id stringlengths 35 35 | setting_key stringclasses 1
value | setting_name stringclasses 0
values | messages listlengths 1 1 | ground_truth stringclasses 26
values | dataset stringclasses 1
value |
|---|---|---|---|---|---|
combinatory_distribution_train_0200 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'r': 2, 'i': 2}, place them into 2 indistinguishable boxes with sizes [2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0201 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'i': 1, 'v': 3} and need to distribute them into 2 identical boxes with capacities [2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1 | math |
combinatory_distribution_train_0202 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'b': 2, 'h': 3} into 2 undistinguishable boxes with capacities [3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0203 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'m': 2, 'e': 2} into 2 undistinguishable boxes with capacities [2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0204 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'i': 3, 'q': 3} and need to distribute them into 2 different boxes with capacities [2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0205 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'p': 3, 'e': 2}, place them into 2 labeled boxes with sizes [1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0206 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'c': 2, 'e': 2} into 2 undistinguishable boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0207 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'a': 4, 'u': 2} and need to distribute them into 2 different boxes with capacities [3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0208 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'h': 3, 'z': 3} into 2 undistinguishable boxes with sizes [4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0209 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'p': 3, 's': 3} and need to distribute them into 2 different boxes with capacities [5, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0210 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'v': 2, 'x': 4} into 2 uniquely identified boxes that can hold [2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0211 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'a': 3, 'x': 2} into 2 distinctively labeled boxes with sizes [2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0212 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'k': 4, 'z': 2} into 2 undistinguishable boxes with capacities [2, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0213 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'a': 3, 'w': 3}, place them into 2 labeled boxes with sizes [3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
combinatory_distribution_train_0214 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'o': 1, 'i': 3}, place them into 2 labeled boxes with sizes [2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0215 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'q': 3, 'n': 1}, place them into 2 labeled boxes with sizes [2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0216 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'z': 1, 'w': 4} into 2 undistinguishable boxes with sizes [2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0217 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'g': 2, 'v': 2} among 2 distinguishable boxes with capacities [3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0218 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'a': 3, 's': 2} into 2 undistinguishable boxes with sizes [2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0219 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'x': 2, 'j': 3} among 2 distinguishable boxes with capacities [3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0220 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'e': 4, 'l': 2} into 2 distinctively labeled boxes with sizes [3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0221 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'p': 3, 'b': 1}, place them into 2 indistinguishable boxes with sizes [2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1 | math |
combinatory_distribution_train_0222 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'j': 2, 'o': 2} and need to distribute them into 2 identical boxes with capacities [3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0223 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'o': 3, 'q': 2} among 2 identical containers that can hold [2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0224 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'u': 1, 'a': 3} into 2 distinctively labeled boxes with sizes [3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0225 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'c': 3, 'w': 2}, place them into 2 indistinguishable boxes with sizes [2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0226 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'c': 2, 'x': 4}, place them into 2 labeled boxes with sizes [3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0227 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'e': 2, 'n': 2} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0228 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'x': 3, 'o': 3} among 2 distinguishable boxes with capacities [2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0229 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'c': 3, 'e': 2} and need to distribute them into 2 identical boxes with capacities [2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0230 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'l': 1, 'b': 3} among 2 identical containers that can hold [2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1 | math |
combinatory_distribution_train_0231 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'l': 3, 'x': 1} among 2 identical containers that can hold [1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0232 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'k': 3, 'p': 3} and need to distribute them into 2 different boxes with capacities [2, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0233 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'n': 1, 'v': 3} into 2 distinctively labeled boxes with sizes [3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0234 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'a': 3, 'o': 2} into 2 uniquely identified boxes that can hold [2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0235 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'m': 3, 'y': 3} and need to distribute them into 2 different boxes with capacities [3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
combinatory_distribution_train_0236 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'m': 3, 'w': 2}, place them into 2 labeled boxes with sizes [3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0237 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'b': 2, 'k': 2}, place them into 2 labeled boxes with sizes [3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0238 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'s': 4, 'n': 1} into 2 undistinguishable boxes with sizes [2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0239 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'w': 4, 'z': 2} into 2 undistinguishable boxes with sizes [2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0240 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'k': 3, 'n': 2} among 2 identical containers that can hold [4, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0241 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'t': 3, 'p': 2} and need to distribute them into 2 identical boxes with capacities [4, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0242 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'i': 3, 'l': 3} into 2 distinctively labeled boxes with sizes [3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
combinatory_distribution_train_0243 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'x': 2, 'f': 2} among 2 distinguishable boxes with capacities [3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0244 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'f': 1, 'u': 4}, place them into 2 indistinguishable boxes with sizes [2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0245 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'z': 3, 'y': 1} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0246 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'e': 4, 'n': 1} into 2 undistinguishable boxes with capacities [1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0247 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'z': 2, 'o': 3} into 2 undistinguishable boxes with sizes [3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0248 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'q': 1, 'x': 3} among 2 distinguishable boxes with capacities [3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0249 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'q': 2, 'g': 2} into 2 uniquely identified boxes that can hold [3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0250 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'t': 3, 'i': 3}, 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}"
