need to distribute them into 4 identical boxes with capacities [5, 2, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 1, 'e': 2, 'w': 4, 'n': 5}, place them into 4 labeled boxes with sizes [4, 3, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 6, 'e': 1, 'm': 2, 'r': 3} among 4 distinguishable boxes with capacities [4, 4, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 4, 'm': 2, 'g': 3, 'p': 3} into 4 undistinguishable boxes with sizes [3, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 3, 'g': 3, 'e': 3, 'x': 3} 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"}], "ground_truth": "844", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 5, 'j': 5, 'b': 1, 't': 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"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 6, 'j': 2, 'b': 2, 'y': 2} and need to distribute them into 4 different boxes with capacities [5, 4, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'g': 4, 'k': 3, 'm': 2}, place them into 4 labeled boxes with sizes [2, 4, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 4, 'v': 2, 's': 3, 'z': 3} into 4 uniquely identified boxes that can hold [2, 3, 3, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 2, 'g': 5, 'z': 4, 'o': 1} among 4 distinguishable boxes with capacities [6, 1, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 4, 'j': 2, 'q': 2, 'a': 4}, place them into 4 labeled boxes with sizes [3, 2, 2, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 2, 'c': 2, 'r': 4, 'y': 4} among 4 distinguishable boxes with capacities [5, 2, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 2, 'x': 5, 'y': 3, 'q': 2}, place them into 4 labeled boxes with sizes [5, 2, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 3, 'v': 2, 'f': 3, 'l': 4} among 4 distinguishable boxes with capacities [1, 4, 2, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 3, 'y': 2, 'm': 5, 'u': 2} among 4 distinguishable boxes with capacities [3, 3, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 3, 'z': 1, 'p': 4, 'q': 4} into 4 distinctively labeled boxes with sizes [4, 3, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 2, 'c': 4, 'h': 3, 'g': 3} among 4 distinguishable boxes with capacities [2, 5, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 4, 'y': 1, 'l': 4, 'a': 3} 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"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 3, 'e': 3, 'f': 1, 's': 5} into 4 distinctively labeled boxes with sizes [2, 4, 5, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 3, 'h': 2, 'e': 4, 'd': 3} and need to distribute them into 4 different boxes with capacities [4, 2, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 3, 's': 4, 'g': 3, 'n': 2} and need to distribute them into 4 identical boxes with capacities [4, 4, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 3, 'f': 3, 'd': 3, 'a': 3} 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"}], "ground_truth": "472", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 4, 'x': 2, 't': 4, 'i': 2} and need to distribute them into 4 different boxes with capacities [4, 4, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1002", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 4, 'x': 2, 'z': 4, 'g': 2} among 4 distinguishable boxes with capacities [2, 4, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 3, 'k': 3, 'r': 3, 'p': 3} into 4 distinctively labeled boxes with sizes [4, 2, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1374", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 4, 'a': 3, 'l': 1, 'n': 4} among 4 distinguishable boxes with capacities [4, 3, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 6, 'i': 3, 'd': 1, 's': 2} and need to distribute them into 4 different boxes with capacities [5, 3, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 3, 'a': 3, 'o': 4, 'm': 2}, place them into 4 labeled boxes with sizes [1, 2, 6, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 4, 'h': 2, 'c': 2, 'd': 4} among 4 identical containers that can hold [7, 1, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 5, 'q': 3, 'o': 3, 'b': 1} 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"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 3, 'i': 3, 'o': 3, 'c': 3} 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"}], "ground_truth": "844", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 3, 'y': 2, 'e': 2, 'j': 5} into 4 distinctively labeled boxes with sizes [3, 2, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 3, 'x': 1, 'k': 3, 'y': 5} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 3, 'd': 3, 'i': 3, 'z': 3}, place them into 4 labeled boxes with sizes [2, 3, 6, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'v': 2, 'h': 2, 'm': 5, 'n': 3} into 4 distinctively labeled boxes with sizes [5, 4, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 3, 'v': 3, 'd': 4, 'y': 2} into 4 uniquely identified boxes that can hold [1, 5, 4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 4, 'd': 3, 'r': 3, 'l': 2} among 4 distinguishable boxes with capacities [1, 5, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 5, 'l': 3, 'r': 2, 'v': 2} into 4 distinctively labeled boxes with sizes [5, 2, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 1, 'x': 5, 'w': 2, 't': 4} and need to distribute them into 4 identical boxes with capacities [3, 2, 3, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 6, 'j': 1, 'a': 2, 'y': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 2, 6]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 3, 'o': 3, 'q': 2, 'f': 4}, place them into 4 indistinguishable boxes with sizes [3, 4, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 3, 'x': 2, 'n': 1, 'g': 6} and need to distribute them into 4 different boxes with capacities [3, 2, 2, 5]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'e': 5, 'g': 2, 'o': 2}, place them into 4 labeled boxes with sizes [4, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 1, 'c': 2, 'd': 6, 's': 3}, place them into 4 labeled boxes with sizes [4, 5, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 4, 'e': 1, 'm': 3, 'x': 4}, place them into 4 indistinguishable boxes with sizes [3, 2, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 5, 'm': 2, 'c': 3, 'r': 2} among 4 identical containers that can hold [2, 4, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 4, 'f': 2, 'p': 3, 'm': 3} into 4 undistinguishable boxes with capacities [4, 3, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 2, 'p': 3, 'h': 4, 'e': 3} 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"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 4, 'y': 3, 'n': 2, 'a': 3} among 4 distinguishable boxes with capacities [2, 4, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 3, 'x': 3, 'g': 2, 'p': 4} into 4 uniquely identified boxes that can hold [2, 6, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 1, 'v': 6, 'k': 3, 'g': 2} into 4 undistinguishable boxes with capacities [4, 4, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 4, 'f': 4, 'p': 3, 'u': 1} among 4 identical containers that can hold [3, 2, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 2, 'i': 2, 'v': 2, 'h': 6} into 4 undistinguishable boxes with capacities [3, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 2, 'j': 5, 'b': 4, 'r': 1} among 4 identical containers that can hold [5, 2, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 2, 'v': 4, 'j': 3, 'n': 3}, place them into 4 indistinguishable boxes with sizes [1, 6, 4, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 5, 'd': 3, 'u': 2, 'a': 2} into 4 undistinguishable boxes with capacities [3, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 3, 'r': 1, 'h': 5, 'k': 3} among 4 distinguishable boxes with capacities [2, 2, 4, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 3, 'u': 1, 'v': 3, 'r': 5} and need to distribute them into 4 identical boxes with capacities [2, 3, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 3, 'k': 3, 'i': 3, 'p': 3} into 4 undistinguishable boxes with capacities [2, 2, 5, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 1, 'y': 1, 'q': 7, 'w': 3} and need to distribute them into 4 different boxes with capacities [1, 7, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 3, 'e': 4, 'y': 3, 'x': 2} into 4 uniquely identified boxes that can hold [3, 5, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 2, 'g': 1, 'm': 5, 't': 4} 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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 'j': 5, 'z': 2, 'b': 3}, place them into 4 indistinguishable boxes with sizes [3, 3, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 4, 'x': 4, 'h': 1, 'c': 3} into 4 undistinguishable boxes with capacities [3, 3, 5, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 1, 'l': 6, 't': 4, 'r': 1}, place them into 4 indistinguishable boxes with sizes [3, 4, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 3, 'h': 3, 'g': 3, 'j': 3} into 4 undistinguishable boxes with capacities [4, 3, 4, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'q': 3, 'r': 3, 'i': 4} and need to distribute them into 4 different boxes with capacities [2, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 3, 'c': 3, 'n': 3, 'o': 3} into 4 undistinguishable boxes with capacities [2, 4, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 2, 'a': 2, 'j': 3, 'h': 5} into 4 uniquely identified boxes that can hold [1, 2, 4, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 2, 'h': 4, 'e': 3, 'g': 3}, place them into 4 indistinguishable boxes with sizes [2, 2, 5, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 4, 'b': 3, 'a': 2, 'n': 3} and need to distribute them into 4 different boxes with capacities [4, 3, 2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'b': 1, 's': 6, 'e': 3, 'g': 2} 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"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 3, 'u': 3, 'n': 5, 'e': 1}, place them into 4 labeled boxes with sizes [2, 2, 4, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 1, 't': 3, 'd': 2, 'h': 6} 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"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 3, 'g': 1, 'j': 3, 'i': 5} among 4 distinguishable boxes with capacities [4, 3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 1, 'a': 4, 'n': 2, 'v': 5} and need to distribute them into 4 identical boxes with capacities [5, 3, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 4, 'v': 4, 's': 2, 'p': 2}, place them into 4 indistinguishable boxes with sizes [1, 5, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 3, 'd': 3, 'n': 2, 'e': 4} into 4 undistinguishable boxes with capacities [1, 3, 3, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 4, 'n': 1, 'i': 4, 'z': 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"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 3, 'k': 1, 'w': 4, 'm': 4} among 4 identical containers that can hold [2, 2, 4, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 3, 'k': 3, 'm': 2, 'w': 4}, place them into 4 indistinguishable boxes with sizes [2, 4, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 4, 'n': 5, 'a': 1, 'u': 2}, place them into 4 indistinguishable boxes with sizes [3, 2, 4, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 2, 'f': 1, 'x': 4, 'm': 5}, place them into 4 indistinguishable boxes with sizes [4, 4, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 4, 'b': 3, 'e': 2, 'u': 3} and need to distribute them into 4 identical boxes with capacities [1, 1, 7, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'v': 4, 'q': 3, 'n': 2, 'l': 3} into 4 distinctively labeled boxes with sizes [2, 3, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 4, 's': 2, 'd': 3, 'z': 3} into 4 uniquely identified boxes that can hold [4, 2, 2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 3, 'd': 2, 'l': 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 3, 'y': 4, 'v': 3, 'g': 2} into 4 undistinguishable boxes with sizes [3, 2, 2, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'q': 1, 'd': 4, 's': 4, 'o': 3} into 4 undistinguishable boxes with capacities [3, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 1, 'd': 3, 'k': 4, 'm': 4} into 4 undistinguishable boxes with sizes [3, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 1, 'k': 5, 'r': 1, 'c': 5}, place them into 4 labeled boxes with sizes [3, 2, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "384", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 2, 'z': 3, 'a': 2, 'u': 5} 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"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 4, 'i': 4, 'h': 1, 'l': 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"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 4, 'b': 1, 'l': 3, 's': 4} among 4 identical containers that can hold [2, 3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'q': 5, 'm': 1, 't': 3} into 4 undistinguishable boxes with capacities [2, 3, 4, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 5, 'j': 2, 'f': 2, 'b': 3} into 4 undistinguishable boxes with sizes [2, 1, 3, 6]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 2, 'z': 4, 'b': 4, 'u': 2} among 4 distinguishable boxes with capacities [2, 3, 6, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 2, 'z': 3, 'y': 3, 'i': 4} and need to distribute them into 4 different boxes with capacities [2, 2, 2, 6]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'d': 4, 'w': 2, 'c': 3, 'a': 3}, place them into 4 labeled boxes with sizes [1, 4, 6, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 3, 'm': 4, 'e': 3, 'i': 2} and need to distribute them into 4 different boxes with capacities [2, 3, 3, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 3, 'c': 2, 'h': 4, 'j': 3} into 4 undistinguishable boxes with sizes [3, 3, 1, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 2, 'u': 2, 'f': 3, 'i': 5} into 4 undistinguishable boxes with sizes [2, 4, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 4, 'e': 1, 'a': 2, 'n': 5} and need to distribute them into 4 identical boxes with capacities [5, 3, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 3, 'c': 3, 'i': 3, 'r': 3}, place them into 4 labeled boxes with sizes [2, 7, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 4, 'y': 1, 'd': 3, 'r': 4} among 4 identical containers that can hold [3, 3, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 4, 'l': 2, 