<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Mrs. Široká was expecting guests in the evening. First, she prepared 25 open-faced sandwiches. She then calculated that if each guest took two sandwiches, three of them would not have enough. She then thought that if she made 10 more sandwiches, each guest could take three, but four of them would not have enough. This still seemed insufficient to her. Finally, she prepared a total of 52 sandwiches. Each guest could then take four sandwiches, but not all of them could take five. How many guests was Mrs. Široká expecting? She herself is on a diet and never eats in the evening. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
11
Mrs. Široká was expecting guests in the evening. First, she prepared 25 open-faced sandwiches. She then calculated that if each guest took two sandwiches, three of them would not have enough. She then thought that if she made 10 more sandwiches, each guest could take three, but four of them would not have enough. This still seemed insufficient to her. Finally, she prepared a total of 52 sandwiches. Each guest could then take four sandwiches, but not all of them could take five. How many guests was Mrs. Široká expecting? She herself is on a diet and never eats in the evening.
test