{"messages": [{"content": "Distribute the letters {'a': 6, 'u': 1, 'm': 2, 't': 2} among 4 distinguishable boxes with capacities [5, 2, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 4, 'l': 2, 'y': 2, 'c': 3} into 4 distinctively labeled boxes with sizes [1, 2, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 3, 'e': 3, 'w': 2, 'n': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "495", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 2, 't': 4, 'c': 2, 'h': 3}, place them into 4 indistinguishable boxes with sizes [1, 1, 3, 6]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 2, 'y': 5, 'w': 2, 'z': 2} into 4 uniquely identified boxes that can hold [3, 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": "343", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 2, 'y': 1, 'i': 5, 'k': 3} into 4 undistinguishable boxes with capacities [2, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 4, 'j': 3, 't': 2, 'n': 2}, place them into 4 labeled boxes with sizes [4, 2, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 1, 'f': 4, 'y': 2, 'p': 4}, place them into 4 indistinguishable boxes with sizes [2, 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": "263", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 1, 'i': 2, 'f': 5, 't': 3} into 4 undistinguishable boxes with sizes [5, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 4, 'f': 2, 'y': 1, 'g': 4}, place them into 4 indistinguishable boxes with sizes [3, 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": "295", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 4, 'r': 1, 'h': 3, 'e': 3}, place them into 4 labeled boxes with sizes [2, 2, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 4, 'c': 4, 'l': 1, 'i': 2} among 4 identical containers that can hold [3, 2, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 3, 'k': 2, 'w': 2, 's': 4} into 4 uniquely identified boxes that can hold [3, 5, 2, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 2, 't': 3, 'b': 3, 'h': 3} among 4 identical containers that can hold [2, 2, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 3, 'n': 1, 's': 4, 'g': 3} into 4 undistinguishable boxes with capacities [1, 2, 4, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "194", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 3, 'n': 2, 'y': 2, 'h': 4} into 4 distinctively labeled boxes with sizes [2, 3, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 4, 's': 3, 'b': 2, 'w': 2} among 4 identical containers that can hold [4, 1, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 4, 'm': 3, 'x': 2, 'i': 2} into 4 uniquely identified boxes that can hold [1, 3, 1, 6] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'z': 3, 'b': 5, 'w': 1} and need to distribute them into 4 different boxes with capacities [2, 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": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 3, 'u': 2, 'x': 4, 'o': 2} into 4 distinctively labeled boxes with sizes [2, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 1, 'u': 3, 'j': 4, 'k': 3}, place them into 4 labeled boxes with sizes [4, 4, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'a': 3, 'k': 2, 'm': 3}, place them into 4 indistinguishable boxes with sizes [3, 1, 4, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 4, 'l': 1, 'r': 1, 'x': 5}, place them into 4 labeled boxes with sizes [3, 3, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 1, 'h': 4, 'm': 3, 'b': 3} among 4 identical containers that can hold [1, 4, 5, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 3, 'z': 1, 'q': 4, 'd': 3} among 4 identical containers that can hold [3, 2, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 1, 'j': 3, 'v': 4, 'a': 3} among 4 distinguishable boxes with capacities [1, 3, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 4, 'n': 4, 's': 2, 'e': 1} into 4 distinctively labeled boxes with sizes [2, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 2, 'f': 1, 'm': 4, 'l': 4} into 4 distinctively labeled boxes with sizes [2, 5, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 2, 'x': 2, 'r': 2, 'o': 5} among 4 identical containers that can hold [3, 1, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'f': 2, 'm': 2, 'c': 4, 'h': 3} into 4 undistinguishable boxes with sizes [3, 1, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 2, 'p': 1, 'r': 5, 'l': 3} into 4 uniquely identified boxes that can hold [3, 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": "495", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 1, 'd': 3, 'q': 2, 'j': 5} among 4 distinguishable boxes with capacities [3, 2, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 2, 'k': 3, 'p': 4, 'a': 2} into 4 uniquely identified boxes that can hold [2, 5, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 4, 'd': 1, 'm': 5, 't': 1}, place them into 4 labeled boxes with sizes [1, 5, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 6, 'f': 3, 'w': 1, 'g': 1}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'b': 3, 'q': 2, 'f': 2, 'o': 4} into 4 uniquely identified boxes that can hold [2, 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": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 2, 'w': 3, 'o': 1, 'p': 5} and need to distribute them into 4 identical boxes with capacities [2, 4, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 5, 'h': 1, 'p': 2, 'u': 3} into 4 uniquely identified boxes that can hold [2, 5, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 2, 'b': 3, 'e': 3, 'f': 3} into 4 uniquely identified boxes that can hold [4, 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": "567", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 1, 'a': 4, 's': 4, 'k': 2}, place them into 4 labeled boxes with sizes [2, 2, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 3, 'p': 3, 'r': 3, 'w': 2} and need to distribute them into 4 identical boxes with capacities [4, 1, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 2, 'z': 2, 'j': 3, 'r': 4}, place them into 4 indistinguishable boxes with sizes [3, 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": "298", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'a': 3, 'i': 2, 'h': 3, 'v': 3} into 4 undistinguishable boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 1, 'x': 2, 'i': 4, 'z': 4} and need to distribute them into 4 different boxes with capacities [3, 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": "295", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 2, 'u': 4, 'q': 3, 'h': 2} into 4 undistinguishable boxes with sizes [4, 3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 2, 'u': 3, 'c': 1, 'q': 5} into 4 uniquely identified boxes that can hold [4, 1, 3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 4, 'w': 2, 'b': 3, 'e': 2} among 4 identical containers that can hold [3, 3, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 2, 'g': 3, 'n': 3, 'f': 3} among 4 identical containers that can hold [1, 4, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 1, 'k': 5, 'h': 1, 'g': 4} into 4 undistinguishable boxes with sizes [4, 2, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 5, 'b': 1, 'v': 3, 'd': 2}, place them into 4 indistinguishable boxes with sizes [4, 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": "175", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'j': 2, 'd': 2, 's': 5} and need to distribute them into 4 different boxes with capacities [4, 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": "562", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 1, 'a': 5, 'x': 2, 'q': 3} into 4 undistinguishable boxes with capacities [4, 2, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 3, 't': 4, 'f': 2, 'u': 2} and need to distribute them into 4 different boxes with capacities [3, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 3, 'f': 3, 'k': 3, 'e': 2} among 4 distinguishable boxes with capacities [3, 4, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 3, 'e': 2, 'q': 3, 'k': 3} and need to distribute them into 4 different boxes with capacities [4, 1, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 3, 'o': 2, 'e': 3, 'm': 3}, place them into 4 indistinguishable boxes with sizes [1, 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": "285", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 3, 'h': 3, 'm': 2, 'v': 3} among 4 identical containers that can hold [2, 1, 3, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 3, 'e': 1, 'j': 2, 'u': 5} among 4 distinguishable boxes with capacities [3, 3, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 6, 'k': 2, 'v': 2, 'w': 1} into 4 distinctively labeled boxes with sizes [2, 2, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "291", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 1, 'n': 5, 'b': 3, 'r': 2} and need to distribute them into 4 different boxes with capacities [1, 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": "270", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 2, 'f': 3, 'd': 2, 'p': 4} into 4 undistinguishable boxes with capacities [3, 2, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 3, 'q': 2, 'g': 4, 'u': 2} into 4 undistinguishable boxes with capacities [4, 4, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 3, 'e': 4, 'l': 3, 'i': 1} among 4 distinguishable boxes with capacities [3, 2, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 5, 'z': 3, 'v': 2, 't': 1}, place them into 4 labeled boxes with sizes [3, 1, 2, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 2, 'o': 2, 'y': 4, 'w': 3} among 4 distinguishable boxes with capacities [3, 2, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 2, 'x': 5, 'c': 1, 'u': 3} and need to distribute them into 4 different boxes with capacities [2, 4, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 5, 'l': 3, 'n': 2, 'y': 1} into 4 distinctively labeled boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 2, 'w': 3, 'b': 4, 'o': 2} among 4 identical containers that can hold [3, 1, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 3, 'z': 1, 'h': 3, 'b': 4} among 4 distinguishable boxes with capacities [3, 3, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 3, 'm': 1, 'j': 3, 'o': 4} among 4 identical containers that can hold [3, 3, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 2, 'i': 2, 'c': 2, 't': 5} into 4 distinctively labeled boxes with sizes [3, 2, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 1, 'f': 3, 'e': 3, 'w': 4} into 4 uniquely identified boxes that can hold [4, 3, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 2, 'h': 2, 'o': 2, 'n': 5} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 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": "Divide the letters from {'i': 2, 's': 4, 'y': 3, 'k': 2} into 4 undistinguishable boxes with sizes [1, 2, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 3, 'r': 1, 'v': 3, 'u': 4} among 4 distinguishable boxes with capacities [5, 3, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 3, 'y': 2, 'x': 2, 'o': 4} among 4 identical containers that can hold [3, 2, 1, 5] 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": "Distribute the letters {'h': 4, 'e': 3, 't': 3, 'j': 1} among 4 identical containers that can hold [3, 3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 2, 's': 3, 'x': 3, 'g': 3} into 4 undistinguishable boxes with sizes [5, 3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 2, 'w': 3, 'l': 1, 'p': 5} among 4 distinguishable boxes with capacities [2, 2, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 2, 'p': 1, 'b': 4, 'z': 4} among 4 distinguishable boxes with capacities [2, 2, 2, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 1, 'v': 3, 'z': 5, 'q': 2} and need to distribute them into 4 identical boxes with capacities [3, 4, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 2, 'e': 2, 'k': 3, 'z': 4}, place them into 4 indistinguishable boxes with sizes [3, 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": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 3, 'v': 3, 'p': 3, 'c': 2} and need to distribute them into 4 different boxes with capacities [4, 1, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 2, 'z': 4, 'r': 2, 'm': 3}, place them into 4 indistinguishable boxes with sizes [2, 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": "404", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 2, 'e': 4, 's': 3, 'i': 2} into 4 undistinguishable boxes with capacities [2, 2, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 5, 'a': 2, 'c': 1, 'r': 3} and need to distribute them into 4 different boxes with capacities [1, 4, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 'i': 2, 'b': 3, 'z': 4}, place them into 4 labeled boxes with sizes [3, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 3, 'n': 2, 'i': 3, 'c': 3} into 4 distinctively labeled boxes with sizes [2, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1081", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 1, 'f': 2, 'c': 5, 'd': 3}, place them into 4 labeled boxes with sizes [1, 1, 1, 8]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 2, 'e': 2, 'z': 2, 'd': 5} among 4 distinguishable boxes with capacities [1, 2, 6, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "253", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 3, 'b': 3, 'h': 2, 'd': 3}, place them into 4 indistinguishable boxes with sizes [3, 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": "190", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 3, 'a': 3, 'y': 4, 's': 1}, place them into 4 labeled boxes with sizes [4, 2, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 3, 'i': 2, 'o': 5, 'q': 1} into 4 distinctively labeled boxes with sizes [7, 1, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 1, 'x': 3, 'o': 1, 'h': 6}, place them into 4 labeled boxes with sizes [2, 4, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 2, 'd': 1, 'l': 4, 'o': 4}, place them into 4 labeled boxes with sizes [4, 1, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 2, 's': 1, 'k': 4, 'q': 4} among 4 identical containers that can hold [3, 3, 4, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 3, 'c': 3, 'p': 3, 'h': 2}, place them into 4 labeled boxes with sizes [2, 4, 1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 4, 'a': 3, 'h': 1, 'n': 3} among 4 distinguishable boxes with capacities [3, 3, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 5, 'i': 4, 'k': 1, 'b': 1} into 4 distinctively labeled boxes with sizes [2, 2, 2, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 4, 'f': 1, 'm': 1, 'p': 5} into 4 uniquely identified boxes that can hold [3, 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": "279", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 4, 'a': 2, 'c': 2, 'x': 3} among 4 identical containers that can hold [4, 2, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 3, 'h': 4, 'p': 3, 'v': 1} among 4 identical containers that can hold [4, 1, 5, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 3, 't': 3, 'j': 2, 'l': 3} among 4 distinguishable boxes with capacities [5, 4, 1, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'e': 2, 's': 3, 'd': 4} and need to distribute them into 4 identical boxes with capacities [1, 5, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 'm': 4, 'c': 2, 's': 3}, place them into 4 labeled boxes with sizes [3, 1, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 3, 'm': 3, 'b': 2, 'r': 3} among 4 identical containers that can hold [1, 5, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 3, 'u': 2, 'w': 2, 'a': 4} and need to distribute them into 4 different boxes with capacities [2, 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": "562", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'v': 2, 's': 3, 'p': 3} into 4 undistinguishable boxes with capacities [2, 3, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 3, 'f': 5, 'k': 1, 'n': 2} into 4 undistinguishable boxes with capacities [3, 3, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 2, 's': 4, 'd': 4, 't': 1}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 4, 'e': 3, 'c': 1, 'w': 3}, place them into 4 indistinguishable boxes with sizes [3, 3, 1, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'t': 1, 'e': 4, 'h': 3, 'j': 3} into 4 uniquely identified boxes that can hold [1, 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": "456", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 1, 'j': 4, 'f': 2, 'g': 4} and need to distribute them into 4 different boxes with capacities [4, 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": "334", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 5, 'd': 1, 'o': 3, 'x': 2} into 4 undistinguishable boxes with capacities [3, 1, 1, 6]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 2, 'j': 5, 'a': 2, 's': 2} and need to distribute them into 4 different boxes with capacities [4, 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": "373", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 1, 'x': 1, 'f': 2, 'z': 7} into 4 undistinguishable boxes with capacities [1, 3, 5, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 3, 'm': 3, 'b': 2, 'x': 3}, place them into 4 indistinguishable boxes with sizes [1, 1, 5, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 2, 'r': 5, 'f': 2, 'i': 2}, place them into 4 indistinguishable boxes with sizes [5, 2, 1, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 4, 'l': 2, 'n': 3, 'q': 2}, place them into 4 indistinguishable boxes with sizes [4, 3, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 1, 'a': 2, 'e': 5, 'f': 3} and need to distribute them into 4 different boxes with capacities [1, 4, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 3, 'b': 3, 'm': 2, 'r': 3} into 4 uniquely identified boxes that can hold [2, 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": "645", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 1, 'v': 2, 'g': 4, 