'x': 3, 'w': 3} and need to distribute them into 4 different boxes with capacities [3, 1, 3, 5]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 5, 'i': 1, 'e': 2, 'k': 4} among 4 identical containers that can hold [4, 4, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 3, 'p': 3, 'u': 4, 'f': 2} into 4 uniquely identified boxes that can hold [2, 3, 5, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 'v': 2, 'y': 2, 'm': 5} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 2, 'b': 2, 'r': 3, 'y': 5} into 4 undistinguishable boxes with capacities [4, 3, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 3, 'i': 1, 'o': 4, 'h': 4} among 4 identical containers that can hold [2, 4, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 3, 'z': 3, 'm': 4, 'q': 2} and need to distribute them into 4 different boxes with capacities [7, 2, 2, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 2, 'p': 5, 'b': 2, 'd': 3} among 4 identical containers that can hold [4, 2, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 2, 't': 6, 'x': 3, 'm': 1}, place them into 4 indistinguishable boxes with sizes [4, 1, 5, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 1, 'z': 5, 'l': 2, 'i': 4}, place them into 4 indistinguishable boxes with sizes [5, 3, 1, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "217", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 2, 'l': 2, 'i': 4, 'o': 4} into 4 uniquely identified boxes that can hold [1, 4, 3, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 4, 's': 2, 'r': 3, 'm': 3} 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"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 3, 'g': 2, 'e': 5, 'l': 2}, 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"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 2, 'j': 3, 'z': 5, 'c': 2} and need to distribute them into 4 different boxes with capacities [3, 4, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 4, 'w': 2, 'r': 3, 'p': 3}, place them into 4 indistinguishable boxes with sizes [2, 4, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'i': 2, 'g': 3, 'n': 4, 'b': 3} into 4 uniquely identified boxes that can hold [5, 3, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 4, 'i': 4, 'y': 2, 'f': 2} into 4 uniquely identified boxes that can hold [5, 2, 1, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 2, 'l': 3, 'u': 4, 'y': 3} and need to distribute them into 4 different boxes with capacities [4, 2, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 2, 'i': 3, 't': 3, 'j': 4} into 4 distinctively labeled boxes with sizes [2, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 3, 'z': 2, 'v': 4, 'i': 3} into 4 undistinguishable boxes with capacities [2, 5, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 2, 'l': 6, 'f': 3, 'h': 1} 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"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 4, 'w': 4, 'a': 3, 'y': 1}, place them into 4 indistinguishable boxes with sizes [4, 3, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 4, 'g': 4, 'r': 2, 'h': 2} 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"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'i': 6, 'j': 1, 'h': 2, 'u': 3} into 4 undistinguishable boxes with capacities [5, 3, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 2, 'i': 4, 'l': 5, 'm': 1} and need to distribute them into 4 identical boxes with capacities [4, 1, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 5, 'z': 3, 'd': 2, 'q': 2} among 4 distinguishable boxes with capacities [2, 3, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 3, 'o': 3, 'c': 3, 'a': 3} and need to distribute them into 4 identical boxes with capacities [2, 3, 3, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 4, 'o': 1, 'a': 3, 'w': 4}, 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"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 2, 'z': 3, 'i': 4, 'w': 3} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 7, 'k': 3, 'y': 1, 'g': 1}, place them into 4 indistinguishable boxes with sizes [3, 1, 4, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'm': 3, 'p': 3, 'a': 3} into 4 uniquely identified boxes that can hold [1, 3, 5, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 3, 't': 3, 's': 3, 'e': 3} into 4 distinctively labeled boxes with sizes [1, 3, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 4, 't': 4, 'b': 1, 'y': 3} into 4 distinctively labeled boxes with sizes [2, 5, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 1, 'o': 5, 'n': 3, 'a': 3} among 4 distinguishable boxes with capacities [5, 1, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 5, 'y': 2, 's': 3, 'k': 2} into 4 undistinguishable boxes with capacities [2, 2, 6, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 2, 'q': 3, 'u': 4, 'x': 3} among 4 distinguishable boxes with capacities [3, 5, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 4, 'h': 5, 'a': 1, 't': 2} 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"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 3, 'k': 2, 'f': 2, 'b': 5} into 4 distinctively labeled boxes with sizes [3, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 2, 'p': 4, 'x': 3, 'y': 3} 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"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 4, 'v': 3, 'c': 3, 'k': 2} and need to distribute them into 4 different boxes with capacities [3, 4, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 5, 'h': 2, 'a': 2, 't': 3}, place them into 4 indistinguishable boxes with sizes [2, 3, 4, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 1, 'x': 2, 'l': 4, 'g': 5} into 4 undistinguishable boxes with capacities [3, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 4, 'd': 1, 'e': 5, 'h': 2} and need to distribute them into 4 different boxes with capacities [3, 3, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 5, 'w': 2, 't': 2, 'g': 3} into 4 distinctively labeled boxes with sizes [4, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 3, 'm': 2, 'o': 2, 'k': 5}, place them into 4 indistinguishable boxes with sizes [5, 3, 1, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 3, 'y': 4, 'j': 2, 'g': 3} among 4 distinguishable boxes with capacities [3, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 2, 'k': 4, 't': 4, 'l': 2} among 4 identical containers that can hold [3, 4, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 4, 'p': 4, 'z': 1, 'q': 3}, place them into 4 indistinguishable boxes with sizes [3, 4, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 4, 'q': 3, 't': 3, 'f': 2} and need to distribute them into 4 different boxes with capacities [5, 2, 1, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 2, 'v': 1, 's': 5, 't': 4} and need to distribute them into 4 different boxes with capacities [2, 3, 5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 3, 'l': 5, 'a': 2, 'y': 2} into 4 undistinguishable boxes with capacities [1, 4, 5, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 2, 't': 2, 'y': 3, 'b': 5} among 4 identical containers that can hold [1, 4, 5, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 3, 'b': 5, 'm': 2, 'j': 2} into 4 undistinguishable boxes with capacities [2, 2, 2, 6]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 6, 'v': 2, 'n': 2, 'q': 2} into 4 distinctively labeled boxes with sizes [1, 4, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "471", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 3, 'p': 3, 'j': 4, 's': 2} and need to distribute them into 4 identical boxes with capacities [3, 1, 7, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 4, 's': 2, 'l': 4, 't': 2} into 4 undistinguishable boxes with sizes [2, 4, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 4, 'i': 3, 'f': 2, 'e': 3} 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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 2, 'a': 1, 't': 5, 'e': 4} among 4 distinguishable boxes with capacities [2, 4, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 1, 'q': 3, 'j': 5, 't': 3}, place them into 4 indistinguishable boxes with sizes [4, 5, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 2, 'x': 4, 'l': 2, 'u': 4} among 4 distinguishable boxes with capacities [3, 6, 2, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 4, 'l': 4, 'q': 3, 'y': 1} and need to distribute them into 4 identical boxes with capacities [1, 3, 5, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 2, 'o': 5, 'w': 4, 'p': 1}, place them into 4 indistinguishable boxes with sizes [3, 2, 4, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 2, 'u': 4, 'k': 3, 'h': 3} and need to distribute them into 4 identical boxes with capacities [4, 2, 4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 1, 'x': 1, 'n': 5, 'b': 5} among 4 identical containers that can hold [5, 1, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 6, 'p': 2, 'j': 2, 'd': 2}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 1, 'y': 2, 'u': 4, 'c': 5} into 4 distinctively labeled boxes with sizes [2, 6, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 3, 'k': 3, 'p': 2, 'q': 4} among 4 distinguishable boxes with capacities [3, 3, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 4, 'x': 4, 'a': 2, 'r': 2} among 4 distinguishable boxes with capacities [3, 4, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 2, 'a': 4, 'n': 2, 's': 4} into 4 undistinguishable boxes with sizes [2, 5, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 2, 'r': 4, 'c': 3, 'y': 3} into 4 undistinguishable boxes with capacities [4, 2, 1, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 4, 'e': 4, 'b': 3, 'g': 1} into 4 uniquely identified boxes that can hold [3, 2, 3, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'v': 5, 'g': 3, 'd': 1, 'e': 3} 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"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 4, 'w': 4, 'b': 1, 'v': 3}, place them into 4 labeled boxes with sizes [5, 4, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'p': 3, 'f': 3, 'i': 3, 'z': 3}, place them into 4 labeled boxes with sizes [1, 4, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1060", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 2, 'a': 3, 'z': 4, 'u': 3} among 4 identical containers that can hold [2, 3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 2, 'u': 4, 'p': 5, 'v': 1} into 4 uniquely identified boxes that can hold [3, 2, 4, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 2, 'q': 2, 'a': 4, 'x': 4}, place them into 4 indistinguishable boxes with sizes [2, 2, 4, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 2, 'q': 6, 'k': 2, 'i': 2} into 4 uniquely identified boxes that can hold [1, 4, 2, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 2, 'm': 3, 'h': 2, 'f': 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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 2, 'i': 3, 'q': 5, 's': 2} among 4 identical containers that can hold [5, 1, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 4, 'e': 3, 'g': 2, 'i': 3}, place them into 4 labeled boxes with sizes [2, 2, 5, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 4, 'c': 4, 'e': 2, 'b': 2} into 4 undistinguishable boxes with sizes [5, 3, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 3, 'u': 2, 'g': 4, 'm': 3} into 4 undistinguishable boxes with capacities [3, 4, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'p': 2, 't': 4, 'a': 3} into 4 undistinguishable boxes with capacities [5, 1, 5, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 2, 'i': 3, 'r': 3, 'e': 4} among 4 distinguishable boxes with capacities [2, 1, 7, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'f': 4, 'y': 2, 'j': 2, 'd': 4} 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"}], "ground_truth": "277", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 4, 'x': 4, 'g': 2, 'r': 2} into 4 uniquely identified boxes that can hold [6, 1, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 1, 'k': 5, 'm': 5, 'p': 1} 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"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 2, 'c': 3, 'b': 4, 't': 3} among 4 identical containers that can hold [5, 1, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 3, 'j': 3, 'a': 3, 'd': 3} into 4 undistinguishable boxes with capacities [3, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 2, 'h': 3, 'o': 4, 'z': 3} and need to distribute them into 4 identical boxes with capacities [3, 6, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 3, 'i': 1, 'g': 4, 't': 4}, place them into 4 labeled boxes with sizes [3, 3, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1060", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 2, 'x': 5, 'e': 2, 'w': 3} among 4 distinguishable boxes with capacities [4, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 2, 'z': 3, 'i': 3, 'k': 4} and need to distribute them into 4 identical boxes with capacities [1, 6, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 3, 'y': 1, 'o': 5, 'x': 3} among 4 identical containers that can hold [3, 2, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 3, 'j': 4, 'g': 2, 'n': 3} among 4 distinguishable boxes with capacities [1, 4, 5, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 1, 'q': 2, 'm': 5, 'l': 4} and need to distribute them into 4 different boxes with capacities [4, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 3, 'b': 2, 'z': 1, 'h': 6} into 4 undistinguishable boxes with capacities [4, 3, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 4, 'f': 3, 'w': 2, 'j': 3} among 4 identical containers that can hold [2, 3, 5, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 4, 's': 3, 'k': 2, 'x': 3} into 4 uniquely identified boxes that can hold [3, 2, 5, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 5, 'g': 1, 'b': 3, 'e': 3} among 4 identical containers that can hold [3, 1, 5, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "251", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 5, 'm': 2, 'f': 4, 'd': 1} into 4 uniquely identified boxes that can hold [4, 1, 5, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 2, 't': 3, 'e': 4, 'r': 3} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 3, 's': 2, 'x': 3, 'y': 4} among 4 distinguishable boxes with capacities [2, 5, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 1, 'c': 4, 'f': 4, 'p': 3} among 4 identical containers that can hold [5, 2, 4, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 