data.jsonl

{"messages": [{"content": "Arrange the letters {'h': 3, 'j': 4} into 3 undistinguishable boxes with capacities [3, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'t': 1, 'f': 3, 'h': 2} into 2 distinctively labeled boxes with sizes [3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "You have {'b': 3, 'g': 7} and need to distribute them into 3 different boxes with capacities [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": "10", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 8, 'p': 1} into 2 undistinguishable boxes with capacities [6, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'k': 2, 'b': 4} into 3 uniquely identified boxes that can hold [2, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 5, 's': 2, 'w': 1} among 3 distinguishable boxes with capacities [3, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'x': 2, 'b': 5, 'h': 2} into 3 distinctively labeled boxes with sizes [4, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'a': 4, 'i': 3, 'g': 3} among 3 distinguishable boxes with capacities [2, 3, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 4, 'a': 2}, place them into 2 indistinguishable boxes with sizes [2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'o': 3, 'l': 7} into 2 undistinguishable boxes with sizes [6, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'v': 3, 'f': 5} into 3 undistinguishable boxes with capacities [4, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 1, 'm': 1, 'a': 4}, place them into 2 indistinguishable boxes with sizes [4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'m': 4, 'd': 3} among 3 identical containers that can hold [1, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'o': 1, 'h': 6, 'w': 2}, place them into 3 indistinguishable boxes with sizes [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": "17", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'f': 3, 'g': 2, 'r': 5} into 3 distinctively labeled boxes with sizes [2, 5, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'m': 3, 'c': 3} into 2 undistinguishable boxes with sizes [1, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'e': 3, 'w': 1, 'r': 5} into 2 uniquely identified boxes that can hold [2, 7] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 2, 'r': 2, 't': 5} into 2 uniquely identified boxes that can hold [3, 6] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 6, 'j': 4} among 2 distinguishable boxes with capacities [7, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 3, 't': 5, 'q': 2} and need to distribute them into 2 identical boxes with capacities [5, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 3, 'u': 4}, place them into 2 indistinguishable boxes with sizes [3, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'p': 4, 'r': 2}, place them into 2 labeled boxes with sizes [4, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 4, 'z': 3} and need to distribute them into 3 identical boxes with capacities [3, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'o': 2, 'w': 4, 'd': 4} into 3 undistinguishable boxes with capacities [2, 2, 6]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'s': 2, 'm': 4, 'v': 3}, place them into 3 labeled boxes with sizes [2, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 4, 'i': 2, 'z': 2}, place them into 2 indistinguishable boxes with sizes [7, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 4, 'a': 6} among 2 distinguishable boxes with capacities [2, 8]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 4, 's': 4} and need to distribute them into 2 different boxes with capacities [3, 5]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "You have {'n': 4, 'l': 3, 'h': 1} and need to distribute them into 2 different boxes with capacities [4, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'y': 7, 'l': 2} among 3 distinguishable boxes with capacities [3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 3, 'k': 3}, place them into 2 indistinguishable boxes with sizes [1, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 5, 'd': 3} among 2 identical containers that can hold [4, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'k': 2, 'p': 4}, place them into 2 indistinguishable boxes with sizes [3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 5, 'v': 4, 'd': 1} among 2 identical containers that can hold [5, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 2, 'i': 3, 'y': 3} into 3 uniquely identified boxes that can hold [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": "35", "dataset": "MATH"}
{"messages": [{"content": "You have {'e': 2, 'k': 4} and need to distribute them into 2 identical boxes with capacities [4, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 3, 'i': 4} and need to distribute them into 2 identical boxes with capacities [2, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 2, 'c': 7}, place them into 3 labeled boxes with sizes [2, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'p': 3, 'm': 6} among 2 distinguishable boxes with capacities [4, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "You have {'k': 4, 'y': 6} and need to distribute them into 3 identical boxes with capacities [1, 2, 7]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 1, 'e': 3, 'n': 1, 's': 2} among 3 identical containers that can hold [1, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'r': 3, 'd': 2, 'a': 2, 'w': 1}, place them into 3 indistinguishable boxes with sizes [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": "30", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'f': 1, 'q': 3, 'i': 3, 'y': 2} into 4 undistinguishable boxes with sizes [2, 1, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'d': 3, 'r': 4, 'a': 3} among 3 identical containers that can hold [2, 5, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'w': 4, 'q': 2, 'i': 2, 'j': 2}, place them into 4 labeled boxes with sizes [2, 4, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "441", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'u': 2, 'q': 2, 'z': 2, 'f': 4} among 4 distinguishable boxes with capacities [5, 3, 1, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'n': 2, 'l': 3, 't': 2, 'q': 2} into 4 undistinguishable boxes with capacities [2, 4, 1, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 1, 'm': 3, 'c': 3} and need to distribute them into 4 identical boxes with capacities [3, 1, 1, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'f': 4, 'l': 3, 'n': 2, 'c': 1} into 4 distinctively labeled boxes with sizes [2, 1, 1, 6]. 