'r': 4} into 4 undistinguishable boxes with capacities [2, 3, 2, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'v': 2, 'm': 3, 'y': 4, 'r': 2} into 4 distinctively labeled boxes with sizes [4, 3, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 2, 'f': 3, 'x': 2, 'v': 4} among 4 distinguishable boxes with capacities [1, 4, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 3, 'r': 3, 'e': 2, 's': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "645", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 1, 'h': 3, 's': 4, 'i': 3} into 4 uniquely identified boxes that can hold [2, 4, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 2, 'h': 3, 'a': 5, 'l': 1} into 4 undistinguishable boxes with sizes [4, 2, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 2, 'e': 3, 'm': 4, 'i': 2}, place them into 4 indistinguishable boxes with sizes [1, 1, 5, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 2, 'i': 4, 'm': 4, 'x': 1} into 4 undistinguishable boxes with sizes [2, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 4, 'r': 2, 'h': 2, 'd': 3} among 4 distinguishable boxes with capacities [2, 2, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 2, 'y': 3, 'w': 5, 'n': 1} among 4 identical containers that can hold [3, 2, 2, 4] 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": "You have {'o': 6, 'h': 2, 's': 1, 'n': 2} and need to distribute them into 4 different boxes with capacities [2, 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": "291", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 4, 'x': 3, 'p': 2, 'g': 2} and need to distribute them into 4 identical boxes with capacities [1, 4, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 4, 'd': 3, 'k': 2, 'g': 2} into 4 undistinguishable boxes with sizes [6, 1, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 3, 'l': 4, 'f': 1, 't': 3}, place them into 4 indistinguishable boxes with sizes [2, 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": "308", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 3, 'm': 3, 'q': 3, 'a': 2} among 4 identical containers that can hold [2, 2, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 3, 'l': 4, 'w': 2, 'v': 2} into 4 undistinguishable boxes with sizes [1, 2, 4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 1, 'f': 3, 'r': 3, 'z': 4} into 4 uniquely identified boxes that can hold [2, 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": "685", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 2, 'o': 2, 'w': 5, 'a': 2} and need to distribute them into 4 different boxes with capacities [1, 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": "343", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 3, 's': 1, 'b': 2, 'u': 5}, place them into 4 labeled boxes with sizes [3, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'d': 3, 'h': 3, 's': 2, 'n': 3}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 2, 'e': 2, 'h': 3, 'g': 4} among 4 distinguishable boxes with capacities [1, 2, 4, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 1, 'w': 3, 'j': 4, 'u': 3} into 4 distinctively labeled boxes with sizes [3, 4, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 2, 'i': 3, 'w': 3, 'n': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "321", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 1, 'o': 2, 'g': 5, 'w': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 2, 'l': 3, 'g': 5, 'f': 1} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 3, 'j': 2, 'm': 3, 'g': 3} into 4 undistinguishable boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 5, 's': 2, 'r': 2, 'q': 2} into 4 distinctively labeled boxes with sizes [2, 2, 2, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "450", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 2, 'q': 2, 'u': 5, 't': 2} into 4 uniquely identified boxes that can hold [2, 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": "645", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 3, 'v': 3, 'f': 1, 'u': 4} into 4 uniquely identified boxes that can hold [3, 1, 4, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 2, 'f': 1, 'e': 7, 'k': 1} among 4 distinguishable boxes with capacities [5, 2, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 4, 't': 3, 'f': 3, 'm': 1} into 4 undistinguishable boxes with sizes [1, 2, 2, 6]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 2, 'h': 4, 'p': 3, 'g': 2} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'d': 3, 'z': 2, 'u': 2, 'w': 4}, place them into 4 indistinguishable boxes with sizes [4, 3, 3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 2, 'n': 3, 'y': 4, 'k': 2} into 4 distinctively labeled boxes with sizes [1, 4, 5, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 2, 'n': 1, 'h': 4, 'l': 4} into 4 uniquely identified boxes that can hold [3, 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": "489", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 4, 'l': 2, 'p': 2, 'y': 3} and need to distribute them into 4 different boxes with capacities [4, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 3, 'q': 4, 'x': 1, 'l': 3} among 4 identical containers that can hold [1, 3, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 3, 'e': 2, 'd': 2, 'm': 4} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 2, 'v': 3, 'd': 3, 'g': 3} into 4 undistinguishable boxes with capacities [1, 6, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 3, 'h': 1, 't': 4, 'p': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "456", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 2, 'a': 5, 'v': 1, 'f': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 1, 'i': 3, 's': 2, 'x': 5} among 4 distinguishable boxes with capacities [3, 4, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 5, 'l': 1, 'f': 2, 'n': 3} among 4 distinguishable boxes with capacities [1, 2, 5, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 4, 'f': 2, 'm': 3, 'e': 2} into 4 uniquely identified boxes that can hold [2, 3, 5, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 1, 'b': 2, 'd': 4, 'j': 4} among 4 identical containers that can hold [4, 1, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 3, 'p': 3, 'i': 1, 'w': 4} and need to distribute them into 4 different boxes with capacities [3, 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": "685", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 2, 'r': 4, 'e': 2, 'i': 3} into 4 uniquely identified boxes that can hold [3, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 1, 'p': 4, 'h': 4, 'x': 2}, place them into 4 labeled boxes with sizes [1, 3, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 2, 'd': 3, 'f': 2, 'c': 4}, place them into 4 indistinguishable boxes with sizes [3, 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": "298", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 2, 'q': 1, 'c': 4, 'e': 4} among 4 distinguishable boxes with capacities [2, 2, 5, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'h': 3, 'e': 2, 'd': 3}, place them into 4 labeled boxes with sizes [1, 3, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 1, 'y': 1, 'j': 5, 'n': 4} and need to distribute them into 4 identical boxes with capacities [1, 4, 3, 3]. 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": "Arrange the letters {'b': 2, 'l': 3, 'w': 3, 'd': 3} into 4 undistinguishable boxes with capacities [1, 4, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 3, 'e': 4, 'k': 2, 'f': 2} into 4 distinctively labeled boxes with sizes [3, 3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 2, 't': 1, 'n': 4, 'w': 4} into 4 undistinguishable boxes with sizes [4, 1, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'w': 2, 'k': 3, 'o': 3}, place them into 4 indistinguishable boxes with sizes [2, 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": "474", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 3, 'g': 3, 'p': 2, 'n': 3} into 4 uniquely identified boxes that can hold [1, 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": "685", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'r': 2, 'a': 3, 'f': 3} into 4 distinctively labeled boxes with sizes [2, 2, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 4, 'x': 2, 'n': 3, 'v': 2}, place them into 4 indistinguishable boxes with sizes [2, 4, 1, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 5, 'c': 1, 'n': 1, 't': 4} among 4 distinguishable boxes with capacities [3, 3, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "227", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 3, 'r': 3, 'a': 2, 'u': 3} and need to distribute them into 4 different boxes with capacities [3, 1, 3, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 4, 'k': 2, 'c': 1, 'e': 4} into 4 undistinguishable boxes with sizes [1, 6, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 3, 'z': 3, 'o': 2, 'u': 3} among 4 distinguishable boxes with capacities [3, 6, 1, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "247", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 4, 'y': 3, 'w': 1, 'b': 3}, place them into 4 indistinguishable boxes with sizes [3, 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": "122", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 3, 'b': 3, 'c': 2, 'g': 3}, place them into 4 labeled boxes with sizes [4, 4, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 2, 'v': 3, 'b': 3, 'k': 3} into 4 distinctively labeled boxes with sizes [2, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 2, 'r': 3, 'f': 2, 'c': 4} and need to distribute them into 4 identical boxes with capacities [4, 4, 1, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 3, 'q': 3, 'j': 3, 'm': 2} into 4 undistinguishable boxes with capacities [1, 4, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 2, 'r': 4, 'g': 1, 'p': 4} into 4 undistinguishable boxes with sizes [6, 1, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 1, 'o': 1, 'i': 3, 'p': 6}, place them into 4 indistinguishable boxes with sizes [3, 2, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 2, 'n': 3, 'w': 5, 'q': 1}, place them into 4 labeled boxes with sizes [4, 1, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 3, 'b': 2, 'd': 3, 'r': 3} and need to distribute them into 4 different boxes with capacities [2, 6, 2, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 3, 'e': 4, 'b': 2, 'x': 2} among 4 distinguishable boxes with capacities [3, 3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 4, 'u': 2, 's': 2, 'j': 3} into 4 distinctively labeled boxes with sizes [4, 2, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 2, 'p': 4, 'v': 2, 't': 3} into 4 distinctively labeled boxes with sizes [2, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'a': 3, 'd': 2, 'b': 4, 'u': 2} into 4 undistinguishable boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 't': 2, 'c': 5, 'd': 1} into 4 undistinguishable boxes with capacities [2, 4, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 3, 'g': 3, 'l': 3, 'y': 2}, place them into 4 labeled boxes with sizes [2, 2, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 5, 'a': 2, 'q': 3, 's': 1} and need to distribute them into 4 different boxes with capacities [5, 2, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 3, 's': 2, 'c': 3, 'a': 3} and need to distribute them into 4 different boxes with capacities [2, 2, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 3, 'i': 3, 'd': 3, 'b': 2} into 4 undistinguishable boxes with sizes [1, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 4, 'm': 2, 'd': 2, 'c': 3} among 4 identical containers that can hold [4, 3, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 1, 'j': 4, 'q': 2, 'r': 4}, place them into 4 indistinguishable boxes with sizes [1, 3, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 3, 'q': 2, 'm': 3, 'n': 3}, place them into 4 labeled boxes with sizes [5, 3, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 4, 'c': 2, 'w': 2, 'n': 3} into 4 uniquely identified boxes that can hold [3, 5, 2, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 3, 'd': 3, 'v': 3, 'y': 2} and need to distribute them into 4 identical boxes with capacities [4, 2, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 3, 'o': 2, 'l': 2, 'c': 4} into 4 undistinguishable boxes with sizes [3, 3, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 3, 'h': 3, 'm': 2, 'x': 3} into 4 undistinguishable boxes with capacities [3, 4, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 3, 'o': 3, 'v': 2, 'c': 3} among 4 identical containers that can hold [1, 2, 4, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 3, 'k': 2, 't': 3, 'c': 3} and need to distribute them into 4 identical boxes with capacities [3, 3, 1, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 2, 'j': 3, 'v': 4, 'u': 2} and need to distribute them into 4 different boxes with capacities [2, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 2, 'i': 5, 'v': 2, 'k': 2} into 4 undistinguishable boxes with sizes [2, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 2, 'q': 4, 'g': 4, 'y': 1} and need to distribute them into 4 identical boxes with capacities [2, 3, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 1, 'e': 4, 'c': 5, 'j': 1}, place them into 4 labeled boxes with sizes [3, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 7, 'z': 1, 'd': 1, 'i': 2} into 4 undistinguishable boxes with sizes [4, 2, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 1, 'z': 2, 'p': 5, 'i': 3} into 4 uniquely identified boxes that can hold [4, 3, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 3, 'g': 2, 'm': 3, 't': 3} into 4 undistinguishable boxes with capacities [4, 1, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 2, 'f': 4, 'd': 2, 'q': 3} into 4 distinctively labeled boxes with sizes [2, 2, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 3, 'n': 1, 'q': 4, 'x': 3}, place them into 4 labeled boxes with sizes [2, 4, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 2, 'b': 4, 'm': 4, 'g': 1}, place them into 4 indistinguishable boxes with sizes [3, 1, 2, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 4, 'k': 3, 'o': 3, 'x': 1} into 4 uniquely identified boxes that can hold [2, 2, 2, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 4, 'x': 2, 'r': 3, 'j': 2} into 4 distinctively labeled boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 4, 'l': 3, 'y': 3, 't': 1} into 4 distinctively labeled boxes with sizes [4, 1, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 2, 'i': 2, 'k': 6, 'e': 1} among 4 identical containers that can hold [1, 2, 3, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'t': 2, 'd': 2, 'g': 2, 'u': 5} into 4 uniquely identified boxes that can hold [3, 3, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 3, 's': 1, 'a': 2, 'w': 5} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 4, 's': 2, 'e': 3, 'u': 2}, place them into 4 labeled boxes with sizes [1, 3, 5, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 3, 'r': 3, 'f': 2, 'd': 3} into 4 undistinguishable boxes with sizes [4, 3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 5, 'b': 2, 'n': 3, 'u': 1} among 4 identical containers that can hold [4, 3, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 3, 'h': 5, 'q': 2, 'z': 1} and need to distribute them into 4 different boxes with capacities [1, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 2, 'n': 4, 'd': 1, 'q': 4} among 4 identical containers that can hold [4, 2, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 1, 'i': 4, 'd': 1, 'r': 5} into 4 undistinguishable boxes with capacities [3, 1, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 3, 'x': 6, 'v': 1, 'c': 1}, place them into 4 labeled boxes with sizes [2, 2, 6, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 's': 6, 'h': 1, 'f': 1} into 4 uniquely identified boxes that can hold [4, 2, 1, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 2, 'j': 3, 'k': 3, 'd': 3} into 4 undistinguishable boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 2, 'r': 3, 'q': 3, 'g': 3} and need to distribute them into 4 different boxes with capacities [3, 1, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 2, 'b': 2, 'n': 3, 'k': 4} into 4 undistinguishable boxes with capacities [1, 3, 5, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 3, 'r': 2, 'k': 3, 'f': 3} into 4 undistinguishable boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 5, 'h': 2, 'z': 3, 'l': 1}, place them into 4 indistinguishable boxes with sizes [4, 1, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 3, 'h': 3, 'v': 2, 'c': 3}, place them into 4 indistinguishable boxes with sizes [1, 2, 5, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 4, 'd': 3, 'e': 2, 'j': 2}, place them into 4 labeled boxes with sizes [2, 3, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'l': 2, 't': 2, 'x': 1, 's': 6} into 4 undistinguishable boxes with capacities [3, 2, 5, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 2, 'n': 5, 'x': 2, 'd': 2} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 4, 'm': 3, 'x': 2, 'i': 2} and need to distribute them into 4 different boxes with capacities [3, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 2, 'x': 4, 'v': 4, 'l': 1} and need to distribute them into 4 different boxes with capacities [1, 4, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 3, 'v': 2, 'c': 3, 's': 3} into 4 distinctively labeled boxes with sizes [2, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'a': 2, 'c': 1, 'f': 6, 'v': 2} into 4 distinctively labeled boxes with sizes [3, 3, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 2, 'a': 3, 'j': 2, 's': 4} among 4 identical containers that can hold [4, 2, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 2, 'r': 3, 'a': 2, 'k': 4} among 4 distinguishable boxes with capacities [1, 4, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 2, 'g': 5, 'c': 1, 'u': 3} into 4 undistinguishable boxes with capacities [2, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 1, 'a': 2, 'u': 4, 'p': 4}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 5, 'v': 3, 'k': 2, 'o': 1} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 3, 'u': 3, 'd': 2, 'm': 3} into 4 distinctively labeled boxes with sizes [1, 4, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 2, 'k': 2, 'd': 2, 't': 5} into 4 distinctively labeled boxes with sizes [4, 2, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 2, 'i': 3, 'w': 4, 'n': 2}, place them into 4 indistinguishable boxes with sizes [3, 4, 3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 1, 's': 2, 'f': 4, 'o': 4} among 4 identical containers that can hold [3, 1, 5, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 2, 'n': 3, 'q': 5, 'c': 1} among 4 distinguishable boxes with capacities [3, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 3, 'd': 5, 'z': 2, 'k': 1} among 4 distinguishable boxes with capacities [4, 2, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 2, 'm': 1, 't': 5, 's': 3}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 3, 'x': 4, 'u': 2, 'e': 2} into 4 uniquely identified boxes that can hold [2, 2, 4, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 2, 'z': 2, 'r': 3, 'y': 4} into 4 uniquely identified boxes that can hold [4, 2, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 3, 'v': 1, 'x': 3, 'a': 4} among 4 identical containers that can hold [2, 5, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 1, 'r': 4, 'c': 4, 'g': 2}, place them into 4 indistinguishable boxes with sizes [3, 2, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'c': 2, 'p': 5, 'm': 2} and need to distribute them into 4 different boxes with capacities [4, 1, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 5, 'z': 1, 'd': 2, 'f': 3} among 4 identical containers that can hold [2, 3, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 4, 'w': 3, 'n': 2, 'c': 2} into 4 undistinguishable boxes with capacities [2, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 4, 'h': 4, 'f': 2, 't': 1}, place them into 4 indistinguishable boxes with sizes [3, 3, 4, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 3, 'n': 3, 'a': 4, 'l': 1} and need to distribute them into 4 identical boxes with capacities [4, 3, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 2, 'n': 3, 'k': 5, 't': 1}, place them into 4 indistinguishable boxes with sizes [2, 3, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 4, 'a': 1, 'i': 3, 'r': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 5, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 2, 'd': 3, 'w': 3, 'j': 3} among 4 distinguishable boxes with capacities [5, 1, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 1, 'h': 3, 'd': 3, 'p': 4}, place them into 4 indistinguishable boxes with sizes [4, 2, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 4, 'a': 1, 'r': 3, 'y': 3}, place them into 4 labeled boxes with sizes [3, 5, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 4, 'k': 4, 'a': 2, 'd': 1} into 4 uniquely identified boxes that can hold [2, 1, 3, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 4, 'x': 3, 'i': 2, 'r': 2} into 4 distinctively labeled boxes with sizes [3, 4, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'q': 2, 'v': 2, 'j': 5} and need to distribute them into 4 different boxes with capacities [4, 5, 1, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 1, 'f': 3, 'g': 4, 'a': 3} into 4 distinctively labeled boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 2, 'i': 3, 'c': 4, 'a': 2} among 4 distinguishable boxes with capacities [2, 2, 2, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 2, 'k': 2, 'b': 4, 'd': 3} into 4 distinctively labeled boxes with sizes [1, 3, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 3, 'k': 2, 'g': 5, 'v': 1} among 4 identical containers that can hold [3, 3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 3, 'o': 2, 'x': 3, 'r': 3} among 4 distinguishable boxes with capacities [2, 2, 2, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 3, 'y': 3, 'k': 4, 'd': 1}, place them into 4 indistinguishable boxes with sizes [2, 2, 6, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 3, 'e': 3, 'u': 2, 'p': 3} and need to distribute them into 4 different boxes with capacities [2, 4, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 3, 'v': 2, 'o': 5, 'j': 1} among 4 identical containers that can hold [2, 3, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'e': 5, 'n': 2, 'i': 2} and need to distribute them into 4 different boxes with capacities [1, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 2, 'r': 3, 'q': 3, 'o': 3} among 4 identical containers that can hold [1, 4, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 1, 'u': 3, 'p': 3, 't': 4}, place them into 4 labeled boxes with sizes [4, 2, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 4, 'b': 3, 'x': 2, 'w': 2} among 4 distinguishable boxes with capacities [3, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 1, 'c': 6, 's': 2, 'e': 2} and need to distribute them into 4 identical boxes with capacities [4, 2, 1, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 5, 'k': 1, 'c': 2, 'h': 3}, place them into 4 indistinguishable boxes with sizes [3, 1, 2, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 4, 't': 3, 'r': 2, 's': 2} into 4 undistinguishable boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 4, 'g': 2, 'w': 1, 'f': 4} into 4 undistinguishable boxes with capacities [3, 4, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'h': 2, 'a': 3, 'e': 4} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 4, 'h': 3, 'c': 2, 'x': 2}, place them into 4 labeled boxes with sizes [3, 2, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 2, 'i': 2, 'q': 4, 'e': 3} and need to distribute them into 4 different boxes with capacities [3, 4, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 3, 'a': 2, 'y': 2, 'd': 4} and need to distribute them into 4 identical boxes with capacities [1, 2, 2, 6]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 5, 'v': 1, 'd': 2, 'n': 3} into 4 undistinguishable boxes with capacities [4, 4, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 3, 't': 2, 'c': 4, 'a': 2} into 4 undistinguishable boxes with capacities [2, 6, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 4, 'b': 3, 'e': 3, 'd': 1} into 4 distinctively labeled boxes with sizes [2, 1, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 5, 'c': 2, 'f': 1, 'm': 3} among 4 distinguishable boxes with capacities [3, 3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 2, 'q': 2, 'b': 4, 'l': 3} into 4 undistinguishable boxes with capacities [2, 2, 6, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 1, 's': 3, 'e': 3, 'a': 4} into 4 undistinguishable boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'d': 4, 'a': 1, 'x': 1, 'u': 5} into 4 distinctively labeled boxes with sizes [4, 2, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 1, 'n': 3, 't': 1, 'e': 6}, place them into 4 labeled boxes with sizes [3, 4, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 3, 's': 2, 'y': 2, 'a': 4} into 4 undistinguishable boxes with sizes [4, 4, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 4, 'g': 2, 'c': 3, 'w': 2}, place them into 4 labeled boxes with sizes [2, 3, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 2, 'a': 3, 'z': 3, 'm': 3} into 4 undistinguishable boxes with sizes [2, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 1, 'x': 4, 'g': 2, 'r': 4} into 4 distinctively labeled boxes with sizes [4, 4, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 3, 'y': 1, 'p': 2, 'w': 5}, place them into 4 labeled boxes with sizes [1, 4, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 4, 'i': 1, 'd': 3, 'm': 3} and need to distribute them into 4 different boxes with capacities [1, 2, 6, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 2, 'q': 1, 'd': 3, 'n': 5} into 4 distinctively labeled boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 4, 'p': 2, 'c': 2, 'd': 3}, place them into 4 indistinguishable boxes with sizes [2, 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": "404", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 3, 'j': 2, 'c': 3, 'q': 3} into 4 uniquely identified boxes that can hold [4, 2, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 4, 'o': 4, 'p': 1, 'b': 2} and need to distribute them into 4 different boxes with capacities [4, 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": "489", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 4, 'j': 4, 'r': 1, 's': 2}, place them into 4 indistinguishable boxes with sizes [3, 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": "104", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 1, 'g': 5, 'd': 4, 'n': 1} into 4 undistinguishable boxes with sizes [3, 2, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 3, 'i': 3, 'o': 3, 'y': 2} among 4 distinguishable boxes with capacities [2, 3, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 2, 'x': 4, 'd': 1, 'a': 4} among 4 distinguishable boxes with capacities [3, 3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 4, 'n': 2, 'e': 3, 'o': 2}, place them into 4 indistinguishable boxes with sizes [2, 3, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 3, 'x': 3, 'y': 2, 'z': 3} into 4 uniquely identified boxes that can hold [3, 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": "1081", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'q': 4, 'c': 3, 'g': 2, 'o': 2} into 4 undistinguishable boxes with capacities [3, 4, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 4, 'e': 3, 'k': 1, 'j': 3} and need to distribute them into 4 identical boxes with capacities [3, 3, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 3, 'h': 4, 'o': 2, 'a': 2} and need to distribute them into 4 identical boxes with capacities [4, 1, 4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 3, 'a': 2, 'h': 3, 'j': 3} and need to distribute them into 4 different boxes with capacities [1, 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": "567", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'g': 1, 'v': 4, 'e': 3} into 4 undistinguishable boxes with sizes [4, 2, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 3, 'c': 2, 'r': 2, 'v': 4} among 4 distinguishable boxes with capacities [4, 3, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'g': 3, 'c': 3, 'x': 3} and need to distribute them into 4 identical boxes with capacities [2, 3, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 3, 'b': 2, 'n': 4, 'd': 2} into 4 distinctively labeled boxes with sizes [2, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 2, 'e': 4, 'r': 2, 'k': 3} into 4 distinctively labeled boxes with sizes [1, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 3, 'y': 3, 'h': 4, 'l': 1} and need to distribute them into 4 identical boxes with capacities [5, 3, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 2, 'd': 2, 'x': 2, 'e': 5} into 4 undistinguishable boxes with sizes [1, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 3, 'q': 4, 'b': 2, 'u': 2} and need to distribute them into 4 different boxes with capacities [1, 4, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 3, 'x': 2, 'd': 2, 'q': 4} into 4 uniquely identified boxes that can hold [4, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 3, 'x': 2, 'v': 2, 'q': 4} among 4 distinguishable boxes with capacities [4, 1, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 4, 't': 3, 'f': 2, 'i': 2}, place them into 4 indistinguishable boxes with sizes [2, 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": "404", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 2, 'a': 4, 'w': 1, 'k': 4} into 4 undistinguishable boxes with sizes [2, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'k': 3, 'a': 4, 'j': 2} and need to distribute them into 4 identical boxes with capacities [5, 2, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 3, 'x': 3, 'k': 3, 'b': 2} and need to distribute them into 4 different boxes with capacities [2, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1081", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 2, 's': 2, 'm': 4, 'h': 3} and need to distribute them into 4 identical boxes with capacities [3, 4, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 1, 'y': 5, 'm': 4, 'l': 1} into 4 undistinguishable boxes with capacities [2, 2, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 3, 'd': 4, 'l': 3, 'v': 1} among 4 identical containers that can hold [2, 4, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 2, 'w': 3, 'v': 3, 'e': 3} among 4 identical containers that can hold [2, 2, 6, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'d': 2, 'n': 2, 'b': 2, 'e': 5}, place them into 4 labeled boxes with sizes [2, 3, 1, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 3, 'k': 4, 'g': 3, 'c': 1} into 4 distinctively labeled boxes with sizes [2, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 1, 'h': 4, 'n': 4, 'o': 2} into 4 undistinguishable boxes with sizes [1, 5, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 1, 'f': 5, 'p': 2, 'g': 3} into 4 undistinguishable boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 3, 'r': 2, 'u': 3, 'b': 3}, place them into 4 indistinguishable boxes with sizes [3, 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": "474", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 3, 'q': 4, 'f': 3, 'm': 1} among 4 identical containers that can hold [3, 5, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 2, 'b': 4, 'u': 2, 'q': 3} into 4 undistinguishable boxes with sizes [4, 3, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 2, 'p': 3, 'l': 4, 'y': 2}, place them into 4 indistinguishable boxes with sizes [2, 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": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'v': 3, 'c': 1, 'z': 5} and need to distribute them into 4 identical boxes with capacities [2, 4, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 2, 'z': 3, 'o': 4, 'e': 2} into 4 undistinguishable boxes with capacities [2, 1, 4, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 3, 'r': 2, 'g': 3, 'u': 3} and need to distribute them into 4 different boxes with capacities [4, 3, 1, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 4, 'j': 1, 'o': 4, 'n': 2}, place them into 4 indistinguishable boxes with sizes [2, 1, 2, 6]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 3, 'f': 2, 'l': 4, 'y': 2} into 4 distinctively labeled boxes with sizes [2, 2, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'c': 4, 'u': 2, 'q': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 4, 'y': 3, 'a': 2, 'q': 2} into 4 distinctively labeled boxes with sizes [4, 3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'b': 2, 'd': 3, 'q': 4, 'm': 2} into 4 undistinguishable boxes with capacities [2, 5, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 4, 'b': 2, 'o': 2, 'l': 3} and need to distribute them into 4 identical boxes with capacities [1, 2, 4, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 3, 'n': 4, 'v': 1, 's': 3} into 4 distinctively labeled boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 4, 's': 2, 'j': 3, 'h': 2} into 4 undistinguishable boxes with sizes [2, 1, 4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 3, 'x': 2, 'v': 4, 'z': 2} among 4 distinguishable boxes with capacities [2, 1, 4, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 4, 'i': 3, 'v': 3, 'a': 1} among 4 distinguishable boxes with capacities [1, 2, 3, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 2, 'm': 2, 'z': 5, 'c': 2} into 4 undistinguishable boxes with sizes [3, 4, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 4, 'f': 1, 'c': 2, 'k': 4} among 4 identical containers that can hold [2, 2, 5, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 1, 'd': 4, 'g': 3, 't': 3} into 4 distinctively labeled boxes with sizes [3, 3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 4, 'u': 3, 'd': 1, 'z': 3} among 4 identical containers that can hold [3, 2, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 1, 'i': 4, 'z': 4, 'c': 2} and need to distribute them into 4 different boxes with capacities [3, 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": "489", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 4, 'l': 2, 'b': 2, 'i': 3} into 4 undistinguishable boxes with capacities [3, 2, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 1, 'f': 2, 'r': 4, 'c': 4} among 4 identical containers that can hold [3, 3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 1, 'g': 3, 'q': 3, 'v': 4}, place them into 4 indistinguishable boxes with sizes [3, 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": "122", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'l': 3, 'o': 3, 'k': 2, 'm': 3} into 4 undistinguishable boxes with capacities [1, 5, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 3, 'i': 3, 'a': 3, 'n': 2} among 4 identical containers that can hold [2, 5, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 3, 'j': 5, 'd': 1, 's': 2} into 4 uniquely identified boxes that can hold [2, 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": "343", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 2, 'f': 3, 'k': 3, 'v': 3} into 4 undistinguishable boxes with capacities [2, 3, 1, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 2, 'o': 3, 'x': 3, 'l': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 's': 2, 'g': 5, 'e': 2} and need to distribute them into 4 identical boxes with capacities [4, 2, 4, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'c': 2, 'k': 5, 'd': 2} and need to distribute them into 4 different boxes with capacities [2, 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": "343", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 2, 'e': 4, 'k': 2, 's': 3} and need to distribute them into 4 different boxes with capacities [4, 1, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 2, 's': 3, 'p': 3, 'c': 3} and need to distribute them into 4 identical boxes with capacities [2, 1, 4, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 2, 'o': 4, 's': 2, 'r': 3} among 4 distinguishable boxes with capacities [4, 2, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 5, 'b': 2, 'z': 2, 'w': 2} into 4 undistinguishable boxes with capacities [3, 4, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 1, 'v': 3, 'i': 4, 'o': 3} into 4 undistinguishable boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 3, 'g': 2, 'r': 3, 'x': 3} into 4 uniquely identified boxes that can hold [2, 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": "1081", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 4, 's': 2, 'd': 2, 'c': 3} among 4 identical containers that can hold [2, 2, 5, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 1, 't': 5, 'j': 2, 'w': 3} into 4 uniquely identified boxes that can hold [2, 4, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 3, 'c': 1, 'x': 3, 't': 4} and need to distribute them into 4 different boxes with capacities [1, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 1, 'n': 2, 'k': 5, 'q': 3} and need to distribute them into 4 different boxes with capacities [3, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 3, 'w': 3, 'r': 2, 'k': 3} among 4 distinguishable boxes with capacities [3, 3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1081", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 3, 'm': 2, 'j': 4, 'q': 2} among 4 identical containers that can hold [5, 1, 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": "Distribute the letters {'l': 2, 'q': 2, 'y': 4, 'g': 3} among 4 identical containers that can hold [2, 4, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 1, 't': 3, 'z': 4, 'w': 3} and need to distribute them into 4 different boxes with capacities [2, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 2, 'f': 3, 'a': 2, 'x': 4}, place them into 4 indistinguishable boxes with sizes [3, 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": "162", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 3, 'x': 4, 'o': 1, 'j': 3} among 4 identical containers that can hold [2, 4, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 3, 'c': 2, 'p': 3, 'x': 3} among 4 distinguishable boxes with capacities [2, 5, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'q': 2, 't': 2, 'l': 4} into 4 undistinguishable boxes with sizes [2, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 2, 'f': 3, 'w': 1, 'g': 5}, place them into 4 indistinguishable boxes with sizes [3, 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": "175", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 2, 'w': 5, 'm': 3, 'y': 1} into 4 undistinguishable boxes with capacities [1, 6, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 1, 'z': 5, 'g': 3, 'a': 2} and need to distribute them into 4 different boxes with capacities [2, 1, 5, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 3, 'p': 2, 'k': 3, 'd': 3} and need to distribute them into 4 identical boxes with capacities [1, 3, 2, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 4, 'f': 3, 'j': 2, 's': 2} into 4 distinctively labeled boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 2, 'b': 3, 'n': 2, 't': 4} among 4 identical containers that can hold [2, 4, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 3, 'g': 4, 'v': 2, 'w': 2} into 4 undistinguishable boxes with sizes [2, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 4, 'h': 2, 's': 3, 'o': 2} among 4 distinguishable boxes with capacities [5, 4, 1, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 2, 'p': 5, 'b': 1, 'e': 3} into 4 undistinguishable boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 4, 'j': 4, 's': 1, 'z': 2} among 4 identical containers that can hold [2, 3, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 4, 'o': 2, 't': 2, 'v': 3} among 4 identical containers that can hold [2, 3, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 3, 'q': 4, 'x': 2, 't': 2} into 4 undistinguishable boxes with capacities [4, 5, 1, 1]. 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": "Distribute the letters {'f': 2, 'p': 3, 'l': 3, 'r': 3} among 4 distinguishable boxes with capacities [2, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 3, 'q': 2, 'c': 2, 'u': 4}, place them into 4 labeled boxes with sizes [4, 2, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 4, 'b': 1, 'n': 5, 's': 1} into 4 undistinguishable boxes with capacities [2, 6, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 4, 'h': 2, 't': 4, 's': 1} and need to distribute them into 4 identical boxes with capacities [3, 3, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 4, 'm': 2, 'g': 2, 'i': 3} into 4 distinctively labeled boxes with sizes [2, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 2, 'v': 1, 'c': 4, 'k': 4} among 4 identical containers that can hold [2, 2, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 3, 'j': 4, 'b': 2, 'm': 2} into 4 undistinguishable boxes with capacities [3, 2, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 3, 'g': 3, 'f': 3, 'n': 2} and need to distribute them into 4 different boxes with capacities [2, 1, 2, 6]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 2, 'w': 3, 'j': 3, 'x': 3} and need to distribute them into 4 different boxes with capacities [6, 2, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 2, 'h': 5, 'v': 2, 'e': 2} and need to distribute them into 4 identical boxes with capacities [4, 3, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 2, 'n': 4, 'x': 3, 'e': 2} and need to distribute them into 4 different boxes with capacities [2, 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": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 1, 'y': 4, 't': 3, 'l': 3} and need to distribute them into 4 identical boxes with capacities [2, 3, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 1, 'e': 6, 'o': 2, 'n': 2}, place them into 4 labeled boxes with sizes [3, 1, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'d': 5, 'f': 2, 'y': 2, 't': 2} into 4 undistinguishable boxes with sizes [2, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 5, 'f': 2, 'o': 2, 'v': 2}, place them into 4 indistinguishable boxes with sizes [6, 2, 1, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 3, 'k': 2, 'i': 5, 'e': 1} into 4 uniquely identified boxes that can hold [2, 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": "343", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 2, 'g': 3, 'n': 3, 'x': 3}, place them into 4 labeled boxes with sizes [3, 1, 5, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'b': 5, 'i': 1, 's': 4, 'f': 1}, place them into 4 labeled boxes with sizes [2, 3, 1, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 4, 's': 2, 'g': 3, 'x': 2} among 4 distinguishable boxes with capacities [2, 3, 1, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 5, 'k': 3, 'b': 1, 'w': 2} among 4 distinguishable boxes with capacities [3, 4, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 2, 'n': 3, 'j': 4, 'm': 2} and need to distribute them into 4 identical boxes with capacities [2, 6, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 3, 'b': 1, 'v': 4, 'e': 3} into 4 undistinguishable boxes with capacities [4, 3, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 2, 'j': 3, 'y': 4, 'k': 2} and need to distribute them into 4 identical boxes with capacities [4, 2, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 3, 'r': 3, 'm': 3, 'o': 2} among 4 identical containers that can hold [3, 4, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 2, 'n': 2, 'g': 3, 'k': 4}, place them into 4 labeled boxes with sizes [3, 3, 1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 1, 'c': 5, 'f': 2, 'd': 3} and need to distribute them into 4 identical boxes with capacities [2, 3, 4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 2, 't': 4, 'z': 1, 'u': 4} into 4 undistinguishable boxes with capacities [3, 1, 4, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 2, 'e': 5, 'c': 2, 'w': 2} into 4 undistinguishable boxes with capacities [2, 3, 2, 4]. 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": "Given the letters {'i': 4, 'k': 1, 'l': 3, 'c': 3}, place them into 4 labeled boxes with sizes [4, 1, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 4, 'k': 4, 'a': 2, 'n': 1} into 4 distinctively labeled boxes with sizes [2, 2, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 2, 'd': 5, 'h': 3, 'p': 1} among 4 distinguishable boxes with capacities [2, 5, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'p': 2, 'l': 3, 'd': 3, 'a': 3}, place them into 4 labeled boxes with sizes [5, 2, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 1, 'y': 2, 'o': 3, 'x': 5}, place them into 4 labeled boxes with sizes [5, 2, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'f': 4, 'a': 2, 'u': 2}, place them into 4 labeled boxes with sizes [3, 3, 4, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'u': 3, 'r': 3, 'w': 2, 'e': 3} into 4 undistinguishable boxes with capacities [5, 1, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 2, 'm': 3, 'y': 5, 'u': 1} among 4 identical containers that can hold [3, 1, 2, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'d': 1, 's': 5, 'm': 3, 'b': 2} into 4 undistinguishable boxes with sizes [4, 3, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 3, 'k': 4, 'b': 1, 'v': 3} into 4 undistinguishable boxes with sizes [2, 1, 4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "194", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 2, 'a': 3, 'v': 1, 'f': 5} into 4 distinctively labeled boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 'd': 2, 't': 2, 'b': 4} and need to distribute them into 4 different boxes with capacities [2, 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": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 1, 'y': 4, 't': 4, 'z': 2} and need to distribute them into 4 identical boxes with capacities [5, 1, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'c': 3, 'h': 3, 's': 3} and need to distribute them into 4 identical boxes with capacities [2, 4, 1, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 1, 's': 4, 'r': 4, 't': 2} into 4 undistinguishable boxes with sizes [4, 1, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 4, 'm': 1, 'q': 1, 's': 5} into 4 undistinguishable boxes with capacities [3, 2, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 4, 't': 1, 'r': 5, 'b': 1} into 4 undistinguishable boxes with capacities [4, 2, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 5, 'b': 1, 'y': 4, 'r': 1}, place them into 4 indistinguishable boxes with sizes [2, 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": "103", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 3, 'g': 5, 't': 1, 'w': 2} and need to distribute them into 4 identical boxes with capacities [2, 2, 3, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 1, 'l': 6, 's': 2, 'q': 2} and need to distribute them into 4 different boxes with capacities [2, 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": "253", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 3, 'z': 3, 'q': 2, 'j': 3}, place them into 4 labeled boxes with sizes [2, 5, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 4, 'l': 2, 'e': 1, 'h': 4} into 4 undistinguishable boxes with sizes [3, 4, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 2, 'f': 3, 'v': 1, 'z': 5} and need to distribute them into 4 identical boxes with capacities [4, 3, 1, 3]. 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": "Distribute the letters {'l': 3, 'g': 2, 'a': 4, 'o': 2} among 4 identical containers that can hold [4, 2, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 5, 'r': 2, 'v': 1, 's': 3} into 4 undistinguishable boxes with capacities [1, 3, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 3, 's': 2, 'q': 3, 'd': 3} and need to distribute them into 4 identical boxes with capacities [4, 1, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 4, 'd': 2, 'i': 2, 'j': 3}, place them into 4 indistinguishable boxes with sizes [2, 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": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 3, 'u': 2, 'w': 3, 'j': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "1081", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 1, 'y': 2, 'v': 4, 'l': 4} into 4 undistinguishable boxes with sizes [3, 2, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 4, 'y': 4, 'v': 2, 's': 1} and need to distribute them into 4 identical boxes with capacities [4, 2, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 3, 'f': 3, 'n': 2, 'z': 3} into 4 distinctively labeled boxes with sizes [2, 4, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 3, 'k': 2, 'd': 3, 'z': 3} among 4 identical containers that can hold [3, 4, 1, 3] 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": "You have {'c': 3, 'r': 3, 'j': 3, 'q': 2} and need to distribute them into 4 identical boxes with capacities [2, 1, 6, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 3, 'g': 1, 'h': 5, 'e': 2}, place them into 4 indistinguishable boxes with sizes [3, 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": "90", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 4, 'x': 2, 'o': 2, 'l': 3}, place them into 4 indistinguishable boxes with sizes [2, 3, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 5, 'y': 2, 'q': 3, 'l': 1} and need to distribute them into 4 different boxes with capacities [3, 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": "495", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 3, 'a': 3, 'e': 3, 'i': 2} among 4 distinguishable boxes with capacities [5, 2, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 3, 'g': 2, 'u': 1, 'l': 5} and need to distribute them into 4 identical boxes with capacities [1, 2, 6, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 1, 'q': 3, 'c': 5, 'l': 2} and need to distribute them into 4 different boxes with capacities [5, 2, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 3, 'k': 2, 'i': 3, 'g': 3}, place them into 4 indistinguishable boxes with sizes [3, 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": "474", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 1, 'e': 4, 'l': 2, 'h': 4}, place them into 4 indistinguishable boxes with sizes [3, 2, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 4, 'i': 2, 'u': 2, 'g': 3} into 4 undistinguishable boxes with capacities [2, 1, 3, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 1, 'x': 3, 's': 3, 'm': 4} and need to distribute them into 4 different boxes with capacities [2, 2, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 4, 'x': 3, 'v': 1, 'w': 3} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 3, 'a': 4, 'r': 3, 'n': 1} and need to distribute them into 4 identical boxes with capacities [1, 2, 4, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "194", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 1, 'y': 5, 'f': 1, 'k': 4}, place them into 4 labeled boxes with sizes [2, 3, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 3, 't': 3, 'j': 4, 'i': 1}, place them into 4 indistinguishable boxes with sizes [3, 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": "122", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 3, 't': 3, 'h': 2, 'p': 3} into 4 undistinguishable boxes with sizes [3, 3, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 3, 'f': 3, 'o': 2, 'y': 3} into 4 undistinguishable boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 1, 'd': 4, 'e': 4, 'x': 2} into 4 undistinguishable boxes with sizes [4, 4, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'i': 3, 'k': 1, 'l': 4, 'a': 3} into 4 undistinguishable boxes with capacities [3, 4, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 3, 'l': 4, 'j': 2, 'k': 2} among 4 identical containers that can hold [5, 3, 2, 1] 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": "Distribute the letters {'w': 4, 'i': 4, 'h': 2, 'z': 1} among 4 distinguishable boxes with capacities [2, 3, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 2, 'y': 3, 'k': 3, 'v': 3} among 4 identical containers that can hold [5, 2, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 's': 5, 'c': 1, 'l': 3}, place them into 4 indistinguishable boxes with sizes [3, 4, 3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 3, 'd': 2, 'm': 3, 'e': 3} among 4 distinguishable boxes with capacities [2, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 3, 'd': 3, 'a': 2, 'z': 3} among 4 distinguishable boxes with capacities [2, 5, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 3, 'm': 2, 'i': 4, 'r': 2} among 4 identical containers that can hold [4, 3, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 2, 'f': 4, 'r': 3, 'k': 2} into 4 distinctively labeled boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 2, 'b': 2, 'l': 4, 'i': 3} and need to distribute them into 4 identical boxes with capacities [3, 1, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 3, 'h': 2, 'f': 3, 'n': 3} among 4 identical containers that can hold [2, 3, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 3, 'b': 2, 'k': 4, 'e': 2}, place them into 4 labeled boxes with sizes [2, 4, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 1, 'y': 4, 't': 2, 'g': 4} among 4 identical containers that can hold [4, 1, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 4, 'k': 1, 'l': 3, 'p': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "340", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 4, 'a': 2, 'g': 3, 'v': 2}, place them into 4 indistinguishable boxes with sizes [4, 3, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 2, 'n': 2, 'g': 3, 'x': 4} and need to distribute them into 4 different boxes with capacities [3, 3, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 