5, 'g': 1, 'a': 3, 'm': 3} among 4 distinguishable boxes with capacities [6, 1, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 2, 'x': 2, 'a': 5, 'o': 3} into 4 undistinguishable boxes with capacities [3, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 5, 't': 3, 'x': 1, 'q': 3} into 4 distinctively labeled boxes with sizes [2, 5, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 6, 't': 1, 'v': 3, 'a': 2} into 4 distinctively labeled boxes with sizes [4, 3, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 3, 'm': 2, 'v': 5, 'c': 2} into 4 uniquely identified boxes that can hold [2, 2, 5, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'e': 1, 'w': 5, 'b': 3} into 4 distinctively labeled boxes with sizes [4, 1, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 3, 'c': 4, 'z': 1, 'v': 4}, 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"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 6, 'i': 4, 'f': 1, 'c': 1} and need to distribute them into 4 different boxes with capacities [4, 1, 5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 2, 'h': 3, 'j': 3, 'p': 4}, place them into 4 indistinguishable boxes with sizes [4, 2, 1, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 2, 'f': 3, 'y': 3, 'r': 4}, place them into 4 labeled boxes with sizes [3, 2, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 2, 'n': 4, 'u': 4, 'k': 2} into 4 uniquely identified boxes that can hold [2, 3, 5, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 3, 'k': 2, 'g': 4, 'l': 3} and need to distribute them into 4 different boxes with capacities [3, 4, 2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 2, 'i': 1, 'b': 4, 'z': 5} and need to distribute them into 4 identical boxes with capacities [1, 5, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "217", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 3, 'c': 5, 'y': 1, 'g': 3} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 2, 'o': 3, 'z': 5, 'k': 2}, place them into 4 indistinguishable boxes with sizes [6, 3, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 4, 'e': 4, 'y': 1, 'm': 3} among 4 identical containers that can hold [4, 2, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 4, 'u': 2, 'z': 4, 's': 2} into 4 distinctively labeled boxes with sizes [6, 2, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 2, 'q': 5, 'd': 2, 'x': 3} and need to distribute them into 4 identical boxes with capacities [2, 4, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 2, 'p': 5, 'o': 3, 'l': 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"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 4, 'o': 3, 'w': 3, 'c': 2}, place them into 4 indistinguishable boxes with sizes [2, 5, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 1, 'j': 5, 'u': 4, 'd': 2} into 4 undistinguishable boxes with sizes [2, 1, 6, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 3, 'h': 2, 'n': 5, 'm': 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"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 2, 'r': 3, 'c': 6, 'z': 1}, 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"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 5, 'a': 2, 'o': 2, 'k': 3} into 4 undistinguishable boxes with capacities [4, 4, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 5, 'i': 2, 'x': 2, 'c': 3} into 4 uniquely identified boxes that can hold [2, 2, 1, 7] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "292", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 3, 'a': 2, 'g': 2, 'q': 5} and need to distribute them into 4 different boxes with capacities [2, 2, 5, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 6, 's': 2, 'v': 1, 'u': 3} and need to distribute them into 4 different boxes with capacities [3, 6, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 3, 'f': 3, 'j': 4, 'a': 2}, place them into 4 labeled boxes with sizes [2, 5, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 2, 'v': 3, 'z': 3, 'j': 4} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 1, 'n': 4, 'p': 3, 'c': 4} 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"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 3, 'd': 4, 'f': 2, 't': 3} among 4 distinguishable boxes with capacities [4, 5, 2, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 3, 'o': 3, 's': 2, 'i': 4} and need to distribute them into 4 identical boxes with capacities [2, 1, 1, 8]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 3, 'b': 5, 'l': 1, 'i': 3} 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"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 3, 'e': 1, 'x': 3, 'j': 5} among 4 distinguishable boxes with capacities [3, 1, 5, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 2, 'm': 1, 'w': 5, 'b': 4} 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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 2, 'i': 4, 'r': 4, 'j': 2} into 4 undistinguishable boxes with capacities [3, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 5, 'n': 3, 'k': 2, 'r': 2} among 4 distinguishable boxes with capacities [3, 2, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 1, 'u': 2, 'j': 3, 'h': 6} and need to distribute them into 4 different boxes with capacities [2, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 4, 'u': 4, 'p': 3, 'z': 1}, place them into 4 labeled boxes with sizes [2, 2, 3, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 4, 'o': 1, 'x': 3, 'u': 4} into 4 distinctively labeled boxes with sizes [5, 2, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 3, 'a': 3, 't': 3, 'e': 3} and need to distribute them into 4 different boxes with capacities [4, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 3, 'o': 3, 'j': 2, 'r': 4} 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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 3, 'q': 1, 'k': 4, 'f': 4}, place them into 4 labeled boxes with sizes [4, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 2, 'y': 1, 'g': 6, 'r': 3}, place them into 4 labeled boxes with sizes [2, 2, 4, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 3, 'q': 2, 'y': 5, 'u': 2} into 4 undistinguishable boxes with sizes [1, 3, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 2, 'k': 1, 'b': 4, 'y': 5} 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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 5, 'u': 2, 'k': 1, 'c': 4}, place them into 4 labeled boxes with sizes [3, 2, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 4, 'z': 1, 'f': 2, 'c': 5} 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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'b': 5, 'l': 4, 's': 1} and need to distribute them into 4 identical boxes with capacities [2, 5, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 4, 'b': 2, 'n': 3, 'g': 3} among 4 identical containers that can hold [4, 2, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'d': 3, 'w': 3, 'o': 2, 'h': 4} into 4 undistinguishable boxes with sizes [5, 3, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 4, 'c': 2, 's': 2, 'y': 4}, place them into 4 labeled boxes with sizes [2, 7, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 5, 'j': 1, 'y': 4, 'c': 2} 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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 5, 'a': 1, 'q': 4, 'c': 2} into 4 undistinguishable boxes with sizes [2, 4, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 4, 'k': 2, 'h': 1, 'd': 5} 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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 6, 'q': 2, 'c': 1, 's': 3} into 4 distinctively labeled boxes with sizes [3, 4, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 4, 'x': 2, 'z': 5, 'k': 1} into 4 uniquely identified boxes that can hold [4, 4, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 4, 'o': 3, 'f': 3, 'j': 2} into 4 uniquely identified boxes that can hold [1, 5, 4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 5, 'p': 3, 'm': 2, 'w': 2} and need to distribute them into 4 different boxes with capacities [4, 2, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 3, 'f': 4, 'l': 3, 'y': 2} into 4 distinctively labeled boxes with sizes [3, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 4, 'z': 2, 'k': 1, 'x': 5} and need to distribute them into 4 different boxes with capacities [3, 2, 6, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 4, 'm': 2, 'a': 5, 'k': 1} and need to distribute them into 4 identical boxes with capacities [6, 1, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 1, 'j': 3, 'b': 3, 'o': 5} among 4 distinguishable boxes with capacities [1, 5, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 3, 'x': 4, 'h': 3, 'b': 2} and need to distribute them into 4 identical boxes with capacities [2, 5, 4, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 2, 's': 5, 'q': 2, 'l': 3} and need to distribute them into 4 identical boxes with capacities [2, 6, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 1, 'q': 4, 'i': 3, 'd': 4} into 4 distinctively labeled boxes with sizes [3, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 3, 's': 6, 'u': 2, 'd': 1} among 4 identical containers that can hold [3, 2, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 1, 'a': 5, 'e': 2, 't': 4}, place them into 4 indistinguishable boxes with sizes [2, 2, 3, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 1, 'f': 3, 'p': 6, 'r': 2} and need to distribute them into 4 different boxes with capacities [3, 4, 2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 4, 'j': 3, 'f': 1, 'g': 4} into 4 distinctively labeled boxes with sizes [2, 4, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 3, 't': 2, 'h': 4, 'l': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 6, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 1, 'x': 4, 'v': 5, 'b': 2} into 4 distinctively labeled boxes with sizes [3, 2, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 1, 'x': 3, 'q': 5, 'c': 3} into 4 distinctively labeled boxes with sizes [3, 3, 5, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'm': 4, 's': 3, 'w': 2} into 4 distinctively labeled boxes with sizes [2, 2, 4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 2, 'i': 5, 'p': 1, 'k': 4} among 4 distinguishable boxes with capacities [5, 2, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 4, 'w': 4, 'm': 2, 'b': 2} 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"}], "ground_truth": "394", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 4, 'c': 6, 'd': 1, 't': 1} and need to distribute them into 4 identical boxes with capacities [2, 1, 2, 7]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 5, 'j': 1, 'w': 3, 'v': 3} and need to distribute them into 4 identical boxes with capacities [4, 2, 5, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 4, 'c': 2, 'o': 4, 'l': 2} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 3, 'c': 3, 'o': 2, 'w': 4} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 4, 'm': 2, 's': 2, 'u': 4}, place them into 4 labeled boxes with sizes [4, 2, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1002", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 7, 'a': 2, 's': 1, 'l': 2} among 4 distinguishable boxes with capacities [3, 4, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 2, 'g': 4, 'e': 3, 'p': 3} among 4 distinguishable boxes with capacities [4, 1, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 2, 'd': 2, 't': 4, 'm': 4} into 4 undistinguishable boxes with sizes [3, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 3, 'k': 2, 'w': 1, 'y': 6} among 4 identical containers that can hold [2, 2, 3, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 3, 'm': 3, 'u': 1, 'k': 5} into 4 distinctively labeled boxes with sizes [3, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 1, 'y': 3, 'v': 4, 'j': 4} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 3, 'p': 3, 'h': 3, 'x': 3}, 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"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 4, 'p': 3, 'z': 2, 'e': 3} among 4 distinguishable boxes with capacities [4, 1, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 3, 'a': 4, 'g': 2, 'd': 3} and need to distribute them into 4 identical boxes with capacities [3, 2, 3, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 5, 'g': 3, 'z': 1, 'd': 3}, place them into 4 indistinguishable boxes with sizes [3, 1, 5, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "251", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 3, 'x': 1, 'i': 3, 'k': 5} into 4 distinctively labeled boxes with sizes [2, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 2, 'r': 3, 'c': 6, 'l': 1} among 4 identical containers that can hold [5, 1, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 4, 'p': 1, 'w': 3, 'n': 4}, place them into 4 labeled boxes with sizes [2, 1, 6, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 3, 'g': 4, 'h': 2, 'o': 3} among 4 distinguishable boxes with capacities [3, 2, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 3, 'n': 2, 'i': 3, 'k': 4} among 4 distinguishable boxes with capacities [4, 4, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 4, 'z': 3, 'f': 1, 'h': 4} into 4 undistinguishable boxes with sizes [4, 2, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 3, 'v': 3, 'w': 1, 'l': 5} among 4 distinguishable boxes with capacities [1, 4, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 2, 'i': 3, 'l': 5, 't': 2} 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"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 2, 'h': 3, 's': 3, 'e': 4}, place them into 4 indistinguishable boxes with sizes [3, 6, 1, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 2, 'b': 4, 'y': 4, 'm': 2}, 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"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'l': 2, 'a': 3, 'p': 4, 'r': 3} into 4 undistinguishable boxes with capacities [1, 2, 4, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'d': 5, 't': 1, 'w': 4, 'r': 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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 1, 'w': 5, 'f': 4, 'h': 2} among 4 distinguishable boxes with capacities [2, 4, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 4, 'w': 3, 'q': 2, 'z': 3} among 4 distinguishable boxes with capacities [3, 3, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'t': 1, 'm': 3, 'o': 4, 'c': 4} into 4 undistinguishable boxes with capacities [4, 3, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'l': 