<|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 Anchuria, there is a checkers championship that takes place over several rounds. The days and cities hosting the rounds are determined by a draw. According to the rules of the championship, no two rounds can be held in the same city, and no two rounds can be held on the same day. A lottery is conducted among the fans: the grand prize goes to the person who correctly guesses which cities and on which days all rounds will be held before the championship begins. If no one guesses correctly, the grand prize goes to the championship organizing committee. There are a total of eight cities in Anchuria, and the championship spans a total of eight days. How many rounds should be in the championship so that the organizing committee has the highest probability of winning the grand prize? 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
6
In Anchuria, there is a checkers championship that takes place over several rounds. The days and cities hosting the rounds are determined by a draw. According to the rules of the championship, no two rounds can be held in the same city, and no two rounds can be held on the same day. A lottery is conducted among the fans: the grand prize goes to the person who correctly guesses which cities and on which days all rounds will be held before the championship begins. If no one guesses correctly, the grand prize goes to the championship organizing committee. There are a total of eight cities in Anchuria, and the championship spans a total of eight days. How many rounds should be in the championship so that the organizing committee has the highest probability of winning the grand prize?
test