4, 'b': 3, 'y': 2, 'm': 2} and need to distribute them into 4 different boxes with capacities [2, 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": "755", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 4, 's': 3, 'p': 3, 'j': 1}, place them into 4 indistinguishable boxes with sizes [1, 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": "194", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 4, 'l': 3, 'p': 3, 'a': 1} among 4 identical containers that can hold [5, 1, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 2, 'p': 3, 'h': 4, 'j': 2} and need to distribute them into 4 different boxes with capacities [2, 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": "755", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 2, 'd': 4, 'l': 3, 'a': 2} into 4 undistinguishable boxes with sizes [1, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 3, 'v': 1, 'a': 2, 'e': 5} among 4 identical containers that can hold [1, 3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 5, 'd': 2, 'j': 2, 'w': 2}, place them into 4 indistinguishable boxes with sizes [2, 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": "190", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 3, 'f': 3, 'o': 3, 'e': 2} among 4 identical containers that can hold [3, 3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 5, 't': 2, 'b': 1, 'e': 3} into 4 undistinguishable boxes with sizes [2, 2, 2, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 3, 'w': 1, 'b': 3, 'j': 4} and need to distribute them into 4 identical boxes with capacities [3, 2, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 3, 'n': 2, 'c': 4, 'r': 2}, place them into 4 indistinguishable boxes with sizes [3, 3, 1, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 7, 'u': 1, 'j': 1, 's': 2} among 4 distinguishable boxes with capacities [5, 3, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 4, 'x': 1, 'w': 3, 'f': 3}, place them into 4 labeled boxes with sizes [3, 2, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 3, 'a': 3, 'v': 2, 'm': 3}, place them into 4 labeled boxes with sizes [3, 2, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 4, 'l': 4, 'i': 1, 'q': 2} into 4 undistinguishable boxes with capacities [3, 3, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'l': 2, 't': 4, 'x': 4, 'j': 1} into 4 uniquely identified boxes that can hold [2, 5, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 4, 'b': 2, 'l': 3, 'i': 2} and need to distribute them into 4 identical boxes with capacities [2, 4, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 3, 's': 4, 'z': 2, 'e': 2} into 4 distinctively labeled boxes with sizes [3, 1, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 4, 'k': 2, 'n': 3, 'q': 2} into 4 uniquely identified boxes that can hold [4, 1, 4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 5, 'q': 2, 'm': 2, 'k': 2} into 4 distinctively labeled boxes with sizes [5, 3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 4, 'e': 3, 'p': 1, 'y': 3} into 4 undistinguishable boxes with sizes [3, 1, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 3, 't': 3, 'h': 3, 'n': 2} into 4 undistinguishable boxes with capacities [2, 2, 4, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 2, 'o': 4, 'd': 4, 's': 1} among 4 distinguishable boxes with capacities [2, 4, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 4, 'd': 3, 'a': 2, 't': 2} and need to distribute them into 4 different boxes with capacities [3, 4, 3, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 2, 'i': 3, 'p': 2, 'u': 4} into 4 uniquely identified boxes that can hold [2, 4, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 4, 'p': 4, 'k': 1, 'h': 2} among 4 identical containers that can hold [4, 3, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'a': 3, 'q': 3, 'w': 2} into 4 undistinguishable boxes with sizes [3, 2, 5, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 3, 't': 2, 'm': 2, 'x': 4}, place them into 4 labeled boxes with sizes [3, 2, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 5, 'k': 2, 'a': 1, 'v': 3} among 4 distinguishable boxes with capacities [4, 2, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 3, 'e': 3, 'u': 2, 'l': 3} into 4 undistinguishable boxes with capacities [3, 3, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 1, 'f': 4, 'j': 2, 'l': 4} among 4 identical containers that can hold [2, 2, 5, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 3, 'k': 2, 'f': 3, 'a': 3} into 4 distinctively labeled boxes with sizes [1, 4, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 2, 'r': 3, 'z': 4, 'e': 2} and need to distribute them into 4 different boxes with capacities [3, 1, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 4, 'y': 3, 'e': 3, 'f': 1} into 4 distinctively labeled boxes with sizes [4, 2, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 3, 'k': 3, 'w': 4, 'v': 1} and need to distribute them into 4 identical boxes with capacities [1, 5, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'f': 2, 'r': 2, 'i': 4, 's': 3} into 4 undistinguishable boxes with sizes [5, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'd': 3, 'z': 1, 'u': 5} and need to distribute them into 4 different boxes with capacities [3, 4, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 2, 'e': 4, 'w': 2, 'f': 3} into 4 undistinguishable boxes with sizes [3, 2, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 2, 'u': 2, 'm': 3, 'x': 4} and need to distribute them into 4 different boxes with capacities [4, 2, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 3, 'c': 3, 'e': 3, 'a': 2} and need to distribute them into 4 different boxes with capacities [4, 1, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'d': 1, 'i': 3, 's': 5, 'w': 2} into 4 distinctively labeled boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'z': 2, 'h': 1, 'k': 3, 'p': 5} into 4 undistinguishable boxes with capacities [4, 2, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'l': 2, 'u': 3, 'p': 3} into 4 distinctively labeled boxes with sizes [3, 2, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 4, 'h': 1, 'm': 3, 'd': 3} into 4 uniquely identified boxes that can hold [2, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 1, 'k': 6, 'j': 1, 'f': 3} among 4 identical containers that can hold [2, 3, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 1, 'k': 2, 'u': 5, 'z': 3} into 4 undistinguishable boxes with sizes [4, 3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 2, 'n': 5, 'f': 3, 'l': 1} and need to distribute them into 4 identical boxes with capacities [1, 3, 3, 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": "Distribute the letters {'t': 1, 'v': 3, 'l': 4, 'p': 3} among 4 distinguishable boxes with capacities [2, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 4, 'o': 2, 'g': 3, 't': 2} into 4 uniquely identified boxes that can hold [3, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 6, 'm': 1, 'x': 2, 'b': 2}, place them into 4 labeled boxes with sizes [1, 5, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 1, 'u': 3, 'h': 3, 'x': 4} and need to distribute them into 4 different boxes with capacities [3, 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": "456", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 2, 'r': 2, 'p': 5, 'q': 2} and need to distribute them into 4 different boxes with capacities [3, 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": "645", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 2, 't': 1, 'q': 6, 'f': 2} into 4 uniquely identified boxes that can hold [3, 4, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 3, 'j': 4, 'r': 2, 'z': 2} and need to distribute them into 4 identical boxes with capacities [2, 3, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 3, 'f': 3, 'g': 3, 'x': 2} into 4 undistinguishable boxes with capacities [2, 3, 1, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 4, 'l': 4, 'z': 2, 'c': 1} into 4 distinctively labeled boxes with sizes [2, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "You have {'z': 3, 'v': 4, 'f': 1, 's': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 2, 'n': 3, 't': 3, 'h': 3} into 4 undistinguishable boxes with sizes [2, 3, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'i': 3, 's': 4, 'g': 3, 'o': 1} into 4 undistinguishable boxes with capacities [3, 2, 4, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 3, 'b': 2, 'l': 4, 'f': 2} into 4 undistinguishable boxes with sizes [2, 3, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 3, 'f': 3, 'v': 4, 'k': 1}, place them into 4 labeled boxes with sizes [5, 3, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 2, 'd': 5, 'w': 3, 'r': 1} and need to distribute them into 4 identical boxes with capacities [4, 3, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 2, 'd': 5, 'b': 3, 'f': 1} into 4 undistinguishable boxes with sizes [1, 5, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 3, 'k': 4, 'v': 3, 'h': 1} and need to distribute them into 4 different boxes with capacities [5, 3, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 3, 'z': 3, 'k': 2, 'd': 3} into 4 undistinguishable boxes with sizes [2, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 2, 'a': 2, 'd': 4, 'n': 3} into 4 undistinguishable boxes with sizes [3, 4, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 3, 'o': 3, 'j': 3, 'a': 2} into 4 undistinguishable boxes with sizes [2, 2, 2, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 3, 'i': 1, 'b': 2, 'x': 5} and need to distribute them into 4 different boxes with capacities [4, 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": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 2, 'q': 4, 'w': 3, 'i': 2} among 4 identical containers that can hold [4, 2, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 2, 'j': 3, 'o': 4, 'b': 2} among 4 identical containers that can hold [3, 3, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 1, 'f': 3, 'b': 2, 'c': 5} into 4 distinctively labeled boxes with sizes [2, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 4, 'l': 3, 'z': 2, 'c': 2} into 4 distinctively labeled boxes with sizes [3, 1, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 3, 'y': 4, 'v': 1, 'd': 3}, place them into 4 labeled boxes with sizes [2, 3, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 3, 'i': 2, 'o': 4, 'a': 2} into 4 undistinguishable boxes with sizes [2, 2, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 3, 'o': 3, 'i': 2, 'c': 3} among 4 identical containers that can hold [2, 4, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 4, 'y': 1, 'q': 3, 'w': 3} among 4 distinguishable boxes with capacities [2, 3, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 3, 'c': 2, 'l': 3, 'h': 3} among 4 distinguishable boxes with capacities [3, 4, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 1, 'v': 5, 'w': 2, 'j': 3}, place them into 4 labeled boxes with sizes [3, 4, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 4, 'b': 3, 'p': 2, 'v': 2} and need to distribute them into 4 different boxes with capacities [2, 4, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 1, 'a': 3, 'u': 4, 'c': 3} into 4 undistinguishable boxes with sizes [3, 4, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 1, 'z': 4, 'w': 2, 'p': 4} into 4 uniquely identified boxes that can hold [2, 4, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'e': 2, 'w': 2, 'j': 6, 'z': 1} among 4 identical containers that can hold [2, 1, 5, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 2, 't': 2, 'd': 4, 'r': 3} among 4 distinguishable boxes with capacities [3, 3, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 2, 'f': 4, 't': 2, 'w': 3} among 4 distinguishable boxes with capacities [3, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 5, 'v': 2, 'e': 2, 'r': 2} among 4 distinguishable boxes with capacities [5, 2, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "450", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 1, 'p': 3, 'd': 2, 'h': 5}, place them into 4 labeled boxes with sizes [2, 4, 1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 2, 'w': 3, 'b': 3, 'f': 3} among 4 distinguishable boxes with capacities [4, 2, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 2, 'e': 1, 'j': 2, 'w': 6} and need to distribute them into 4 different boxes with capacities [2, 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": "291", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 3, 'k': 2, 'e': 4, 'l': 2} into 4 undistinguishable boxes with sizes [2, 5, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 1, 's': 3, 'f': 4, 'o': 3} among 4 distinguishable boxes with capacities [3, 2, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 4, 'c': 3, 'e': 2, 'm': 2} into 4 undistinguishable boxes with sizes [3, 3, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 2, 'x': 3, 'd': 3, 'a': 3} and need to distribute them into 4 different boxes with capacities [3, 4, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 2, 'y': 3, 'c': 3, 'f': 3} into 4 undistinguishable boxes with capacities [3, 4, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 2, 'j': 1, 'r': 3, 'a': 5} into 4 distinctively labeled boxes with sizes [4, 1, 5, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 3, 'p': 2, 'x': 4, 'k': 2} into 4 undistinguishable boxes with sizes [2, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 3, 'j': 3, 'u': 1, 'h': 4} and need to distribute them into 4 different boxes with capacities [4, 4, 2, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 2, 'l': 3, 'j': 3, 'i': 3}, place them into 4 labeled boxes with sizes [3, 1, 2, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 1, 'u': 7, 'f': 1, 'n': 2} into 4 distinctively labeled boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "147", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 5, 'd': 3, 'y': 2, 'v': 1}, place them into 4 labeled boxes with sizes [3, 1, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 1, 'o': 4, 'u': 2, 'x': 4} into 4 undistinguishable boxes with capacities [4, 2, 4, 1]. 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": "Given the letters {'g': 1, 't': 3, 'p': 3, 'r': 4}, place them into 4 indistinguishable boxes with sizes [1, 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": "233", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 5, 'u': 2, 'c': 2, 's': 2} and need to distribute them into 4 different boxes with capacities [3, 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": "562", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 3, 'i': 2, 'n': 3, 'w': 3} and need to distribute them into 4 identical boxes with capacities [3, 2, 4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 2, 'f': 3, 'p': 2, 'y': 4}, place them into 4 indistinguishable boxes with sizes [1, 5, 1, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 2, 'i': 4, 'o': 3, 'c': 2} among 4 distinguishable boxes with capacities [1, 4, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 4, 't': 3, 'd': 3, 'l': 1} among 4 distinguishable boxes with capacities [3, 3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 5, 'o': 1, 'h': 2, 'v': 3}, place them into 4 indistinguishable boxes with sizes [3, 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": "232", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'l': 4, 'k': 2, 'g': 2, 'q': 3} into 4 undistinguishable boxes with capacities [2, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 's': 3, 'b': 3, 'c': 2} and need to distribute them into 4 different boxes with capacities [2, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 3, 's': 1, 'e': 4, 'n': 3}, place them into 4 labeled boxes with sizes [3, 2, 5, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 4, 'q': 3, 'p': 3, 'r': 1} into 4 undistinguishable boxes with capacities [3, 5, 1, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 3, 'l': 3, 'b': 2, 'e': 3} into 4 undistinguishable boxes with capacities [3, 1, 5, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 3, 'z': 4, 'i': 3, 'f': 1} into 4 distinctively labeled boxes with sizes [3, 3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 4, 'p': 1, 'm': 2, 'l': 4}, place them into 4 indistinguishable boxes with sizes [4, 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": "263", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'m': 3, 'b': 3, 'g': 1, 'c': 4} into 4 uniquely identified boxes that can hold [4, 1, 2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 3, 'p': 2, 'f': 3, 'g': 3} into 4 uniquely identified boxes that can hold [2, 2, 2, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 3, 'm': 4, 'x': 3, 's': 1} into 4 distinctively labeled boxes with sizes [2, 5, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 5, 't': 3, 'h': 1, 'k': 2} into 4 undistinguishable boxes with sizes [1, 5, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 3, 'q': 1, 'b': 4, 'x': 3} among 4 distinguishable boxes with capacities [3, 5, 2, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 2, 'a': 2, 'u': 4, 'm': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "562", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 3, 'l': 3, 'm': 2, 'y': 3} into 4 undistinguishable boxes with sizes [4, 3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 2, 'q': 4, 'h': 2, 'm': 3}, place them into 4 indistinguishable boxes with sizes [3, 5, 1, 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 {'y': 4, 'd': 4, 't': 2, 'u': 1}, place them into 4 indistinguishable boxes with sizes [2, 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": "263", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 2, 'e': 4, 'i': 1, 'f': 4} among 4 distinguishable boxes with capacities [4, 2, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 4, 'r': 1, 's': 4, 'k': 2} and need to distribute them into 4 identical boxes with capacities [2, 1, 3, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 2, 