Topic:

A straight hallway has five doors along one side. Behind one of the doors is a cat. Your task is to find the cat by opening the correct door. You can only open one door each day. If the cat is there, you win.

If the cat is not there, the door will close, and you have to wait until the next day before you can open the door again. The cat is constantly moving, and each night it moves to sit behind a different door. The door it moves to will be either the left or right door of where it is currently.

How many days do you need to be sure you find the cat?

The problem is asking you to find a strategy that guarantees you will catch the cat within a fixed number of days, regardless of which door it starts behind and where it moves to at night. The key to solving the problem is to start with a smaller number of doors, figure out the pattern, and then increase the number of doors.

Let's start with the case where there are only three doors. If you open the middle door two days in a row, you're guaranteed to catch the cat, because if the cat isn't behind the middle door on day one, it must be behind one of the doors at either end. And if it's behind one of the doors at either end on day one, it has no choice but to move to the middle door on day two.

If there are four doors, you can catch the cat in four days. You can find the explanation in the answer below, but before that, try to explain it yourself. Remember, the cat only moves to the door immediately to its right or left and can return to the door it was behind before. Believe that you will feel happy when you find the explanation.

>>> Answer

Vo Quoc Ba Can

Math Teacher, Archimedes School Hanoi