5, 'n': 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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'q': 5, 'y': 3, 'n': 2, 'm': 2} into 4 uniquely identified boxes that can hold [2, 3, 2, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 'x': 3, 'o': 5, 'u': 2}, place them into 4 indistinguishable boxes with sizes [2, 1, 6, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 3, 'd': 4, 'x': 2, 'q': 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"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 2, 'n': 2, 'e': 4, 'd': 4} 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"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'b': 3, 'x': 4, 't': 1, 'y': 4} into 4 uniquely identified boxes that can hold [3, 3, 3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1060", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 2, 'q': 3, 'd': 3, 'v': 4} into 4 undistinguishable boxes with sizes [1, 2, 3, 6]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 2, 't': 5, 'z': 2, 's': 3}, place them into 4 labeled boxes with sizes [3, 4, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'a': 3, 'p': 6, 's': 1} and need to distribute them into 4 different boxes with capacities [4, 1, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 3, 'w': 3, 'n': 2, 'x': 4} among 4 identical containers that can hold [4, 4, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 2, 't': 4, 'i': 3, 'n': 3} into 4 uniquely identified boxes that can hold [2, 4, 1, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 3, 't': 6, 'b': 1, 'n': 2} among 4 identical containers that can hold [4, 2, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "130", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 6, 'y': 3, 'w': 1, 'n': 2}, place them into 4 labeled boxes with sizes [3, 2, 5, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 'm': 3, 'g': 2, 'k': 4} and need to distribute them into 4 identical boxes with capacities [4, 2, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 2, 'o': 1, 'w': 3, 'v': 6} and need to distribute them into 4 identical boxes with capacities [6, 2, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 3, 'o': 3, 'y': 2, 'j': 4}, place them into 4 labeled boxes with sizes [4, 3, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 5, 'l': 3, 'd': 1, 'b': 3}, place them into 4 indistinguishable boxes with sizes [1, 4, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "273", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 3, 'j': 4, 'p': 2, 'k': 3} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 4, 'a': 2, 'e': 2, 'b': 4} into 4 uniquely identified boxes that can hold [5, 3, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 2, 'r': 3, 'p': 2, 'e': 5} among 4 identical containers that can hold [3, 3, 1, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 2, 'i': 5, 'p': 2, 'v': 3} into 4 distinctively labeled boxes with sizes [4, 3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 2, 'b': 4, 'u': 4, 'm': 2} into 4 distinctively labeled boxes with sizes [4, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 3, 't': 4, 'b': 1, 'j': 4} and need to distribute them into 4 different boxes with capacities [3, 2, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 6, 'd': 3, 'o': 1, 'l': 2} 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"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 1, 'm': 3, 'g': 4, 'j': 4}, place them into 4 labeled boxes with sizes [2, 2, 4, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 4, 'v': 4, 'r': 3, 'k': 1} 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"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 3, 't': 3, 'k': 2, 'e': 4} and need to distribute them into 4 different boxes with capacities [4, 2, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 4, 'v': 2, 'z': 5, 'b': 1} into 4 distinctively labeled boxes with sizes [2, 1, 4, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'q': 3, 'd': 3, 'l': 4} 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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 4, 'l': 1, 's': 4, 'x': 3} among 4 identical containers that can hold [1, 4, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 's': 4, 'w': 3, 'j': 3}, place them into 4 labeled boxes with sizes [3, 2, 2, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 1, 'i': 4, 'y': 3, 'z': 4} and need to distribute them into 4 identical boxes with capacities [1, 2, 2, 7]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 3, 'j': 6, 'd': 2, 'l': 1} 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"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 2, 'f': 1, 'h': 6, 'z': 3} and need to distribute them into 4 identical boxes with capacities [3, 3, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 2, 'q': 3, 'e': 4, 'u': 3} among 4 identical containers that can hold [2, 3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 3, 'm': 3, 'j': 4, 'n': 2} among 4 identical containers that can hold [2, 3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'u': 4, 'n': 4, 'm': 2} and need to distribute them into 4 identical boxes with capacities [3, 2, 5, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 2, 'm': 5, 'b': 2, 'h': 3} among 4 distinguishable boxes with capacities [4, 3, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 2, 'x': 2, 'm': 4, 's': 4} into 4 distinctively labeled boxes with sizes [2, 3, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 5, 'v': 1, 'p': 4, 'c': 2} 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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 4, 'o': 3, 'b': 2, 'j': 3}, place them into 4 labeled boxes with sizes [2, 2, 5, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 1, 'n': 5, 'e': 5, 'i': 1} into 4 undistinguishable boxes with capacities [3, 5, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 7, 'l': 1, 'h': 2, 'q': 2} 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"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 3, 'j': 4, 'f': 2, 'v': 3} and need to distribute them into 4 different boxes with capacities [3, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 3, 'v': 2, 'i': 2, 'x': 5} and need to distribute them into 4 different boxes with capacities [3, 2, 2, 5]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 3, 't': 2, 'w': 5, 'e': 2} 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"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 3, 'u': 3, 'o': 3, 'i': 3} and need to distribute them into 4 identical boxes with capacities [6, 2, 1, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 2, 'd': 3, 'b': 5, 'u': 2} into 4 uniquely identified boxes that can hold [3, 2, 3, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'q': 3, 'b': 5, 'a': 3, 's': 1} into 4 uniquely identified boxes that can hold [5, 4, 1, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 1, 'i': 3, 'r': 3, 'y': 5} and need to distribute them into 4 different boxes with capacities [2, 3, 5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 3, 'v': 4, 'a': 4, 'n': 1} and need to distribute them into 4 different boxes with capacities [4, 1, 1, 6]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 6, 'y': 3, 'j': 1, 't': 2} among 4 identical containers that can hold [4, 1, 2, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 1, 'p': 5, 'g': 4, 'b': 2} and need to distribute them into 4 identical boxes with capacities [2, 4, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 2, 'r': 4, 'c': 3, 'p': 3} and need to distribute them into 4 identical boxes with capacities [6, 3, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 3, 'f': 4, 'y': 2, 'c': 3} and need to distribute them into 4 different boxes with capacities [4, 4, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 4, 'x': 1, 'j': 4, 'r': 3}, place them into 4 indistinguishable boxes with sizes [4, 3, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'b': 2, 'k': 3, 'q': 4, 'i': 3} into 4 uniquely identified boxes that can hold [6, 1, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 3, 'w': 4, 'u': 2, 'e': 3} among 4 distinguishable boxes with capacities [3, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 4, 'u': 1, 'h': 4, 'v': 3} and need to distribute them into 4 different boxes with capacities [2, 2, 3, 5]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 5, 'n': 2, 'u': 3, 'a': 2} 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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 5, 's': 4, 'v': 1, 'i': 2} and need to distribute them into 4 different boxes with capacities [2, 2, 2, 6]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 1, 'u': 5, 'f': 3, 'g': 3} among 4 identical containers that can hold [6, 1, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 4, 'y': 3, 'w': 1, 'j': 4} 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"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 1, 'j': 3, 'q': 4, 'c': 4} into 4 undistinguishable boxes with sizes [3, 1, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 4, 'z': 3, 'w': 3, 's': 2}, 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"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 1, 's': 5, 'd': 2, 'm': 4} into 4 distinctively labeled boxes with sizes [1, 2, 4, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 3, 'a': 2, 'q': 5, 'u': 2} into 4 undistinguishable boxes with sizes [2, 5, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 3, 'g': 2, 'b': 3, 'y': 4} into 4 uniquely identified boxes that can hold [3, 5, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'i': 4, 't': 3, 'v': 3, 'd': 2} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'u': 4, 'n': 4, 'h': 2, 'c': 2} into 4 uniquely identified boxes that can hold [2, 4, 2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1002", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 2, 'x': 3, 'v': 5, 'a': 2} among 4 identical containers that can hold [2, 4, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 2, 'f': 4, 'd': 2, 'p': 4}, 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"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 5, 'h': 4, 'd': 2, 'o': 1} and need to distribute them into 4 identical boxes with capacities [3, 6, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 5, 'e': 4, 'm': 2, 'p': 1} among 4 identical containers that can hold [4, 2, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 1, 'y': 4, 'q': 4, 'f': 3}, place them into 4 labeled boxes with sizes [4, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 4, 'e': 1, 'v': 3, 'n': 4} 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"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 2, 'h': 3, 'n': 6, 't': 1} 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"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'f': 2, 'm': 3, 'p': 4} into 4 uniquely identified boxes that can hold [3, 2, 3, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 2, 'o': 3, 'b': 3, 'k': 4} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 5, 's': 2, 'd': 2, 'x': 3} into 4 uniquely identified boxes that can hold [5, 3, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 'h': 2, 'z': 4, 'q': 4}, place them into 4 labeled boxes with sizes [2, 3, 2, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 5, 'z': 1, 'n': 2, 'y': 4} into 4 undistinguishable boxes with sizes [3, 4, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 4, 'c': 4, 'm': 2, 'a': 2} and need to distribute them into 4 identical boxes with capacities [2, 5, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 2, 'j': 1, 't': 3, 'x': 6} and need to distribute them into 4 identical boxes with capacities [5, 3, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 2, 'o': 1, 'u': 6, 'j': 3} among 4 identical containers that can hold [2, 2, 4, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "130", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 1, 'm': 6, 't': 3, 'l': 2}, place them into 4 labeled boxes with sizes [3, 3, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 6, 'c': 2, 'x': 2, 'l': 2} into 4 distinctively labeled boxes with sizes [2, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 4, 'j': 4, 'y': 3, 'p': 1} and need to distribute them into 4 identical boxes with capacities [2, 5, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 2, 's': 2, 'b': 5, 'd': 3} and need to distribute them into 4 different boxes with capacities [5, 2, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 2, 'a': 2, 'e': 2, 'l': 6} among 4 distinguishable boxes with capacities [5, 3, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'y': 4, 's': 4, 'p': 2} and need to distribute them into 4 identical boxes with capacities [3, 1, 4, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "394", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 3, 'g': 6, 'o': 2, 'a': 1} into 4 uniquely identified boxes that can hold [1, 6, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 6, 'r': 1, 'k': 3, 'd': 2} 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"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 4, 'r': 3, 'u': 2, 's': 3} and need to distribute them into 4 identical boxes with capacities [3, 5, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 3, 'g': 2, 'v': 1, 's': 6} and need to distribute them into 4 different boxes with capacities [1, 2, 5, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 4, 'g': 3, 'h': 2, 'j': 3} among 4 identical containers that can hold [4, 4, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 5, 'v': 3, 'y': 2, 'z': 2}, place them into 4 labeled boxes with sizes [4, 3, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'d': 2, 'w': 4, 'z': 4, 's': 2}, place them into 4 labeled boxes with sizes [4, 1, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'a': 4, 'e': 3, 'k': 3} and need to distribute them into 4 different boxes with capacities [3, 3, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 3, 'f': 6, 's': 2, 'c': 1} into 4 undistinguishable boxes with sizes [3, 2, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 2, 'i': 4, 'z': 2, 'j': 4}, place them into 4 labeled boxes with sizes [4, 2, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 4, 's': 3, 'o': 3, 'h': 2} into 4 undistinguishable boxes with sizes [5, 2, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 3, 'u': 4, 'h': 2, 'a': 3} and need to distribute them into 4 different boxes with capacities [2, 2, 4, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 2, 'w': 3, 'z': 