'g': 4, 'v': 2, 'l': 3} into 4 undistinguishable boxes with sizes [1, 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": "Given the letters {'f': 4, 'z': 3, 'm': 3, 'b': 1}, place them into 4 indistinguishable boxes with sizes [3, 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": "308", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 2, 'b': 2, 'x': 4, 'q': 3} among 4 identical containers that can hold [5, 2, 3, 1] 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": "Given the letters {'n': 6, 'q': 1, 'j': 1, 'z': 3}, place them into 4 labeled boxes with sizes [3, 1, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 2, 'i': 3, 'k': 2, 'b': 4} into 4 uniquely identified boxes that can hold [2, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 5, 'y': 2, 'r': 2, 't': 2}, place them into 4 labeled boxes with sizes [3, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 2, 'j': 3, 'h': 4, 'p': 2} among 4 identical containers that can hold [2, 4, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 3, 'y': 3, 'h': 1, 'c': 4} into 4 undistinguishable boxes with sizes [4, 2, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 3, 'u': 3, 'e': 4, 'y': 1} among 4 identical containers that can hold [3, 4, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'t': 4, 'p': 4, 'g': 1, 'b': 2} into 4 undistinguishable boxes with capacities [4, 3, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 3, 'j': 1, 'x': 2, 'f': 5} among 4 distinguishable boxes with capacities [2, 3, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'c': 3, 't': 2, 'k': 2, 'e': 4} into 4 distinctively labeled boxes with sizes [2, 1, 4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 3, 'e': 4, 'j': 1, 'q': 3} among 4 identical containers that can hold [1, 4, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'q': 1, 'i': 2, 'p': 5, 'm': 3} into 4 uniquely identified boxes that can hold [4, 1, 3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 2, 'k': 2, 'v': 3, 'b': 4} among 4 identical containers that can hold [2, 2, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 1, 'b': 2, 'j': 6, 'v': 2} among 4 distinguishable boxes with capacities [2, 3, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 4, 'b': 3, 'o': 1, 'c': 3} among 4 distinguishable boxes with capacities [4, 1, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 2, 'l': 3, 's': 2, 'i': 4} among 4 distinguishable boxes with capacities [3, 3, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 2, 'h': 3, 'f': 1, 'u': 5} into 4 distinctively labeled boxes with sizes [2, 3, 4, 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 {'c': 3, 'n': 3, 'v': 2, 'h': 3} into 4 undistinguishable boxes with capacities [4, 2, 4, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 1, 'c': 3, 'q': 3, 'f': 4} among 4 identical containers that can hold [2, 5, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 2, 'a': 3, 'e': 2, 'd': 4} into 4 uniquely identified boxes that can hold [2, 3, 5, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 2, 'i': 3, 'f': 1, 'm': 5} into 4 undistinguishable boxes with sizes [4, 4, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 4, 'j': 2, 'o': 2, 'e': 3} among 4 distinguishable boxes with capacities [5, 2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 4, 'j': 3, 'g': 2, 'e': 2}, place them into 4 labeled boxes with sizes [2, 4, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 4, 'y': 2, 'd': 3, 'v': 2} and need to distribute them into 4 different boxes with capacities [4, 2, 2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 1, 'd': 6, 'z': 2, 's': 2}, place them into 4 labeled boxes with sizes [3, 1, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 2, 'r': 3, 'h': 3, 's': 3} into 4 uniquely identified boxes that can hold [3, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 2, 'e': 2, 'r': 6, 'p': 1} among 4 distinguishable boxes with capacities [2, 4, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 4, 'u': 3, 'a': 3, 'k': 1} among 4 identical containers that can hold [5, 2, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 1, 'h': 4, 's': 3, 'l': 3} into 4 distinctively labeled boxes with sizes [3, 4, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 2, 't': 4, 'c': 2, 'f': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'t': 3, 'x': 4, 'y': 2, 'e': 2} into 4 uniquely identified boxes that can hold [3, 2, 5, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 4, 'e': 3, 'h': 1, 'c': 3} among 4 distinguishable boxes with capacities [3, 2, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 3, 'r': 4, 'm': 2, 'k': 2} among 4 distinguishable boxes with capacities [2, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 4, 'u': 3, 'q': 2, 'c': 2} among 4 identical containers that can hold [3, 4, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 2, 'i': 4, 'b': 4, 'p': 1} among 4 identical containers that can hold [1, 5, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'q': 3, 'z': 4, 'u': 2, 'x': 2} into 4 undistinguishable boxes with capacities [2, 3, 2, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 3, 'v': 1, 'x': 2, 'k': 5} among 4 distinguishable boxes with capacities [3, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 2, 'j': 3, 'm': 3, 'w': 3} among 4 distinguishable boxes with capacities [4, 1, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 2, 'm': 2, 'i': 3, 'w': 4} into 4 undistinguishable boxes with capacities [2, 4, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 1, 'b': 4, 'd': 2, 'v': 4} into 4 uniquely identified boxes that can hold [4, 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": "385", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'o': 2, 'q': 5, 'w': 1, 'a': 3} among 4 distinguishable boxes with capacities [2, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 2, 'f': 3, 'l': 3, 'r': 3} and need to distribute them into 4 identical boxes with capacities [3, 4, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 2, 'y': 3, 'n': 2, 'm': 4} among 4 identical containers that can hold [3, 3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 3, 'm': 2, 'i': 4, 'l': 2}, place them into 4 indistinguishable boxes with sizes [2, 2, 5, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 3, 'w': 3, 'u': 2, 'a': 3}, place them into 4 indistinguishable boxes with sizes [3, 5, 1, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 2, 'd': 3, 'r': 4, 'l': 2} into 4 uniquely identified boxes that can hold [5, 2, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 1, 'w': 3, 'v': 3, 'z': 4} into 4 undistinguishable boxes with capacities [3, 3, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 4, 'o': 1, 'q': 3, 'z': 3} among 4 identical containers that can hold [3, 1, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 4, 'w': 2, 'r': 4, 'v': 1} into 4 uniquely identified boxes that can hold [3, 3, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 3, 'z': 2, 'o': 4, 'g': 2}, place them into 4 indistinguishable boxes with sizes [2, 3, 5, 1]. 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 {'m': 2, 'e': 4, 'o': 4, 'y': 1}, place them into 4 indistinguishable boxes with sizes [4, 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": "263", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 3, 'c': 3, 'o': 2, 'p': 3}, place them into 4 indistinguishable boxes with sizes [2, 1, 3, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 1, 'u': 3, 'a': 3, 'f': 4} into 4 distinctively labeled boxes with sizes [3, 3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 5, 'j': 2, 'q': 2, 'a': 2} into 4 undistinguishable boxes with sizes [1, 4, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 3, 'f': 3, 'n': 2, 'h': 3} into 4 distinctively labeled boxes with sizes [2, 2, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 1, 'a': 4, 'k': 3, 'z': 3}, place them into 4 labeled boxes with sizes [4, 3, 1, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 2, 'c': 2, 'j': 4, 'v': 3}, place them into 4 indistinguishable boxes with sizes [1, 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": "298", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 2, 'y': 4, 'd': 1, 'h': 4} into 4 undistinguishable boxes with capacities [4, 4, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 3, 'b': 3, 'h': 2, 'y': 3} and need to distribute them into 4 different boxes with capacities [1, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 3, 'k': 1, 'a': 2, 'v': 5} and need to distribute them into 4 different boxes with capacities [4, 1, 4, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 2, 'm': 5, 'c': 2, 'h': 2} into 4 distinctively labeled boxes with sizes [2, 3, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 3, 't': 3, 'p': 2, 'h': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 4, 's': 2, 'v': 3, 'p': 2}, place them into 4 indistinguishable boxes with sizes [2, 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": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 2, 'x': 3, 's': 4, 'a': 2} among 4 identical containers that can hold [3, 2, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 4, 'k': 2, 't': 3, 'u': 2} among 4 identical containers that can hold [3, 3, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 4, 'z': 1, 'o': 5, 'q': 1} and need to distribute them into 4 identical boxes with capacities [2, 4, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 2, 's': 3, 'u': 2, 'o': 4} into 4 undistinguishable boxes with sizes [3, 2, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 2, 'm': 3, 'v': 3, 'p': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 2, 'b': 2, 'v': 3, 'i': 4} into 4 distinctively labeled boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'d': 4, 'n': 2, 't': 4, 'g': 1}, place them into 4 indistinguishable boxes with sizes [1, 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": "295", "dataset": "MATH"}
{"messages": [{"content": "You have {'m': 4, 'd': 4, 'h': 2, 'r': 1} and need to distribute them into 4 different boxes with capacities [3, 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": "489", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 5, 'i': 4, 'm': 1, 't': 1} into 4 undistinguishable boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 4, 'f': 2, 'q': 2, 'a': 3} into 4 undistinguishable boxes with sizes [2, 5, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 2, 'o': 2, 'v': 4, 'i': 3} and need to distribute them into 4 identical boxes with capacities [1, 3, 1, 6]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 2, 'l': 4, 'd': 4, 'w': 1}, place them into 4 labeled boxes with sizes [2, 1, 4, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 1, 'l': 2, 'a': 2, 'd': 6}, place them into 4 indistinguishable boxes with sizes [2, 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": "159", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 2, 'g': 2, 't': 4, 'c': 3}, place them into 4 labeled boxes with sizes [1, 4, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 3, 'x': 2, 'j': 3, 'b': 3}, place them into 4 labeled boxes with sizes [3, 2, 4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 2, 'h': 1, 'g': 5, 'e': 3} into 4 distinctively labeled boxes with sizes [5, 3, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 3, 'e': 3, 'x': 2, 'r': 3} and need to distribute them into 4 different boxes with capacities [4, 1, 2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "You have {'g': 6, 'l': 1, 'w': 1, 'p': 3} and need to distribute them into 4 identical boxes with capacities [3, 4, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 2, 'n': 2, 'i': 2, 'f': 5} and need to distribute them into 4 identical boxes with capacities [3, 2, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 3, 'n': 3, 'r': 2, 'c': 3} and need to distribute them into 4 different boxes with capacities [1, 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": "495", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 2, 'j': 4, 'c': 2, 'i': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "755", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 6, 'b': 1, 'z': 2, 'q': 2} into 4 uniquely identified boxes that can hold [3, 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": "291", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 3, 's': 4, 'c': 2, 'p': 2} among 4 identical containers that can hold [4, 4, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 2, 'e': 3, 'j': 3, 'd': 3} into 4 uniquely identified boxes that can hold [2, 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": "567", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 2, 'b': 2, 'p': 4, 's': 3}, place them into 4 labeled boxes with sizes [2, 2, 2, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 3, 'y': 1, 'i': 4, 'e': 3} and need to distribute them into 4 different boxes with capacities [2, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 2, 'p': 4, 'y': 3, 'i': 2} among 4 identical containers that can hold [3, 3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 3, 'a': 3, 'j': 1, 'c': 4} and need to distribute them into 4 identical boxes with capacities [3, 2, 5, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 3, 'k': 4, 'j': 2, 'n': 2} into 4 undistinguishable boxes with sizes [2, 3, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 4, 'p': 1, 'm': 4, 'q': 2}, place them into 4 labeled boxes with sizes [3, 3, 4, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 2, 't': 4, 'z': 3, 'x': 2} among 4 distinguishable boxes with capacities [2, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 3, 'e': 2, 'z': 3, 'q': 3} into 4 undistinguishable boxes with sizes [3, 4, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'i': 2, 'g': 2, 'h': 5, 'u': 2} into 4 distinctively labeled boxes with sizes [2, 3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 3, 'w': 1, 'h': 1, 'x': 6} among 4 identical containers that can hold [4, 3, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 1, 'j': 2, 't': 3, 'a': 5} into 4 uniquely identified boxes that can hold [5, 1, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 3, 'k': 5, 'u': 2, 'p': 1} among 4 distinguishable boxes with capacities [4, 2, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 4, 'i': 3, 'm': 2, 'v': 2} into 4 undistinguishable boxes with sizes [1, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 3, 's': 2, 'k': 3, 'u': 3} and need to distribute them into 4 identical boxes with capacities [1, 5, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 4, 'q': 3, 'z': 3, 'd': 1} and need to distribute them into 4 identical boxes with capacities [4, 2, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 2, 'w': 1, 'a': 5, 'e': 3} into 4 undistinguishable boxes with capacities [3, 4, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 3, 'w': 2, 'y': 4, 'j': 2} into 4 undistinguishable boxes with sizes [1, 3, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 5, 'e': 2, 's': 1, 'm': 3} into 4 distinctively labeled boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'e': 2, 'r': 4, 'j': 4, 'y': 1} into 4 undistinguishable boxes with sizes [3, 1, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'p': 4, 'h': 2, 'f': 4, 'a': 1}, place them into 4 labeled boxes with sizes [1, 3, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 1, 'u': 1, 'e': 5, 'k': 4} among 4 identical containers that can hold [2, 3, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 2, 'x': 4, 'i': 2, 'q': 3} among 4 distinguishable boxes with capacities [2, 1, 3, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 3, 'w': 4, 'c': 1, 'k': 3} among 4 distinguishable boxes with capacities [4, 3, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 3, 'p': 5, 'i': 1, 'u': 2} among 4 distinguishable boxes with capacities [3, 2, 5, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'c': 4, 'l': 1, 'q': 3} into 4 undistinguishable boxes with sizes [2, 4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 4, 'a': 1, 'j': 2, 'q': 4} among 4 identical containers that can hold [3, 2, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 2, 'q': 2, 'i': 6, 'v': 1} into 4 undistinguishable boxes with capacities [2, 4, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 1, 'p': 3, 'i': 4, 'j': 3} among 4 distinguishable boxes with capacities [5, 2, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 3, 'e': 2, 'y': 2, 'g': 4} into 4 uniquely identified boxes that can hold [2, 1, 6, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "291", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 2, 'v': 3, 'o': 2, 'j': 4} among 4 identical containers that can hold [2, 7, 1, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 2, 'k': 3, 'w': 1, 'y': 5}, place them into 4 labeled boxes with sizes [4, 4, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 3, 'y': 4, 'v': 1, 'e': 3} into 4 undistinguishable boxes with capacities [2, 3, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 2, 'r': 3, 'g': 4, 'j': 2} and need to distribute them into 4 identical boxes with capacities [5, 2, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'b': 4, 'w': 2, 'p': 3} and need to distribute them into 4 different boxes with capacities [4, 2, 2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 2, 'g': 2, 'd': 3, 'h': 4}, place them into 4 indistinguishable boxes with sizes [3, 3, 1, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 3, 'q': 2, 'z': 3, 'k': 3}, place them into 4 indistinguishable boxes with sizes [3, 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": "474", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 3, 'q': 2, 'e': 2, 't': 4} and need to distribute them into 4 identical boxes with capacities [2, 4, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 3, 'e': 3, 'c': 3, 'g': 2} among 4 identical containers that can hold [1, 3, 3, 4] 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": "Given the letters {'c': 2, 'y': 3, 'u': 3, 'q': 3}, place them into 4 labeled boxes