There are 5 boxes and a cat

Logic Level 2

A cat hides in one of the 5 boxes labeled 1~5 from left to right, and you need to catch the cat.

Every night it switches places to an adjacent box; for example, if the cat was in #3 and didn't get caught during the day, it moves to #2 or to #4 in the night. Then, everyday when the night is over, you can check only 1 box to find the cat.

Applying the optimal strategy, you are guaranteed to find the cat in at most \(X\) days. What is \(X?\)

Note: If the cat was in #5 during the day, it can only move to #4 in the night. Similarly, #1 has only one adjacent box, #2. The boxes are kept closed at all times, but the cat can slip through the folds on top during the night.


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