<|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
 In a room, there are 15 chairs arranged in a circle. Three jewelers, when no one is watching, sit on three consecutive chairs, and the jeweler sitting in the middle chair hides a diamond in the chair he is sitting on. The inspector has several detectors that indicate whether or not someone has sat on a chair. What is the minimum number of detectors that need to be placed on the chairs before the jewelers visit, such that their readings can determine where the diamond is hidden? 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
9
In a room, there are 15 chairs arranged in a circle. Three jewelers, when no one is watching, sit on three consecutive chairs, and the jeweler sitting in the middle chair hides a diamond in the chair he is sitting on. The inspector has several detectors that indicate whether or not someone has sat on a chair. What is the minimum number of detectors that need to be placed on the chairs before the jewelers visit, such that their readings can determine where the diamond is hidden?
test