with sizes [2, 4, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 2, 'v': 4, 'q': 2, 'x': 3} into 4 distinctively labeled boxes with sizes [3, 1, 1, 6]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 5, 'h': 2, 'e': 2, 'y': 2} among 4 distinguishable boxes with capacities [3, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 4, 'x': 2, 'c': 4, 'n': 1} into 4 undistinguishable boxes with sizes [2, 3, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 'p': 4, 'm': 1, 'y': 4} and need to distribute them into 4 different boxes with capacities [3, 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": "567", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 3, 'b': 2, 'j': 4, 'h': 2}, place them into 4 labeled boxes with sizes [2, 1, 1, 7]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "139", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 2, 'j': 3, 'g': 4, 'i': 2} and need to distribute them into 4 identical boxes with capacities [2, 4, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 3, 'c': 2, 'x': 3, 'g': 3} and need to distribute them into 4 different boxes with capacities [4, 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": "567", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 2, 'p': 3, 'q': 3, 'k': 3} among 4 distinguishable boxes with capacities [2, 5, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 4, 'n': 2, 'y': 2, 'q': 3} into 4 uniquely identified boxes that can hold [4, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 5, 'd': 2, 'f': 2, 'i': 2} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 3, 'o': 2, 'z': 4, 'y': 2} and need to distribute them into 4 different boxes with capacities [1, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 3, 'e': 3, 'g': 2, 'b': 3} among 4 distinguishable boxes with capacities [2, 3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'h': 1, 'b': 3, 'p': 5} and need to distribute them into 4 different boxes with capacities [3, 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": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 2, 'e': 3, 'r': 2, 'z': 4} among 4 distinguishable boxes with capacities [2, 3, 5, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 2, 'j': 3, 'e': 5, 'x': 1} into 4 uniquely identified boxes that can hold [3, 3, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 1, 'n': 4, 's': 3, 'd': 3} into 4 undistinguishable boxes with capacities [1, 3, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 3, 'e': 2, 'j': 2, 'k': 4}, place them into 4 indistinguishable boxes with sizes [2, 3, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 4, 'a': 4, 'b': 1, 'm': 2} and need to distribute them into 4 identical boxes with capacities [2, 3, 4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 6, 'g': 2, 'h': 1, 'y': 2} among 4 distinguishable boxes with capacities [1, 3, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 'p': 3, 'h': 2, 'w': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "645", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 2, 'o': 3, 'u': 4, 'p': 2} into 4 uniquely identified boxes that can hold [2, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 3, 'i': 1, 'n': 3, 'u': 4} into 4 undistinguishable boxes with capacities [2, 4, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "194", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 2, 'x': 5, 'c': 2, 'a': 2} into 4 uniquely identified boxes that can hold [5, 2, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 2, 'j': 3, 'i': 5, 'o': 1}, place them into 4 indistinguishable boxes with sizes [3, 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": "90", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 2, 'b': 1, 'v': 6, 'j': 2}, place them into 4 labeled boxes with sizes [2, 3, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "291", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 4, 'b': 1, 'g': 4, 'a': 2} among 4 distinguishable boxes with capacities [5, 1, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 1, 'i': 3, 'h': 3, 'j': 4} and need to distribute them into 4 identical boxes with capacities [3, 4, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 2, 'd': 5, 't': 1, 'x': 3} into 4 undistinguishable boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'k': 3, 'z': 4, 'u': 3, 'h': 1} among 4 distinguishable boxes with capacities [2, 2, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 2, 'n': 5, 't': 3, 's': 1} among 4 distinguishable boxes with capacities [4, 1, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 2, 'z': 4, 'j': 2, 'a': 3} into 4 uniquely identified boxes that can hold [4, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 5, 'c': 1, 'h': 2, 'r': 3} into 4 undistinguishable boxes with capacities [1, 4, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 2, 'y': 2, 'b': 3, 'q': 4} into 4 undistinguishable boxes with sizes [2, 1, 4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 3, 'i': 4, 'z': 1, 'h': 3} among 4 identical containers that can hold [3, 4, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 3, 'z': 3, 'u': 3, 'm': 2} among 4 distinguishable boxes with capacities [3, 2, 1, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 3, 'f': 2, 's': 3, 'p': 3}, place them into 4 labeled boxes with sizes [3, 1, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 3, 't': 2, 'n': 3, 'v': 3}, place them into 4 indistinguishable boxes with sizes [3, 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": "349", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 3, 'y': 3, 'r': 3, 'e': 2}, place them into 4 indistinguishable boxes with sizes [4, 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": "474", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 2, 'e': 2, 'b': 2, 'g': 5} among 4 distinguishable boxes with capacities [2, 2, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'f': 3, 'e': 2, 'q': 2, 'n': 4} into 4 uniquely identified boxes that can hold [3, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 2, 'x': 4, 't': 2, 'g': 3} into 4 distinctively labeled boxes with sizes [4, 3, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'i': 3, 'g': 2, 'm': 4, 'l': 2} into 4 uniquely identified boxes that can hold [1, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 2, 'z': 4, 'r': 2, 'i': 3} into 4 distinctively labeled boxes with sizes [3, 3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 2, 'a': 3, 'b': 4, 'v': 2} into 4 distinctively labeled boxes with sizes [1, 3, 5, 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 {'l': 2, 't': 3, 'h': 5, 'c': 1} into 4 uniquely identified boxes that can hold [2, 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": "431", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'l': 2, 'm': 2, 'z': 4, 'a': 3} into 4 undistinguishable boxes with capacities [2, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 2, 'o': 5, 'l': 2, 't': 2} and need to distribute them into 4 identical boxes with capacities [2, 5, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 2, 'p': 4, 'k': 2, 'o': 3} among 4 distinguishable boxes with capacities [3, 2, 1, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 6, 'c': 2, 'v': 1, 'b': 2}, place them into 4 labeled boxes with sizes [2, 6, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 3, 'f': 3, 'o': 1, 'x': 4} and need to distribute them into 4 different boxes with capacities [2, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 2, 's': 3, 'r': 1, 'c': 5} into 4 undistinguishable boxes with capacities [2, 3, 2, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 3, 'v': 3, 'c': 4, 's': 1}, place them into 4 labeled boxes with sizes [4, 3, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 2, 'd': 3, 't': 3, 'c': 3} into 4 uniquely identified boxes that can hold [4, 2, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'l': 2, 's': 4, 'y': 2, 'n': 3} into 4 distinctively labeled boxes with sizes [4, 5, 1, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 2, 'z': 3, 'w': 4, 'b': 2} and need to distribute them into 4 identical boxes with capacities [4, 3, 1, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 3, 'n': 1, 'i': 3, 'e': 4} into 4 undistinguishable boxes with capacities [3, 1, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 3, 'g': 5, 'd': 1, 'y': 2}, place them into 4 labeled boxes with sizes [3, 5, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 1, 'e': 4, 'x': 3, 'q': 3}, place them into 4 labeled boxes with sizes [3, 2, 5, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 4, 'c': 3, 'e': 3, 'b': 1} and need to distribute them into 4 identical boxes with capacities [3, 5, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 3, 'k': 3, 'h': 3, 'p': 2} among 4 identical containers that can hold [4, 2, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 3, 'a': 2, 'u': 5, 'm': 1} among 4 identical containers that can hold [3, 3, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 2, 'g': 5, 'z': 2, 'u': 2}, place them into 4 labeled boxes with sizes [5, 2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "450", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 3, 'n': 2, 's': 2, 'd': 4} into 4 uniquely identified boxes that can hold [4, 3, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 2, 'b': 2, 'd': 2, 't': 5} into 4 undistinguishable boxes with capacities [1, 4, 3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "You have {'t': 4, 'm': 4, 'p': 1, 'j': 2} and need to distribute them into 4 different boxes with capacities [3, 1, 2, 5]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'d': 2, 'k': 4, 'q': 1, 't': 4} into 4 undistinguishable boxes with sizes [7, 1, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 3, 'p': 5, 'j': 1, 'o': 2} among 4 identical containers that can hold [3, 3, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 3, 'g': 3, 'w': 4, 'f': 1}, place them into 4 labeled boxes with sizes [1, 3, 5, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 2, 'i': 2, 'y': 3, 'o': 4}, place them into 4 labeled boxes with sizes [4, 2, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 4, 'r': 2, 'x': 4, 'e': 1} into 4 undistinguishable boxes with sizes [2, 5, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 1, 'r': 5, 'm': 2, 'q': 3} among 4 identical containers that can hold [5, 2, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 2, 'n': 5, 'y': 3, 'e': 1} among 4 distinguishable boxes with capacities [2, 4, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 3, 't': 3, 'v': 3, 'u': 2}, place them into 4 labeled boxes with sizes [4, 3, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'z': 2, 'k': 2, 'h': 4, 't': 3} among 4 distinguishable boxes with capacities [3, 4, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'y': 1, 'x': 2, 'r': 2, 'h': 6} and need to distribute them into 4 different boxes with capacities [2, 1, 5, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 1, 'd': 3, 'k': 3, 'c': 4} among 4 identical containers that can hold [2, 4, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "194", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 4, 'x': 4, 'k': 1, 'i': 2} and need to distribute them into 4 different boxes with capacities [3, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 2, 'b': 3, 'j': 3, 'e': 3} among 4 distinguishable boxes with capacities [3, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 2, 'r': 5, 'p': 1, 'a': 3} among 4 identical containers that can hold [5, 1, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 4, 'v': 4, 'k': 2, 'q': 1}, place them into 4 indistinguishable boxes with sizes [2, 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": "263", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 1, 'c': 5, 'w': 2, 'f': 3} into 4 undistinguishable boxes with sizes [3, 1, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 3, 'f': 2, 'm': 3, 'v': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 5, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 4, 'y': 3, 'l': 2, 'p': 2}, place them into 4 indistinguishable boxes with sizes [1, 3, 3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 3, 'w': 4, 'h': 1, 'q': 3} and need to distribute them into 4 identical boxes with capacities [4, 2, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'d': 1, 'r': 3, 'm': 2, 'b': 5} into 4 undistinguishable boxes with sizes [2, 2, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'b': 2, 'd': 5, 'j': 2, 'm': 2} into 4 undistinguishable boxes with capacities [2, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'i': 4, 'e': 1, 'h': 2, 'x': 4} into 4 undistinguishable boxes with capacities [2, 4, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 1, 'l': 2, 'g': 4, 'k': 4} into 4 undistinguishable boxes with capacities [2, 4, 4, 1]. 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": "Given the letters {'x': 4, 'd': 2, 'm': 2, 'u': 3}, place them into 4 indistinguishable boxes with sizes [2, 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": "431", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'t': 2, 'j': 2, 'e': 4, 'r': 3} into 4 uniquely identified boxes that can hold [2, 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": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 2, 'c': 1, 'z': 3, 'f': 5} and need to distribute them into 4 different boxes with capacities [3, 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": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'q': 4, 'b': 4, 'x': 1, 'u': 2} into 4 distinctively labeled boxes with sizes [1, 5, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 4, 'z': 2, 'n': 3, 'j': 2} into 4 distinctively labeled boxes with sizes [3, 4, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 1, 'r': 5, 'a': 1, 'g': 4} into 4 uniquely identified boxes that can hold [2, 2, 2, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 4, 'j': 4, 'x': 2, 'r': 1} among 4 identical containers that can hold [2, 3, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 2, 'h': 2, 'o': 5, 'u': 2} and need to distribute them into 4 identical boxes with capacities [1, 2, 5, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 4, 'u': 3, 'j': 2, 'l': 2}, place them into 4 labeled boxes with sizes [2, 3, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 1, 'n': 4, 'c': 3, 's': 3} into 4 uniquely identified boxes that can hold [4, 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": "456", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 2, 'q': 2, 'd': 3, 'i': 4}, place them into 4 indistinguishable boxes with sizes [2, 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": "156", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 3, 't': 3, 's': 3, 'b': 2} into 4 undistinguishable boxes with capacities [4, 3, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 3, 'h': 3, 'g': 2, 'f': 3}, place them into 4 indistinguishable boxes with sizes [3, 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": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 4, 'q': 2, 'w': 3, 'u': 2} into 4 distinctively labeled boxes with sizes [4, 4, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 3, 'g': 1, 't': 3, 'd': 4} among 4 distinguishable boxes with capacities [3, 3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'r': 4, 's': 2, 'e': 3, 'm': 2} into 4 uniquely identified boxes that can hold [2, 5, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 3, 'z': 4, 'o': 3, 'h': 1} into 4 distinctively labeled boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 1, 'q': 3, 'h': 3, 'l': 4}, place them into 4 labeled boxes with sizes [5, 1, 4, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "227", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 1, 'd': 3, 'h': 4, 'e': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "685", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 2, 'a': 3, 'n': 2, 'g': 4} into 4 undistinguishable boxes with capacities [3, 3, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 3, 'y': 2, 'z': 1, 'n': 5} among 4 identical containers that can hold [3, 1, 2, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'x': 2, 't': 1, 'g': 4, 'n': 4} into 4 uniquely identified boxes that can hold [2, 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": "295", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 2, 'j': 4, 'd': 4, 'i': 1} into 4 uniquely identified boxes that can hold [5, 2, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 2, 'n': 5, 'r': 2, 'q': 2} among 4 identical containers that can hold [3, 2, 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": "Divide the letters from {'d': 1, 'n': 2, 'k': 4, 'w': 4} into 4 distinctively labeled boxes with sizes [2, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 'p': 2, 'n': 3, 'd': 3} and need to distribute them into 4 different boxes with capacities [4, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 2, 'v': 3, 's': 1, 'm': 5} and need to distribute them into 4 identical boxes with capacities [2, 1, 3, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 1, 'z': 4, 'i': 4, 'g': 2}, place them into 4 indistinguishable boxes with sizes [4, 2, 4, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 2, 'n': 4, 'p': 2, 'j': 3} among 4 identical containers that can hold [3, 5, 1, 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": "Distribute the letters {'t': 4, 's': 3, 'r': 3, 'b': 1} among 4 identical containers that can hold [2, 2, 5, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "You have {'a': 3, 'd': 1, 'q': 3, 'o': 4} and need to distribute them into 4 identical boxes with capacities [3, 3, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 4, 'h': 2, 'c': 2, 'l': 3}, place them into 4 labeled boxes with sizes [2, 2, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 3, 'k': 2, 'e': 4, 'b': 2}, place them into 4 indistinguishable boxes with sizes [3, 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": "298", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 3, 'a': 3, 'n': 2, 'x': 3}, place them into 4 labeled boxes with sizes [2, 3, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1081", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 5, 'g': 2, 'l': 2, 'd': 2} into 4 undistinguishable boxes with capacities [3, 3, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'b': 4, 'l': 2, 'm': 3} and need to distribute them into 4 identical boxes with capacities [3, 1, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 3, 'c': 2, 'a': 3, 'p': 3} among 4 identical containers that can hold [1, 2, 5, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 2, 't': 3, 'b': 2, 'y': 4} into 4 undistinguishable boxes with capacities [5, 1, 1, 4]. 