4, 'a': 3} into 4 distinctively labeled boxes with sizes [5, 2, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 2, 'h': 4, 'z': 4, 'x': 2} 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"}], "ground_truth": "1374", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 4, 'u': 2, 't': 2, 'x': 4}, 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"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 3, 't': 3, 'm': 4, 'w': 2}, place them into 4 indistinguishable boxes with sizes [2, 3, 5, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 2, 'c': 2, 'a': 2, 'n': 6} among 4 distinguishable boxes with capacities [2, 2, 4, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 3, 'z': 4, 'j': 2, 'p': 3} into 4 distinctively labeled boxes with sizes [2, 3, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 4, 'i': 3, 'z': 1, 'j': 4} and need to distribute them into 4 different boxes with capacities [2, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 2, 'h': 5, 'c': 2, 'y': 3}, place them into 4 labeled boxes with sizes [3, 4, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 1, 'o': 4, 'e': 2, 'r': 5} 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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 4, 'p': 3, 'a': 3, 'f': 2}, place them into 4 indistinguishable boxes with sizes [3, 3, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 3, 'v': 4, 'g': 3, 'q': 2} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 2, 'w': 5, 'l': 3, 'u': 2} into 4 uniquely identified boxes that can hold [4, 5, 1, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 4, 'o': 2, 'r': 3, 'i': 3} into 4 undistinguishable boxes with sizes [4, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 4, 'b': 2, 'y': 3, 'p': 3} into 4 undistinguishable boxes with capacities [4, 2, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 5, 'x': 3, 'c': 2, 'm': 2} into 4 distinctively labeled boxes with sizes [3, 1, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 3, 'z': 1, 's': 5, 'q': 3} into 4 undistinguishable boxes with capacities [3, 3, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 2, 'c': 2, 'd': 2, 'a': 6} into 4 uniquely identified boxes that can hold [3, 3, 3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "780", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'t': 2, 'b': 4, 's': 3, 'r': 3} into 4 undistinguishable boxes with capacities [3, 2, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 1, 'h': 4, 'd': 4, 'x': 3} and need to distribute them into 4 different boxes with capacities [2, 3, 3, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 3, 'v': 2, 'y': 4, 'k': 3}, place them into 4 labeled boxes with sizes [2, 4, 5, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 2, 'l': 4, 't': 3, 'x': 3} into 4 distinctively labeled boxes with sizes [2, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 4, 'i': 3, 'x': 2, 's': 3} into 4 undistinguishable boxes with sizes [3, 2, 2, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 4, 't': 2, 'y': 3, 'm': 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"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 5, 'p': 4, 'q': 1, 'h': 2} and need to distribute them into 4 identical boxes with capacities [4, 3, 4, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 2, 'q': 4, 'y': 2, 'z': 4} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 3, 'x': 3, 'd': 4, 'q': 2} among 4 distinguishable boxes with capacities [3, 2, 2, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 3, 'z': 4, 'i': 3, 'p': 2} among 4 identical containers that can hold [1, 5, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'g': 5, 't': 2, 'v': 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"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 2, 't': 4, 'l': 2, 'k': 4} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 3, 's': 2, 'u': 2, 'k': 5} among 4 distinguishable boxes with capacities [4, 3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 4, 'd': 4, 'y': 2, 't': 2}, place them into 4 indistinguishable boxes with sizes [3, 5, 3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 3, 'j': 4, 's': 3, 'h': 2} among 4 distinguishable boxes with capacities [3, 3, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 4, 'i': 3, 'u': 4, 'b': 1} into 4 distinctively labeled boxes with sizes [3, 3, 1, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'p': 4, 't': 3, 'u': 3, 'f': 2}, place them into 4 indistinguishable boxes with sizes [1, 4, 2, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 3, 't': 3, 'k': 3, 'g': 3} and need to distribute them into 4 identical boxes with capacities [4, 1, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 3, 'e': 4, 'p': 1, 'j': 4} among 4 identical containers that can hold [3, 2, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 2, 'n': 1, 'y': 7, 'u': 2} and need to distribute them into 4 identical boxes with capacities [3, 3, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 3, 'v': 2, 'r': 4, 'g': 3} into 4 uniquely identified boxes that can hold [2, 3, 5, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 5, 'c': 4, 'q': 1, 'v': 2} and need to distribute them into 4 identical boxes with capacities [5, 3, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 4, 'j': 1, 'd': 4, 'o': 3} into 4 uniquely identified boxes that can hold [1, 4, 4, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 3, 'f': 2, 'b': 4, 'm': 3} into 4 uniquely identified boxes that can hold [4, 2, 2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 2, 'p': 2, 'a': 3, 'q': 5}, place them into 4 indistinguishable boxes with sizes [2, 1, 4, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'u': 4, 'k': 3, 'v': 2} into 4 distinctively labeled boxes with sizes [1, 3, 3, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 4, 'y': 3, 's': 3, 'm': 2}, 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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'c': 3, 'g': 4, 'z': 3} and need to distribute them into 4 different boxes with capacities [4, 3, 2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 3, 'e': 4, 'v': 2, 'f': 3} into 4 undistinguishable boxes with sizes [1, 2, 6, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'d': 3, 'i': 6, 'j': 1, 't': 2}, place them into 4 labeled boxes with sizes [3, 3, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'a': 4, 'n': 2, 'y': 5, 'g': 1} 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"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 2, 'm': 6, 'w': 1, 'n': 3}, place them into 4 indistinguishable boxes with sizes [6, 3, 1, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 1, 'q': 3, 'b': 1, 'v': 7} and need to distribute them into 4 different boxes with capacities [4, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 2, 'h': 3, 'f': 3, 'n': 4} into 4 undistinguishable boxes with sizes [3, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 2, 'j': 3, 'a': 4, 'h': 3}, place them into 4 indistinguishable boxes with sizes [3, 2, 2, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 4, 'm': 2, 'q': 3, 'x': 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 3, 'p': 4, 'y': 3, 'n': 2} among 4 distinguishable boxes with capacities [5, 4, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 3, 'r': 3, 'l': 3, 'w': 3} among 4 identical containers that can hold [3, 2, 2, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 4, 'b': 2, 'r': 4, 'v': 2} into 4 distinctively labeled boxes with sizes [2, 4, 1, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 1, 'b': 3, 'm': 6, 'i': 2} and need to distribute them into 4 different boxes with capacities [3, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 2, 'l': 6, 'g': 1, 'z': 3} into 4 uniquely identified boxes that can hold [3, 1, 7, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 1, 'i': 5, 'r': 2, 'z': 4} among 4 distinguishable boxes with capacities [4, 3, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 4, 'w': 3, 't': 3, 'm': 2} among 4 distinguishable boxes with capacities [2, 5, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'r': 4, 'v': 3, 'q': 2} into 4 undistinguishable boxes with capacities [1, 8, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 3, 'h': 1, 't': 2, 'q': 6} into 4 undistinguishable boxes with capacities [4, 3, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 5, 'i': 1, 'p': 2, 'h': 4}, 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"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 1, 'j': 5, 'g': 2, 'c': 4} among 4 distinguishable boxes with capacities [1, 4, 1, 6]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 2, 'm': 4, 'f': 3, 'u': 3} 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"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 5, 'w': 3, 'd': 3, 'q': 1}, 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"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 4, 'l': 1, 'i': 2, 'z': 5} and need to distribute them into 4 identical boxes with capacities [2, 4, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 2, 'j': 5, 'k': 3, 'b': 2} into 4 undistinguishable boxes with sizes [3, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'b': 4, 'x': 2, 'j': 3} into 4 undistinguishable boxes with sizes [2, 5, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 3, 'f': 3, 'g': 3, 'c': 3}, place them into 4 indistinguishable boxes with sizes [4, 4, 1, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 2, 'm': 3, 'p': 3, 's': 4} into 4 uniquely identified boxes that can hold [6, 1, 4, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 1, 'm': 5, 'k': 4, 'r': 2} 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"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 1, 'm': 4, 'w': 3, 't': 4} into 4 uniquely identified boxes that can hold [3, 2, 3, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 3, 'y': 3, 'b': 4, 'n': 2} among 4 identical containers that can hold [2, 3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 3, 'w': 3, 'b': 3, 'y': 3} among 4 identical containers that can hold [2, 4, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 1, 'g': 4, 'q': 5, 'n': 2} and need to distribute them into 4 identical boxes with capacities [2, 5, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 4, 'a': 2, 'b': 3, 'e': 3} among 4 distinguishable boxes with capacities [3, 2, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 2, 'y': 3, 'u': 6, 'i': 1}, place them into 4 indistinguishable boxes with sizes [2, 3, 4, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 2, 'n': 3, 'd': 2, 'l': 5} and need to distribute them into 4 identical boxes with capacities [2, 6, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 3, 'j': 1, 'v': 6, 'l': 2}, 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"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 4, 'b': 3, 'i': 4, 'o': 1} into 4 distinctively labeled boxes with sizes [2, 3, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 4, 'i': 2, 'l': 2, 'r': 4} into 4 undistinguishable boxes with sizes [5, 3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'p': 5, 'c': 1, 'n': 2, 'h': 4}, 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"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 2, 'n': 3, 'e': 4, 'p': 3} and need to distribute them into 4 identical boxes with capacities [5, 3, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 2, 'g': 6, 'k': 1, 'z': 3} among 4 distinguishable boxes with capacities [3, 1, 3, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'a': 3, 'd': 3, 't': 3}, place them into 4 indistinguishable boxes with sizes [4, 3, 4, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 2, 'f': 5, 'b': 1, 'm': 4} among 4 distinguishable boxes with capacities [4, 3, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 7, 'x': 2, 'z': 2, 'p': 1} among 4 identical containers that can hold [2, 1, 4, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "207", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 3, 'v': 4, 'w': 2, 'b': 3} among 4 identical containers that can hold [2, 6, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 1, 'd': 7, 'k': 1, 's': 3} and need to distribute them into 4 identical boxes with capacities [2, 4, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 3, 'f': 2, 'h': 2, 'k': 5} into 4 uniquely identified boxes that can hold [2, 2, 3, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'z': 6, 'b': 2, 'v': 1} into 4 uniquely identified boxes that can hold [2, 2, 7, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 2, 'p': 2, 'a': 6, 'm': 2}, place them into 4 indistinguishable boxes with sizes [2, 2, 4, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 4, 'c': 1, 'j': 5, 'w': 2} and need to distribute them into 4 identical boxes with capacities [2, 1, 4, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 3, 'u': 3, 'i': 2, 'n': 4} among 4 distinguishable boxes with capacities [3, 2, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 2, 'y': 3, 't': 4, 'l': 3} into 4 distinctively labeled boxes with sizes [4, 2, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 3, 'g': 5, 'j': 2, 'k': 2} into 4 distinctively labeled boxes with sizes [3, 3, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 5, 'y': 3, 'g': 2, 'a': 2} into 4 undistinguishable boxes with capacities [3, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'k': 5, 'u': 2, 'm': 2}, place them into 4 indistinguishable boxes with sizes [5, 2, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 2, 'k': 2, 'f': 4, 'p': 4}, 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"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 1, 'h': 2, 'q': 7, 'p': 2} into 4 uniquely identified boxes that can hold [2, 4, 1, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "207", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 3, 'h': 3, 'l': 3, 'd': 3} into 4 undistinguishable boxes with capacities [2, 3, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 5, 'm': 3, 'o': 2, 'f': 2} into 4 undistinguishable boxes with capacities [3, 2, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 4, 'l': 3, 'r': 3, 'b': 2} into 4 undistinguishable boxes with capacities [3, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 2, 'j': 4, 'l': 2, 'm': 4} and need to distribute them into 4 different boxes with capacities [1, 3, 4, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 3, 'g': 3, 'j': 3, 'l': 3} into 4 undistinguishable boxes with capacities [3, 2, 5, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 