<|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
 Berk tries to guess the two-digit number that Ayca picks. After each guess, Ayca gives a hint indicating the number of digits which match the number picked. What is the smallest possible number of guesses, n, that Berk needs to guarantee finding Ayca's number? Express your answer as a single integer. 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
10
Berk tries to guess the two-digit number that Ayca picks. After each guess, Ayca gives a hint indicating the number of digits which match the number picked. What is the smallest possible number of guesses, n, that Berk needs to guarantee finding Ayca's number? Express your answer as a single integer.
test