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": "Given the letters {'q': 2, 'l': 1, 'j': 2, 'c': 6}, place them into 4 labeled boxes with sizes [3, 3, 1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 3, 'z': 3, 'h': 2, 'j': 3} into 4 distinctively labeled boxes with sizes [1, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "You have {'u': 2, 'm': 2, 'e': 3, 'j': 4} and need to distribute them into 4 identical boxes with capacities [3, 3, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 2, 'l': 5, 'y': 1, 't': 3} into 4 uniquely identified boxes that can hold [4, 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": "431", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 3, 'z': 2, 'r': 3, 'n': 3} into 4 undistinguishable boxes with sizes [3, 3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 4, 'v': 2, 'a': 2, 'd': 3}, place them into 4 indistinguishable boxes with sizes [3, 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": "162", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 2, 'z': 2, 'q': 2, 't': 5} and need to distribute them into 4 different boxes with capacities [2, 3, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'h': 2, 'f': 5, 'v': 3, 'k': 1} among 4 identical containers that can hold [2, 2, 1, 6] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'v': 2, 'c': 3, 'l': 3, 'u': 3} among 4 identical containers that can hold [3, 3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'d': 4, 'b': 2, 'o': 3, 'g': 2} into 4 distinctively labeled boxes with sizes [3, 2, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 3, 'p': 3, 'f': 2, 'l': 3} and need to distribute them into 4 different boxes with capacities [5, 3, 2, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 2, 'a': 5, 'n': 1, 'p': 3} into 4 undistinguishable boxes with sizes [2, 3, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "You have {'v': 2, 'w': 2, 'q': 4, 'l': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 2, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'w': 2, 'v': 2, 'q': 3, 'n': 4} into 4 distinctively labeled boxes with sizes [2, 3, 5, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 2, 'c': 4, 'j': 2, 's': 3} among 4 identical containers that can hold [2, 3, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "You have {'q': 4, 'i': 3, 'z': 2, 'm': 2} and need to distribute them into 4 different boxes with capacities [4, 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": "489", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'s': 2, 'a': 7, 'i': 1, 'v': 1} into 4 undistinguishable boxes with sizes [1, 4, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'z': 1, 'h': 3, 'c': 3, 'j': 4}, place them into 4 labeled boxes with sizes [5, 2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 4, 'c': 1, 'a': 2, 'o': 4}, place them into 4 indistinguishable boxes with sizes [1, 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": "295", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 2, 'j': 4, 'i': 2, 'f': 3}, place them into 4 indistinguishable boxes with sizes [3, 4, 3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'j': 3, 'g': 2, 'd': 4, 's': 2}, place them into 4 indistinguishable boxes with sizes [3, 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": "162", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 3, 'p': 5, 'v': 1, 'r': 2} into 4 undistinguishable boxes with capacities [3, 1, 5, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 3, 'd': 4, 'e': 2, 'b': 2}, place them into 4 indistinguishable boxes with sizes [4, 2, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'j': 4, 'z': 2, 'w': 3, 't': 2} into 4 distinctively labeled boxes with sizes [3, 4, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 2, 'f': 2, 'a': 4, 'i': 3} among 4 distinguishable boxes with capacities [3, 2, 5, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "You have {'j': 2, 's': 5, 'l': 3, 'q': 1} and need to distribute them into 4 identical boxes with capacities [2, 3, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'u': 2, 'g': 4, 'o': 2, 'p': 3} into 4 uniquely identified boxes that can hold [3, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 3, 'l': 4, 'f': 1, 'r': 3} and need to distribute them into 4 different boxes with capacities [1, 3, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 2, 'p': 3, 'c': 4, 'e': 2} among 4 distinguishable boxes with capacities [1, 4, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'p': 2, 'b': 4, 's': 2, 'h': 3} into 4 distinctively labeled boxes with sizes [4, 3, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 3, 'y': 3, 'w': 4, 'f': 1} among 4 distinguishable boxes with capacities [3, 3, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'v': 2, 'm': 3, 'w': 4, 'o': 2} into 4 undistinguishable boxes with sizes [5, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 2, 'f': 3, 'j': 2, 's': 4} among 4 distinguishable boxes with capacities [1, 5, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 3, 'c': 3, 'f': 2, 's': 3}, place them into 4 labeled boxes with sizes [3, 3, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1081", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 1, 'h': 3, 'o': 2, 'i': 5} among 4 distinguishable boxes with capacities [1, 3, 5, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'q': 3, 'p': 3, 's': 4, 'm': 1} among 4 distinguishable boxes with capacities [3, 3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 3, 'v': 2, 't': 2, 'p': 4} and need to distribute them into 4 different boxes with capacities [2, 2, 4, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 3, 'u': 4, 'm': 3, 'l': 1} into 4 undistinguishable boxes with capacities [2, 2, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 2, 'p': 3, 'e': 5, 'u': 1} among 4 identical containers that can hold [3, 5, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 5, 'x': 3, 'q': 1, 'l': 2} into 4 uniquely identified boxes that can hold [3, 1, 3, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 3, 'x': 2, 'r': 4, 'g': 2} into 4 undistinguishable boxes with capacities [3, 5, 1, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'w': 3, 'r': 3, 'p': 4, 'j': 1} among 4 identical containers that can hold [3, 3, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 5, 'k': 2, 'b': 2, 'e': 2} into 4 uniquely identified boxes that can hold [1, 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": "343", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 2, 'p': 4, 's': 1, 'a': 4}, place them into 4 labeled boxes with sizes [2, 2, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 1, 'l': 7, 'e': 2, 'x': 1} and need to distribute them into 4 identical boxes with capacities [2, 3, 4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "You have {'x': 4, 'd': 3, 'i': 1, 'f': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 2, 'k': 2, 'y': 3, 'd': 4} into 4 uniquely identified boxes that can hold [2, 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": "894", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'h': 3, 'z': 2, 'm': 3, 'g': 3} into 4 distinctively labeled boxes with sizes [2, 1, 4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 4, 'f': 4, 'm': 2, 'c': 1} among 4 identical containers that can hold [5, 3, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'m': 1, 'y': 4, 'i': 4, 'b': 2} into 4 undistinguishable boxes with capacities [2, 1, 3, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 3, 'r': 2, 'y': 1, 'c': 5} among 4 distinguishable boxes with capacities [1, 3, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'a': 2, 'p': 4, 'g': 3, 'w': 2}, place them into 4 indistinguishable boxes with sizes [3, 2, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 5, 'y': 3, 'v': 1, 'b': 2}, place them into 4 labeled boxes with sizes [5, 2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 3, 'k': 2, 'c': 1, 'h': 5} into 4 distinctively labeled boxes with sizes [4, 4, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'q': 3, 'g': 3, 's': 1, 'p': 4}, place them into 4 labeled boxes with sizes [2, 3, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 1, 'z': 5, 'f': 2, 'd': 3}, place them into 4 labeled boxes with sizes [1, 3, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'u': 5, 'i': 1, 's': 1, 'f': 4} into 4 undistinguishable boxes with sizes [3, 3, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 4, 'o': 1, 'b': 4, 's': 2} into 4 undistinguishable boxes with capacities [1, 3, 4, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'y': 4, 'm': 1, 'z': 2, 'o': 4}, place them into 4 labeled boxes with sizes [1, 3, 3, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 2, 'v': 2, 'w': 3, 'r': 4} into 4 uniquely identified boxes that can hold [4, 4, 2, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 2, 'o': 2, 'j': 3, 'v': 4} and need to distribute them into 4 different boxes with capacities [2, 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": "431", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 2, 'l': 5, 't': 3, 'i': 1} into 4 uniquely identified boxes that can hold [1, 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": "340", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 5, 'f': 2, 'l': 2, 't': 2} and need to distribute them into 4 different boxes with capacities [2, 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": "373", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 4, 'g': 2, 'm': 3, 'v': 2} among 4 identical containers that can hold [2, 3, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 2, 'f': 3, 'l': 1, 'a': 5} among 4 distinguishable boxes with capacities [5, 2, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 2, 'm': 5, 'g': 2, 'b': 2} into 4 distinctively labeled boxes with sizes [2, 4, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 2, 'p': 3, 'f': 2, 'x': 4} into 4 uniquely identified boxes that can hold [4, 2, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 5, 'z': 3, 'v': 2, 'r': 1} among 4 identical containers that can hold [3, 1, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'm': 4, 'x': 3, 'q': 1}, place them into 4 labeled boxes with sizes [2, 3, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 4, 'q': 4, 'r': 1, 's': 2} and need to distribute them into 4 different boxes with capacities [3, 2, 3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 3, 'm': 3, 'k': 2, 'z': 3} into 4 distinctively labeled boxes with sizes [3, 2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1081", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'f': 1, 's': 2, 'g': 3, 'm': 5} among 4 identical containers that can hold [4, 3, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 1, 'e': 2, 'u': 6, 'a': 2} into 4 distinctively labeled boxes with sizes [2, 1, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'q': 2, 'r': 1, 'i': 4, 'x': 4} into 4 uniquely identified boxes that can hold [4, 2, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'f': 5, 'g': 3, 'y': 2, 'd': 1} into 4 distinctively labeled boxes with sizes [2, 2, 4, 3]. 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 {'s': 3, 'y': 2, 't': 2, 'd': 4} into 4 undistinguishable boxes with capacities [4, 2, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 4, 'r': 2, 'g': 2, 'a': 3} into 4 distinctively labeled boxes with sizes [3, 4, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'j': 3, 'v': 4, 'd': 3, 'a': 1} into 4 undistinguishable boxes with capacities [3, 2, 5, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'y': 1, 't': 3, 'o': 4, 'x': 3} into 4 uniquely identified boxes that can hold [4, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 2, 'w': 3, 'x': 3, 'b': 3} into 4 distinctively labeled boxes with sizes [2, 2, 2, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'g': 4, 'z': 4, 'e': 1, 's': 2}, place them into 4 indistinguishable boxes with sizes [4, 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": "199", "dataset": "MATH"}
{"messages": [{"content": "You have {'r': 2, 'k': 3, 'x': 3, 'j': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "1081", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 4, 'z': 3, 'j': 3, 'b': 1} into 4 uniquely identified boxes that can hold [3, 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": "579", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 2, 'd': 3, 'e': 2, 's': 4} into 4 undistinguishable boxes with capacities [4, 3, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 3, 'u': 4, 'l': 2, 'e': 2} and need to distribute them into 4 different boxes with capacities [2, 4, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'i': 2, 'u': 5, 'g': 2} and need to distribute them into 4 identical boxes with capacities [2, 1, 2, 6]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 4, 'u': 3, 'o': 1, 'r': 3}, place them into 4 labeled boxes with sizes [4, 3, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 6, 'h': 1, 'v': 1, 't': 3} and need to distribute them into 4 identical boxes with capacities [5, 3, 1, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 2, 'c': 2, 'z': 4, 's': 3} among 4 identical containers that can hold [3, 4, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 4, 'x': 3, 'u': 2, 'a': 2} among 4 distinguishable boxes with capacities [4, 2, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 2, 'g': 2, 'o': 3, 's': 4} and need to distribute them into 4 identical boxes with capacities [3, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 4, 'v': 2, 'b': 2, 'f': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 2, 'e': 3, 's': 2, 'i': 4} among 4 identical containers that can hold [1, 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': 1, 'v': 1, 'c': 6, 'i': 3} and need to distribute them into 4 identical boxes with capacities [1, 2, 6, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 5, 'v': 3, 'm': 1, 'j': 2} into 4 undistinguishable boxes with sizes [2, 3, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'l': 3, 'o': 4, 'b': 2, 'v': 2} among 4 distinguishable boxes with capacities [4, 1, 1, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'f': 5, 'b': 1, 't': 2, 'm': 3}, place them into 4 labeled boxes with sizes [3, 2, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'u': 2, 'b': 3, 'f': 3, 'r': 3} into 4 uniquely identified boxes that can hold [1, 5, 4, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'h': 2, 'o': 3, 'g': 5, 'c': 1}, place them into 4 labeled boxes with sizes [4, 2, 1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 4, 'y': 1, 'e': 2, 'k': 4} among 4 distinguishable boxes with capacities [5, 1, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 4, 'u': 2, 'h': 3, 't': 2} and need to distribute them into 4 different boxes with capacities [4, 2, 2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 1, 's': 4, 'c': 1, 'j': 5} and need to distribute them into 4 different boxes with capacities [2, 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": "279", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'r': 4, 'v': 5, 'e': 1, 'u': 1} into 4 undistinguishable boxes with sizes [2, 2, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 4, 'y': 3, 'i': 2, 'n': 2} into 4 uniquely identified boxes that can hold [2, 4, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'j': 5, 'g': 3, 'x': 1, 'i': 2} among 4 distinguishable boxes with capacities [3, 3, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'g': 4, 'c': 3, 'r': 1, 's': 3} into 4 distinctively labeled boxes with sizes [4, 1, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 3, 'h': 3, 'x': 4, 'u': 1} among 4 distinguishable boxes with capacities [4, 1, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 3, 'd': 2, 'p': 2, 's': 4}, place them into 4 indistinguishable boxes with sizes [3, 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": "162", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 1, 'b': 4, 'i': 4, 'l': 2} into 4 undistinguishable boxes with sizes [3, 2, 1, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 4, 'r': 3, 'w': 2, 'z': 2} into 4 undistinguishable boxes with sizes [4, 1, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 2, 'k': 4, 't': 3, 'l': 2} among 4 identical containers that can hold [2, 4, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 4, 's': 2, 'k': 1, 'b': 4} and need to distribute them into 4 different boxes with capacities [4, 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": "385", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'n': 1, 'm': 2, 'k': 4, 'b': 4} among 4 identical containers that can hold [4, 1, 2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'m': 5, 'x': 4, 'r': 1, 'b': 1} into 4 uniquely identified boxes that can hold [4, 4, 2, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 3, 'u': 4, 'r': 3, 'g': 1} into 4 undistinguishable boxes with capacities [2, 4, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'d': 3, 'b': 2, 'o': 2, 'n': 4} into 4 undistinguishable boxes with sizes [2, 3, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 1, 'm': 1, 'a': 5, 'w': 4}, place them into 4 indistinguishable boxes with sizes [2, 3, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'s': 3, 'c': 3, 'l': 2, 'w': 3} into 4 uniquely identified boxes that can hold [3, 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": "894", "dataset": "MATH"}