3, 'q': 2, 'o': 3, 'r': 4} among 4 identical containers that can hold [3, 3, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 4, 'v': 3, 't': 2, 'e': 3} among 4 distinguishable boxes with capacities [3, 3, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 6, 'c': 2, 't': 3, 'h': 1} and need to distribute them into 4 identical boxes with capacities [2, 5, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 2, 'r': 6, 'i': 2, 'l': 2} among 4 distinguishable boxes with capacities [5, 2, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'q': 4, 'p': 2, 'v': 4, 'r': 2} into 4 undistinguishable boxes with capacities [2, 3, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 2, 'z': 5, 'n': 1, 'd': 4} and need to distribute them into 4 different boxes with capacities [3, 1, 4, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 2, 'a': 4, 'y': 3, 'v': 3}, place them into 4 labeled boxes with sizes [2, 6, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 3, 'i': 4, 'v': 2, 'u': 3} into 4 undistinguishable boxes with capacities [1, 3, 4, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'d': 2, 'n': 2, 't': 5, 'm': 3}, place them into 4 indistinguishable boxes with sizes [4, 2, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 1, 'i': 3, 'k': 2, 'm': 6} and need to distribute them into 4 different boxes with capacities [3, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 5, 'h': 3, 'k': 1, 'm': 3} among 4 distinguishable boxes with capacities [1, 4, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 1, 'y': 3, 'g': 5, 'o': 3} 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"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 4, 'n': 3, 'i': 2, 'b': 3} among 4 distinguishable boxes with capacities [4, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 4, 'u': 2, 'f': 4, 'x': 2} and need to distribute them into 4 different boxes with capacities [4, 2, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1002", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 1, 'm': 3, 'q': 4, 'z': 4} among 4 distinguishable boxes with capacities [4, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'p': 4, 't': 4, 'g': 2, 'o': 2}, place them into 4 labeled boxes with sizes [3, 3, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1374", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 4, 'i': 3, 'w': 3, 'r': 2} into 4 undistinguishable boxes with capacities [4, 1, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 'o': 5, 's': 2, 'b': 2} and need to distribute them into 4 identical boxes with capacities [4, 5, 1, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 1, 'q': 6, 'n': 1, 's': 4} among 4 identical containers that can hold [1, 3, 5, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 3, 'z': 2, 'c': 1, 'x': 6}, place them into 4 labeled boxes with sizes [3, 5, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'a': 3, 'k': 2, 'y': 2, 'l': 5} into 4 undistinguishable boxes with sizes [4, 2, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 5, 'w': 2, 'u': 1, 'b': 4} and need to distribute them into 4 different boxes with capacities [1, 4, 5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 5, 'h': 2, 'c': 2, 'x': 3} into 4 distinctively labeled boxes with sizes [2, 3, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 2, 'd': 2, 'j': 4, 'w': 4} 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"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 2, 'k': 3, 'i': 3, 'z': 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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 1, 'k': 4, 't': 4, 'g': 3}, place them into 4 labeled boxes with sizes [1, 3, 6, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 3, 'o': 4, 'b': 2, 'y': 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 4, 's': 2, 'w': 2, 'a': 4} among 4 distinguishable boxes with capacities [4, 1, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 1, 'z': 4, 'y': 2, 'g': 5} among 4 identical containers that can hold [4, 4, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 3, 'y': 3, 'v': 4, 'c': 2}, place them into 4 labeled boxes with sizes [5, 4, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 4, 'a': 3, 'n': 4, 'q': 1} into 4 undistinguishable boxes with sizes [3, 2, 1, 6]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 3, 'm': 2, 'q': 4, 'p': 3} into 4 undistinguishable boxes with capacities [3, 2, 4, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'h': 4, 'o': 2, 'e': 4} and need to distribute them into 4 identical boxes with capacities [3, 3, 5, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 2, 'k': 4, 'j': 3, 'f': 3} into 4 undistinguishable boxes with sizes [2, 4, 1, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 2, 'z': 5, 'e': 2, 'u': 3} into 4 undistinguishable boxes with capacities [2, 3, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 1, 'a': 3, 'j': 6, 't': 2} and need to distribute them into 4 identical boxes with capacities [3, 3, 5, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 2, 'w': 3, 'a': 3, 'e': 4} among 4 distinguishable boxes with capacities [1, 4, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 1, 'l': 3, 'o': 6, 'v': 2} into 4 undistinguishable boxes with sizes [5, 2, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 3, 'y': 2, 'b': 4, 's': 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 3, 'i': 2, 'p': 3, 'e': 4} and need to distribute them into 4 different boxes with capacities [3, 5, 3, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 3, 'w': 1, 'd': 5, 'b': 3} among 4 identical containers that can hold [3, 4, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 2, 'k': 3, 'n': 4, 'g': 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 4, 't': 1, 'e': 2, 'd': 5} into 4 uniquely identified boxes that can hold [3, 5, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 5, 'v': 1, 'r': 3, 'i': 3} and need to distribute them into 4 identical boxes with capacities [2, 3, 3, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 7, 'a': 1, 'o': 2, 'i': 2}, place them into 4 indistinguishable boxes with sizes [4, 4, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 4, 'm': 2, 'r': 3, 's': 3} into 4 uniquely identified boxes that can hold [2, 4, 2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 2, 'v': 4, 'n': 3, 'b': 3}, place them into 4 indistinguishable boxes with sizes [4, 4, 3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 5, 'g': 3, 'q': 3, 'm': 1} and need to distribute them into 4 different boxes with capacities [1, 2, 7, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 4, 'h': 2, 'x': 3, 'y': 3} and need to distribute them into 4 identical boxes with capacities [5, 4, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 3, 'c': 2, 'u': 4, 't': 3} 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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 2, 'g': 1, 'u': 6, 'v': 3} and need to distribute them into 4 identical boxes with capacities [2, 5, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 2, 'j': 5, 'e': 3, 'a': 2}, place them into 4 labeled boxes with sizes [4, 4, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 4, 'h': 3, 's': 2, 't': 3} and need to distribute them into 4 different boxes with capacities [5, 3, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 4, 'f': 3, 'n': 4, 'e': 1} among 4 identical containers that can hold [5, 2, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 2, 'v': 2, 't': 3, 'a': 5} 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"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 4, 'j': 2, 'i': 1, 'e': 5} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 3, 'h': 2, 'r': 4, 'm': 3} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 3, 'n': 5, 'x': 2, 'v': 2}, place them into 4 labeled boxes with sizes [1, 3, 4, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 1, 'c': 4, 'h': 3, 'k': 4} and need to distribute them into 4 different boxes with capacities [1, 3, 4, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 4, 'w': 4, 'd': 2, 'z': 2}, place them into 4 labeled boxes with sizes [4, 4, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1002", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 3, 'p': 4, 'q': 3, 'a': 2} into 4 undistinguishable boxes with capacities [2, 3, 2, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 2, 'a': 3, 'u': 4, 'v': 3} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 3, 'e': 4, 't': 3, 'x': 2}, place them into 4 labeled boxes with sizes [3, 3, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'b': 5, 'y': 1, 'e': 3, 'w': 3} into 4 uniquely identified boxes that can hold [2, 3, 4, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 5, 'z': 1, 'f': 2, 'v': 4} and need to distribute them into 4 identical boxes with capacities [1, 3, 4, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 6, 'j': 2, 'z': 2, 'y': 2}, place them into 4 indistinguishable boxes with sizes [3, 3, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 2, 'w': 4, 'q': 3, 'y': 3} into 4 undistinguishable boxes with sizes [2, 6, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 2, 'i': 2, 'l': 2, 'm': 6} 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"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 1, 'w': 5, 'o': 2, 'p': 4} and need to distribute them into 4 different boxes with capacities [4, 4, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 4, 'n': 3, 'r': 2, 'z': 3}, place them into 4 indistinguishable boxes with sizes [1, 4, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 2, 'e': 4, 'v': 2, 'o': 4} and need to distribute them into 4 different boxes with capacities [3, 4, 1, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 3, 's': 5, 'e': 2, 'x': 2} and need to distribute them into 4 different boxes with capacities [3, 4, 1, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 2, 'i': 3, 'h': 4, 's': 3} into 4 undistinguishable boxes with capacities [4, 2, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 2, 'y': 4, 'z': 3, 't': 3} into 4 undistinguishable boxes with capacities [2, 2, 2, 6]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 3, 'u': 5, 'n': 3, 'w': 1}, place them into 4 labeled boxes with sizes [2, 1, 7, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 5, 'q': 3, 'r': 1, 'f': 3} among 4 distinguishable boxes with capacities [2, 2, 4, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 4, 'e': 5, 'o': 1, 'm': 2} and need to distribute them into 4 different boxes with capacities [5, 2, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 1, 'n': 4, 'k': 4, 'w': 3} into 4 distinctively labeled boxes with sizes [2, 3, 6, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 2, 'g': 1, 'u': 4, 'j': 5} into 4 uniquely identified boxes that can hold [4, 2, 4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 2, 'w': 3, 'h': 3, 'z': 4} and need to distribute them into 4 different boxes with capacities [1, 5, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 5, 'g': 2, 'v': 2, 'j': 3} among 4 identical containers that can hold [5, 2, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 3, 'o': 1, 'w': 5, 'g': 3} and need to distribute them into 4 identical boxes with capacities [1, 4, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "273", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 3, 't': 2, 'k': 4, 'v': 3} and need to distribute them into 4 identical boxes with capacities [3, 5, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 3, 'b': 2, 'n': 5, 'j': 2} and need to distribute them into 4 identical boxes with capacities [3, 4, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 4, 'l': 3, 'k': 2, 'c': 3} among 4 distinguishable boxes with capacities [1, 3, 4, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 5, 's': 2, 'd': 2, 'q': 3} and need to distribute them into 4 different boxes with capacities [3, 6, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 4, 'f': 5, 'a': 2, 'd': 1} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 2, 's': 5, 'r': 1, 'd': 4} and need to distribute them into 4 different boxes with capacities [3, 3, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 2, 'z': 2, 'n': 5, 'l': 3}, place them into 4 labeled boxes with sizes [1, 1, 4, 6]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 6, 'd': 1, 'w': 2, 'z': 3} among 4 identical containers that can hold [4, 4, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 5, 'w': 1, 'g': 2, 'e': 4} into 4 distinctively labeled boxes with sizes [1, 2, 4, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 5, 'h': 1, 'n': 2, 'f': 4} into 4 undistinguishable boxes with capacities [4, 5, 1, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 3, 'i': 4, 'd': 3, 's': 2}, place them into 4 labeled boxes with sizes [5, 1, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 3, 'k': 2, 'n': 3, 'm': 4} into 4 uniquely identified boxes that can hold [5, 3, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 6, 'g': 2, 'z': 2, 't': 2} among 4 identical containers that can hold [7, 3, 1, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 3, 't': 3, 'u': 3, 'c': 3}, place them into 4 labeled boxes with sizes [1, 2, 4, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "768", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 'h': 4, 'k': 5, 'f': 1}, place them into 4 labeled boxes with sizes [6, 2, 1, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 2, 'u': 3, 'f': 4, 'o': 3} into 4 distinctively labeled boxes with sizes [4, 3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 3, 'x': 4, 'h': 3, 'z': 2} and need to distribute them into 4 different boxes with capacities [2, 3, 5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'f': 2, 'h': 2, 't': 5, 'e': 3} into 4 undistinguishable boxes with sizes [6, 2, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 2, 'q': 3, 'l': 6, 't': 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"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 4, 'v': 3, 'm': 1, 'p': 4} into 4 distinctively labeled boxes with sizes [3, 1, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 3, 's': 4, 'd': 4, 'j': 1} and need to distribute them into 4 different boxes with capacities [2, 4, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 3, 'y': 2, 'x': 3, 'i': 4} into 4 uniquely identified boxes that can hold [5, 4, 1, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 2, 'e': 4, 'o': 3, 'x': 3} into 4 undistinguishable boxes with capacities [3, 1, 5, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 