}
] | 2 | math |
combinatory_distribution_train_0251 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'v': 1, 'n': 3} into 2 uniquely identified boxes that can hold [3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0252 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'c': 2, 'm': 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}"
}
] | 3 | math |
combinatory_distribution_train_0253 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'j': 3, 'z': 2} and need to distribute them into 2 different boxes with capacities [2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0254 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'x': 1, 'q': 4} among 2 identical containers that can hold [1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0255 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'s': 1, 'q': 3} and need to distribute them into 2 different boxes with capacities [1, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0256 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'z': 3, 'q': 1} into 2 undistinguishable boxes with sizes [3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0257 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'r': 1, 'e': 4} and need to distribute them into 2 identical boxes with capacities [2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0258 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'t': 4, 'e': 2} into 2 uniquely identified boxes that can hold [4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0259 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'i': 3, 'w': 1} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1 | math |
combinatory_distribution_train_0260 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'y': 3, 'h': 1} into 2 undistinguishable boxes with capacities [2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1 | math |
combinatory_distribution_train_0261 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'t': 4, 'v': 1}, place them into 2 labeled boxes with sizes [1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0262 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'o': 1, 'c': 4}, place them into 2 indistinguishable boxes with sizes [2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0263 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'j': 3, 'a': 3} and need to distribute them into 2 different boxes with capacities [3, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
combinatory_distribution_train_0264 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'s': 2, 'u': 3} into 2 uniquely identified boxes that can hold [3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0265 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'o': 2, 'q': 2} among 2 distinguishable boxes with capacities [1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0266 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'a': 2, 'y': 2}, place them into 2 labeled boxes with sizes [1, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0267 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'b': 3, 'u': 3}, place them into 2 labeled boxes with sizes [3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
combinatory_distribution_train_0268 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'v': 1, 'q': 3} into 2 uniquely identified boxes that can hold [1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0269 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'c': 3, 'y': 2} into 2 undistinguishable boxes with capacities [3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0270 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'f': 1, 'x': 3} into 2 distinctively labeled boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0271 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'g': 1, 'p': 3} among 2 identical containers that can hold [2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1 | math |
combinatory_distribution_train_0272 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'z': 2, 'p': 3} into 2 undistinguishable boxes with capacities [4, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0273 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'n': 3, 'y': 1} into 2 distinctively labeled boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0274 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'m': 3, 'u': 3} among 2 distinguishable boxes with capacities [4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0275 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'u': 4, 'o': 2} into 2 undistinguishable boxes with capacities [3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0276 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'d': 4, 'e': 2} and need to distribute them into 2 different boxes with capacities [1, 5]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0277 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'b': 2, 'r': 2}, place them into 2 labeled boxes with sizes [3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0278 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'t': 3, 'x': 2} into 2 undistinguishable boxes with capacities [3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0279 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'b': 4, 'z': 2}, 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}"
}
] | 3 | math |
combinatory_distribution_train_0280 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'f': 2, 'p': 2} into 2 distinctively labeled boxes with sizes [1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0281 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'p': 4, 'y': 2} among 2 identical containers that can hold [3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0282 | combinatory_distribution | null | [
{
"role": "user",
"content": "You have {'y': 1, 'n': 3} and need to distribute them into 2 identical boxes with capacities [2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1 | math |
combinatory_distribution_train_0283 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'j': 2, 'c': 4} among 2 identical containers that can hold [2, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0284 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'c': 1, 't': 4} into 2 undistinguishable boxes with capacities [2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0285 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'c': 2, 't': 4}, place them into 2 labeled boxes with sizes [3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0286 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'i': 4, 'p': 1} into 2 undistinguishable boxes with capacities [2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0287 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'a': 2, 'd': 2} among 2 distinguishable boxes with capacities [1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0288 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'s': 3, 'x': 2} into 2 uniquely identified boxes that can hold [3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0289 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'n': 2, 'h': 3} into 2 distinctively labeled boxes with sizes [3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0290 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'l': 3, 'h': 2} into 2 undistinguishable boxes with sizes [2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0291 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'c': 4, 'e': 2}, place them into 2 labeled boxes with sizes [3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0292 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'d': 3, 'y': 1}, place them into 2 indistinguishable boxes with sizes [3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0293 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'o': 1, 'm': 4} into 2 distinctively labeled boxes with sizes [2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0294 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'w': 2, 'j': 2} into 2 undistinguishable boxes with capacities [1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0295 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'e': 2, 'd': 2} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0296 | combinatory_distribution | null | [
{
"role": "user",
"content": "Given the letters {'w': 2, 'z': 3}, place them into 2 indistinguishable boxes with sizes [3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
combinatory_distribution_train_0297 | combinatory_distribution | null | [
{
"role": "user",
"content": "Divide the letters from {'u': 2, 'b': 2} into 2 undistinguishable boxes with sizes [2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0298 | combinatory_distribution | null | [
{
"role": "user",
"content": "Arrange the letters {'y': 2, 'z': 4} into 2 undistinguishable boxes with capacities [3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
combinatory_distribution_train_0299 | combinatory_distribution | null | [
{
"role": "user",
"content": "Distribute the letters {'q': 3, 'n': 1} among 2 distinguishable boxes with capacities [2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
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