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 {'q': 3, 'k': 2, 'd': 2, 's': 2}, place them into 3 labeled boxes with sizes [4, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "You have {'o': 4, 't': 3, 'n': 3} and need to distribute them into 4 different boxes with capacities [2, 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": "123", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'w': 1, 't': 2, 'f': 2, 'g': 1} into 3 undistinguishable boxes with capacities [2, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 1, 'q': 3, 'n': 3, 'x': 1} into 4 undistinguishable boxes with capacities [3, 1, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'y': 2, 'b': 2, 'a': 4} into 4 undistinguishable boxes with sizes [2, 2, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'b': 1, 's': 1, 'o': 2, 'y': 2} into 3 distinctively labeled boxes with sizes [3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'v': 3, 'a': 3, 'k': 2}, place them into 3 indistinguishable boxes with sizes [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": "18", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'r': 3, 'u': 1, 'z': 3, 'q': 2} among 3 identical containers that can hold [2, 3, 4] 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": "Distribute the letters {'m': 2, 'q': 4, 'j': 3} among 3 identical containers that can hold [4, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'z': 3, 'f': 5, 'i': 2} into 4 undistinguishable boxes with sizes [4, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'p': 4, 'l': 1, 'o': 2}, place them into 4 labeled boxes with sizes [2, 2, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'g': 2, 'w': 2, 'p': 1, 'm': 2} among 3 identical containers that can hold [3, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'g': 2, 'x': 4, 'f': 2} into 4 undistinguishable boxes with capacities [3, 1, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 1, 'b': 2, 'z': 2, 'r': 4} and need to distribute them into 3 identical boxes with capacities [2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'b': 1, 'o': 1, 'i': 1, 'z': 4} into 4 undistinguishable boxes with capacities [4, 1, 1, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'h': 1, 'g': 1, 'y': 3, 'p': 2} into 4 uniquely identified boxes that can hold [1, 3, 2, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 1, 'f': 3, 't': 2} and need to distribute them into 3 identical boxes with capacities [2, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'x': 2, 'w': 1, 'd': 1, 'i': 5}, place them into 3 indistinguishable boxes with sizes [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": "46", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'s': 5, 'j': 2, 'd': 2, 'a': 1} among 3 distinguishable boxes with capacities [2, 2, 6]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "You have {'f': 2, 'g': 2, 'n': 2, 'i': 1} and need to distribute them into 4 different boxes with capacities [2, 2, 2, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'i': 4, 's': 3, 'j': 3}, place them into 4 indistinguishable boxes with sizes [5, 1, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "You have {'h': 4, 'x': 1, 'q': 1, 'w': 1} and need to distribute them into 4 different boxes with capacities [1, 1, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "You have {'c': 2, 'f': 4, 'z': 2} and need to distribute them into 4 identical boxes with capacities [3, 1, 1, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'a': 2, 't': 1, 'n': 1, 'r': 2} into 3 undistinguishable boxes with capacities [2, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'d': 1, 'f': 1, 'x': 1, 'z': 3} into 3 undistinguishable boxes with capacities [2, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'c': 3, 'r': 2, 'q': 1, 'y': 4} into 3 uniquely identified boxes that can hold [4, 2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'n': 5, 's': 2, 'f': 2} into 3 distinctively labeled boxes with sizes [3, 4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "You have {'d': 1, 'o': 3, 'e': 2} and need to distribute them into 3 different boxes with capacities [2, 3, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Arrange the letters {'p': 3, 'x': 1, 's': 3} into 3 uniquely identified boxes that can hold [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": "19", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 'r': 1, 's': 3} and need to distribute them into 4 different boxes with capacities [1, 2, 3, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "You have {'w': 3, 'r': 3, 'k': 2} and need to distribute them into 4 identical boxes with capacities [1, 2, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'l': 2, 'u': 2, 'a': 2}, place them into 4 indistinguishable boxes with sizes [1, 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": "12", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'k': 3, 's': 2, 'x': 2, 'b': 1} into 4 undistinguishable boxes with sizes [3, 2, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'b': 1, 'u': 3, 'k': 1, 'v': 3} among 4 distinguishable boxes with capacities [1, 2, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'x': 3, 'b': 4, 'g': 2} among 3 identical containers that can hold [2, 4, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "You have {'i': 3, 'w': 2, 'j': 2, 'g': 3} and need to distribute them into 3 identical boxes with capacities [4, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'c': 1, 'm': 3, 'i': 4, 'n': 2}, place them into 4 labeled boxes with sizes [4, 2, 2, 2]. 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 {'s': 2, 'z': 3, 'e': 1, 'r': 1}, place them into 3 indistinguishable boxes with sizes [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": "15", "dataset": "MATH"}
{"messages": [{"content": "Divide the letters from {'v': 2, 'd': 4, 'i': 3} into 4 distinctively labeled boxes with sizes [2, 3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "You have {'p': 3, 'v': 4, 'k': 3} and need to distribute them into 4 different boxes with capacities [3, 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": "180", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'i': 1, 'j': 4, 'b': 3, 'd': 2} among 3 identical containers that can hold [3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'m': 4, 'z': 3, 'i': 2}, place them into 3 labeled boxes with sizes [2, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "You have {'l': 2, 'c': 1, 'd': 1, 'a': 3} and need to distribute them into 4 identical boxes with capacities [2, 2, 1, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'c': 3, 's': 2, 'b': 1} among 3 distinguishable boxes with capacities [1, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "You have {'s': 4, 'z': 3, 'q': 3} and need to distribute them into 4 identical boxes with capacities [4, 1, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'u': 3, 'b': 1, 'g': 1, 'k': 1}, place them into 3 indistinguishable boxes with sizes [2, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'t': 1, 'b': 3, 'x': 4}, place them into 4 labeled boxes with sizes [1, 2, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'n': 2, 'c': 2, 'o': 1, 'v': 3}, place them into 3 indistinguishable boxes with sizes [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": "43", "dataset": "MATH"}
{"messages": [{"content": "Distribute the letters {'t': 1, 'd': 3, 'j': 4} among 3 identical containers that can hold [2, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Given the letters {'e': 4, 'y': 3, 'l': 1, 'h': 2}, place them into 4 labeled boxes with sizes [2, 4, 2, 2]. 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": "Distribute the letters {'z': 2, 'd': 2, 'c': 1, 'm': 1} among 3 distinguishable boxes with capacities [2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}