5, 't': 1, 's': 3, 'l': 3} into 4 undistinguishable boxes with capacities [4, 4, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 5, 't': 2, 'r': 4, 'i': 1} among 4 identical containers that can hold [3, 4, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 1, 'k': 5, 'x': 2, 'e': 4} into 4 undistinguishable boxes with capacities [1, 3, 3, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "217", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 2, 'x': 4, 't': 3, 'h': 3} among 4 identical containers that can hold [3, 2, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 2, 'm': 2, 'i': 3, 'a': 5} and need to distribute them into 4 different boxes with capacities [5, 3, 3, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'u': 3, 'f': 2, 'j': 4, 'n': 3} 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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 3, 'd': 4, 'g': 4, 'e': 1} among 4 identical containers that can hold [4, 3, 4, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 4, 'c': 3, 'g': 2, 'x': 3} into 4 distinctively labeled boxes with sizes [2, 4, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 2, 'y': 4, 'h': 4, 'u': 2} into 4 uniquely identified boxes that can hold [2, 5, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 3, 'e': 4, 'w': 1, 'o': 4}, place them into 4 labeled boxes with sizes [2, 4, 5, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 1, 'o': 4, 'j': 4, 'x': 3} into 4 undistinguishable boxes with sizes [2, 2, 1, 7]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 5, 'x': 2, 'v': 2, 'h': 3} into 4 uniquely identified boxes that can hold [1, 2, 3, 6] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 1, 's': 6, 'p': 1, 't': 4} and need to distribute them into 4 identical boxes with capacities [2, 1, 5, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 5, 'f': 2, 'h': 3, 't': 2} among 4 distinguishable boxes with capacities [3, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'c': 2, 'g': 6, 'd': 2} and need to distribute them into 4 different boxes with capacities [3, 3, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 2, 'x': 4, 'v': 2, 'g': 4} into 4 distinctively labeled boxes with sizes [3, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 1, 'i': 4, 'h': 4, 'a': 3} into 4 undistinguishable boxes with sizes [1, 3, 4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 2, 'k': 5, 's': 1, 'p': 4} and need to distribute them into 4 different boxes with capacities [5, 2, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 3, 'f': 1, 'g': 5, 'v': 3} and need to distribute them into 4 identical boxes with capacities [5, 2, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "331", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 4, 'h': 3, 'o': 2, 'y': 3} among 4 distinguishable boxes with capacities [3, 1, 6, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 2, 't': 3, 'q': 1, 'w': 6} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 2, 'a': 4, 'm': 3, 'w': 3} and need to distribute them into 4 different boxes with capacities [4, 1, 6, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 3, 'm': 2, 'g': 4, 'd': 3} and need to distribute them into 4 identical boxes with capacities [3, 1, 5, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 3, 'z': 1, 'd': 7, 'w': 1}, place them into 4 indistinguishable boxes with sizes [1, 4, 4, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 4, 'r': 2, 'g': 4, 'v': 2}, place them into 4 labeled boxes with sizes [4, 2, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1002", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'h': 4, 'z': 2, 'b': 4} 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"}], "ground_truth": "394", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 5, 'k': 3, 'u': 2, 'b': 2} into 4 distinctively labeled boxes with sizes [2, 4, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 3, 'm': 3, 'z': 3, 'j': 3} among 4 distinguishable boxes with capacities [5, 3, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1200", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 4, 'd': 3, 'l': 2, 'e': 3} into 4 distinctively labeled boxes with sizes [3, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 4, 'm': 4, 'd': 3, 'g': 1} into 4 uniquely identified boxes that can hold [3, 4, 1, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 5, 'a': 1, 'e': 4, 'q': 2} into 4 undistinguishable boxes with capacities [4, 4, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 4, 'm': 3, 'x': 4, 'o': 1} among 4 distinguishable boxes with capacities [3, 4, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 3, 'v': 3, 'o': 3, 'y': 3} among 4 identical containers that can hold [2, 3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 2, 'i': 3, 'x': 4, 's': 3} among 4 identical containers that can hold [4, 2, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 2, 'w': 5, 'l': 2, 'v': 3}, place them into 4 indistinguishable boxes with sizes [4, 1, 5, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 4, 'u': 2, 'r': 1, 'i': 5} into 4 undistinguishable boxes with capacities [4, 2, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 2, 'k': 5, 'x': 2, 'a': 3} into 4 distinctively labeled boxes with sizes [3, 3, 5, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 1, 'n': 5, 'f': 3, 'h': 3} among 4 distinguishable boxes with capacities [3, 1, 5, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 2, 'f': 3, 'q': 3, 'y': 4} into 4 distinctively labeled boxes with sizes [1, 3, 3, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 3, 'z': 3, 'f': 5, 'i': 1} into 4 distinctively labeled boxes with sizes [2, 7, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 2, 'n': 1, 'j': 4, 'd': 5} and need to distribute them into 4 identical boxes with capacities [2, 4, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'i': 3, 'n': 4, 'z': 1, 'g': 4} into 4 uniquely identified boxes that can hold [5, 2, 4, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 2, 'k': 4, 'h': 4, 'p': 2}, place them into 4 indistinguishable boxes with sizes [3, 2, 6, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 3, 'a': 2, 'o': 4, 'v': 3}, place them into 4 labeled boxes with sizes [3, 3, 1, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 2, 'z': 4, 's': 4, 'u': 2} into 4 undistinguishable boxes with capacities [3, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 3, 'z': 4, 'a': 1, 'd': 4} into 4 undistinguishable boxes with sizes [3, 4, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 3, 'g': 2, 'x': 2, 'd': 5} among 4 identical containers that can hold [4, 4, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 1, 'h': 2, 'z': 1, 'u': 8} and need to distribute them into 4 different boxes with capacities [2, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 1, 'r': 4, 'd': 4, 'l': 3} into 4 undistinguishable boxes with capacities [3, 2, 4, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'l': 4, 'o': 4, 'y': 2, 'w': 2} into 4 uniquely identified boxes that can hold [4, 3, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 4, 'u': 4, 'x': 2, 'v': 2}, place them into 4 labeled boxes with sizes [2, 6, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 5, 'c': 2, 'n': 2, 'o': 3} and need to distribute them into 4 identical boxes with capacities [1, 2, 7, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'z': 1, 'k': 6, 'g': 3} and need to distribute them into 4 different boxes with capacities [2, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'t': 1, 'd': 3, 'm': 3, 'z': 5} into 4 undistinguishable boxes with capacities [2, 2, 2, 6]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 3, 'k': 2, 'r': 5, 'l': 2}, 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"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 4, 'i': 2, 'u': 5, 'g': 1} into 4 undistinguishable boxes with sizes [3, 2, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 3, 'n': 3, 'x': 2, 'm': 4} and need to distribute them into 4 identical boxes with capacities [4, 2, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 3, 'n': 2, 'u': 3, 'q': 4}, place them into 4 indistinguishable boxes with sizes [1, 1, 4, 6]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 5, 'w': 1, 'f': 4, 'm': 2} into 4 distinctively labeled boxes with sizes [3, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 1, 'v': 5, 'r': 3, 'o': 3}, place them into 4 indistinguishable boxes with sizes [2, 2, 4, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 2, 'd': 3, 'v': 4, 'g': 3} into 4 undistinguishable boxes with capacities [4, 3, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 3, 'w': 2, 'o': 3, 'y': 4} among 4 distinguishable boxes with capacities [5, 1, 1, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "384", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 4, 'n': 2, 'k': 4, 'u': 2} into 4 distinctively labeled boxes with sizes [3, 2, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 1, 'a': 2, 'v': 6, 'h': 3} into 4 undistinguishable boxes with capacities [4, 1, 5, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'b': 5, 'x': 3, 'v': 2} and need to distribute them into 4 identical boxes with capacities [3, 3, 1, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 2, 'v': 4, 'd': 2, 'j': 4} among 4 identical containers that can hold [4, 2, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 3, 'e': 5, 'r': 3, 'h': 1}, place them into 4 indistinguishable boxes with sizes [5, 4, 1, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 4, 'o': 3, 'z': 3, 'c': 2} among 4 identical containers that can hold [5, 3, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 3, 'u': 4, 'q': 3, 'r': 2} and need to distribute them into 4 identical boxes with capacities [4, 2, 4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 5, 'n': 2, 'y': 4, 'c': 1}, place them into 4 labeled boxes with sizes [2, 4, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 3, 'y': 1, 's': 3, 'v': 5} and need to distribute them into 4 different boxes with capacities [5, 2, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 3, 'x': 2, 'y': 6, 'e': 1} and need to distribute them into 4 different boxes with capacities [4, 5, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'l': 2, 's': 3, 'j': 4, 'p': 3} 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"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 4, 'f': 2, 'o': 3, 'x': 3} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 2, 'o': 4, 'm': 4, 'a': 2} into 4 undistinguishable boxes with capacities [2, 5, 4, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 1, 'o': 5, 'w': 4, 'j': 2} and need to distribute them into 4 identical boxes with capacities [3, 2, 5, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 2, 'u': 6, 'x': 2, 'l': 2} among 4 identical containers that can hold [2, 7, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 2, 'c': 5, 'l': 4, 'f': 1} among 4 distinguishable boxes with capacities [4, 2, 1, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'b': 2, 'm': 5, 'i': 2} into 4 undistinguishable boxes with sizes [3, 5, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 1, 'p': 1, 'd': 8, 'y': 2}, place them into 4 labeled boxes with sizes [5, 1, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 2, 'q': 3, 'r': 2, 'n': 5} into 4 distinctively labeled boxes with sizes [3, 4, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 2, 'u': 2, 'p': 4, 'd': 4} among 4 distinguishable boxes with capacities [5, 3, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 4, 'e': 1, 't': 5, 'n': 2} and need to distribute them into 4 different boxes with capacities [4, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 4, 'i': 3, 'v': 1, 'r': 4}, place them into 4 labeled boxes with sizes [3, 2, 6, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 5, 'e': 1, 'x': 3, 's': 3} and need to distribute them into 4 identical boxes with capacities [2, 3, 3, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 4, 'l': 3, 'u': 4, 'w': 1} into 4 undistinguishable boxes with capacities [2, 5, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 3, 'u': 2, 'a': 6, 'x': 1}, place them into 4 labeled boxes with sizes [3, 3, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 2, 'o': 5, 'f': 3, 'e': 2} into 4 undistinguishable boxes with capacities [5, 1, 5, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 3, 'c': 2, 'u': 4, 'y': 3} and need to distribute them into 4 different boxes with capacities [3, 4, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 3, 'q': 2, 'u': 5, 'k': 2}, place them into 4 indistinguishable boxes with sizes [4, 5, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'t': 2, 'p': 5, 'u': 2, 'y': 3} into 4 uniquely identified boxes that can hold [3, 2, 4, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 3, 'h': 4, 'a': 1, 'y': 4} among 4 distinguishable boxes with capacities [4, 2, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 2, 'y': 6, 't': 3, 'h': 1} into 4 undistinguishable boxes with capacities [3, 1, 4, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 3, 's': 2, 'u': 1, 'g': 6} into 4 uniquely identified boxes that can hold [1, 7, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 1, 'h': 4, 'd': 5, 'i': 2} into 4 distinctively labeled boxes with sizes [2, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 3, 'e': 1, 'w': 5, 'a': 3}, place them into 4 labeled boxes with sizes [3, 2, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'g': 4, 'w': 3, 'z': 3} and need to distribute them into 4 different boxes with capacities [3, 2, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 2, 'l': 2, 'i': 4, 'z': 4} among 4 identical containers that can hold [2, 4, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 2, 'l': 4, 'o': 1, 'k': 5} and need to distribute them into 4 identical boxes with capacities [3, 1, 4, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 2, 'f': 2, 'm': 7, 'e': 1}, 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"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 1, 'l': 3, 'u': 1, 'i': 7} among 4 identical containers that can hold [4, 2, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 4, 'f': 3, 'l': 2, 's': 3} into 4 uniquely identified boxes that can hold [2, 3, 3, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 3, 'a': 2, 'w': 2, 'c': 5} 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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 4, 'z': 3, 'j': 2, 'w': 3} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 5, 'z': 1, 'g': 3, 'd': 3} into 4 undistinguishable boxes with capacities [2, 3, 2, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "331", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 4, 'u': 2, 'i': 5, 'r': 1} into 4 uniquely identified boxes that can hold [3, 1, 5, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 2, 'm': 4, 'n': 4, 'v': 2} into 4 undistinguishable boxes with sizes [4, 3, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "394", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 3, 'o': 3, 'g': 3, 'x': 3}, place them into 4 labeled boxes with sizes [2, 4, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1374", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 5, 'm': 1, 's': 3, 'w': 3} among 4 identical containers that can hold [4, 1, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "273", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 4, 'm': 2, 'z': 4, 'n': 2} among 4 identical containers that can hold [3, 1, 6, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 1, 'd': 2, 'k': 3, 'h': 6} among 4 distinguishable boxes with capacities [1, 3, 6, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 1, 'v': 5, 'c': 2, 's': 4} into 4 distinctively labeled boxes with sizes [2, 1, 4, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'f': 3, 's': 5, 'b': 2} and need to distribute them into 4 different boxes with capacities [4, 3, 1, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 2, 't': 5, 'f': 1, 'j': 4} and need to distribute them into 4 different boxes with capacities [3, 3, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 3, 'd': 2, 'j': 4, 'n': 3}, place them into 4 indistinguishable boxes with sizes [1, 4, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 2, 'z': 4, 'x': 3, 't': 3} and need to distribute them into 4 different boxes with capacities [2, 6, 1, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 5, 'f': 2, 'w': 1, 's': 4} into 4 undistinguishable boxes with sizes [3, 2, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 'd': 4, 'n': 4, 'z': 2}, place them into 4 labeled boxes with sizes [5, 4, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 4, 'g': 4, 'u': 1, 'y': 3} among 4 distinguishable boxes with capacities [1, 5, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 2, 'j': 2, 'v': 5, 'l': 3}, place them into 4 indistinguishable boxes with sizes [3, 1, 5, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 4, 'z': 2, 'g': 2, 'x': 4} among 4 distinguishable boxes with capacities [2, 2, 3, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 1, 'y': 1, 'q': 6, 'i': 4} among 4 distinguishable boxes with capacities [3, 1, 3, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 4, 'l': 2, 'g': 2, 'c': 4} into 4 undistinguishable boxes with capacities [6, 3, 1, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 3, 'j': 3, 'm': 4, 'n': 2}, place them into 4 indistinguishable boxes with sizes [3, 3, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 4, 'q': 4, 'l': 3, 'n': 1} into 4 undistinguishable boxes with capacities [4, 2, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 3, 'c': 4, 'm': 3, 'i': 2} into 4 undistinguishable boxes with sizes [3, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 4, 'z': 2, 'd': 4, 'g': 2} among 4 identical containers that can hold [4, 5, 1, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 3, 'o': 3, 'k': 2, 'x': 4}, place them into 4 labeled boxes with sizes [1, 6, 4, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 2, 'k': 3, 'r': 4, 'o': 3} and need to distribute them into 4 different boxes with capacities [2, 7, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 3, 'j': 1, 'c': 3, 'p': 5} 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"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 2, 'i': 4, 'r': 3, 'h': 3} into 4 uniquely identified boxes that can hold [2, 2, 2, 6] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 4, 'c': 3, 'd': 3, 'v': 2} and need to distribute them into 4 identical boxes with capacities [2, 2, 6, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 2, 'r': 2, 'v': 4, 'o': 4}, place them into 4 indistinguishable boxes with sizes [1, 4, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "394", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 3, 'n': 3, 'u': 2, 'e': 4}, place them into 4 labeled boxes with sizes [5, 2, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 2, 'r': 3, 'w': 4, 'k': 3} into 4 undistinguishable boxes with capacities [3, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 3, 's': 2, 'j': 5, 't': 2}, place them into 4 indistinguishable boxes with sizes [1, 1, 4, 6]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 3, 'r': 3, 'v': 2, 'n': 4}, place them into 4 indistinguishable boxes with sizes [3, 2, 1, 6]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 3, 'm': 3, 'l': 2, 'h': 4} and need to distribute them into 4 different boxes with capacities [1, 5, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 3, 'r': 2, 'y': 5, 't': 2} and need to distribute them into 4 identical boxes with capacities [3, 3, 5, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 2, 's': 4, 'g': 2, 'v': 4} and need to distribute them into 4 different boxes with capacities [5, 2, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 3, 's': 6, 'm': 1, 'v': 2} and need to distribute them into 4 different boxes with capacities [3, 2, 5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'p': 6, 'i': 2, 'z': 3, 'k': 1}, place them into 4 labeled boxes with sizes [2, 6, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 3, 'd': 2, 'e': 4, 'v': 3} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 2, 'z': 4, 'v': 3, 'r': 3}, place them into 4 labeled boxes with sizes [1, 5, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 4, 'y': 2, 'u': 2, 'c': 4}, place them into 4 labeled boxes with sizes [4, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'i': 1, 'd': 2, 'x': 6, 'm': 3} into 4 undistinguishable boxes with capacities [3, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 'r': 1, 'n': 6, 'o': 3}, place them into 4 labeled boxes with sizes [2, 4, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'l': 3, 's': 5, 'e': 1, 'j': 3} into 4 undistinguishable boxes with capacities [4, 2, 1, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 2, 'm': 3, 'q': 3, 'n': 4}, place them into 4 labeled boxes with sizes [4, 2, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 2, 'z': 3, 'e': 5, 'n': 2} among 4 identical containers that can hold [3, 3, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 3, 'z': 2, 'j': 4, 't': 3} and need to distribute them into 4 different boxes with capacities [3, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1660", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 3, 'a': 4, 't': 2, 'n': 3}, place them into 4 labeled boxes with sizes [1, 1, 3, 7]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 3, 'j': 4, 'm': 2, 'a': 3} among 4 identical containers that can hold [4, 4, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 3, 'a': 1, 'r': 3, 'b': 5} into 4 distinctively labeled boxes with sizes [3, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 2, 'b': 2, 'q': 6, 'z': 2} and need to distribute them into 4 different boxes with capacities [5, 4, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 2, 'd': 2, 'y': 4, 't': 4} into 4 undistinguishable boxes with sizes [4, 3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 3, 'x': 3, 'i': 2, 'o': 4} 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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 4, 'i': 1, 'r': 5, 'z': 2} and need to distribute them into 4 identical boxes with capacities [3, 3, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 4, 'm': 2, 'd': 4, 'w': 2} 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"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 3, 'k': 3, 'n': 3, 'y': 3} into 4 uniquely identified boxes that can hold [4, 4, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1060", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 4, 'j': 3, 's': 4, 'w': 1} among 4 distinguishable boxes with capacities [4, 1, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 1, 'q': 3, 'a': 1, 'x': 7} into 4 undistinguishable boxes with sizes [5, 4, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 3, 'n': 3, 'q': 4, 'l': 2} 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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 4, 'j': 2, 'a': 1, 'g': 5} and need to distribute them into 4 identical boxes with capacities [2, 4, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 2, 'e': 2, 'z': 4, 'p': 4}, place them into 4 labeled boxes with sizes [4, 4, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1002", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 3, 'p': 2, 'h': 2, 's': 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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 5, 'o': 2, 'n': 3, 'j': 2} into 4 distinctively labeled boxes with sizes [3, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 2, 'd': 4, 'w': 3, 'g': 3} among 4 identical containers that can hold [2, 3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 2, 'e': 6, 'v': 2, 'm': 2}, place them into 4 labeled boxes with sizes [1, 4, 2, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 3, 'u': 2, 't': 2, 'p': 5} into 4 uniquely identified boxes that can hold [5, 2, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 3, 'a': 4, 'm': 2, 'f': 3} into 4 undistinguishable boxes with sizes [3, 5, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 4, 'x': 3, 'l': 2, 't': 3} among 4 identical containers that can hold [3, 2, 2, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 4, 'c': 2, 'r': 2, 'f': 4} among 4 identical containers that can hold [2, 3, 5, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 4, 'u': 2, 'e': 3, 'p': 3}, 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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 4, 'q': 2, 'u': 3, 'k': 3} among 4 distinguishable boxes with capacities [4, 2, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 1, 'x': 4, 's': 5, 'l': 2}, 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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 5, 'd': 2, 'b': 2, 'x': 3} among 4 identical containers that can hold [4, 1, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'f': 5, 'q': 3, 'z': 3, 'p': 1} into 4 undistinguishable boxes with sizes [5, 1, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 2, 'r': 4, 'd': 2, 'l': 4} into 4 distinctively labeled boxes with sizes [5, 3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 1, 'd': 7, 'b': 1, 'h': 3} into 4 distinctively labeled boxes with sizes [5, 1, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 2, 'e': 3, 'k': 3, 'g': 4} among 4 distinguishable boxes with capacities [2, 3, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'q': 4, 'e': 3, 'r': 3, 'l': 2} into 4 undistinguishable boxes with capacities [4, 3, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 4, 'u': 3, 'k': 2, 'g': 3}, place them into 4 indistinguishable boxes with sizes [3, 4, 4, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 3, 'w': 4, 'v': 2, 'd': 3} and need to distribute them into 4 different boxes with capacities [5, 3, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 5, 'k': 2, 'p': 3, 'i': 2} among 4 identical containers that can hold [2, 5, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 6, 't': 2, 'y': 3, 'm': 1} and need to distribute them into 4 different boxes with capacities [3, 2, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 2, 'u': 3, 't': 2, 'x': 5} into 4 undistinguishable boxes with capacities [3, 4, 4, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 3, 'l': 4, 'z': 2, 'x': 3} into 4 distinctively labeled boxes with sizes [4, 4, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 3, 'i': 4, 'd': 3, 's': 2}, place them into 4 indistinguishable boxes with sizes [2, 1, 4, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 3, 'u': 3, 'a': 3, 'o': 3}, place them into 4 labeled boxes with sizes [5, 2, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1200", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 3, 'n': 4, 'a': 4, 'g': 1} and need to distribute them into 4 different boxes with capacities [5, 3, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 3, 'h': 4, 'e': 4, 'c': 1}, place them into 4 labeled boxes with sizes [4, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 1, 'g': 3, 'x': 5, 'h': 3} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 4, 'y': 2, 'a': 3, 'g': 3} among 4 distinguishable boxes with capacities [3, 2, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 2, 'h': 3, 'i': 2, 'l': 5} into 4 undistinguishable boxes with sizes [3, 2, 6, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 5, 's': 2, 'i': 4, 'd': 1} into 4 undistinguishable boxes with sizes [1, 4, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 4, 's': 3, 'j': 2, 'b': 3} and need to distribute them into 4 different boxes with capacities [4, 2, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 3, 'o': 1, 'p': 5, 'y': 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"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 3, 'm': 4, 'y': 3, 'p': 2}, place them into 4 labeled boxes with sizes [3, 1, 2, 6]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "928", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "185", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "217", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "690", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "690", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "277", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "311", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "164", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "928", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "137", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "331", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "471", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "185", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1060", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "441", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1172", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"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"}], "ground_truth": "464", "dataset": "MATH"}