Here's a puzzle that finds out whether your brain cells are more efficient than your feline friend's:
A straight corridor has seven doors along one side. Behind one of the doors sits a cat. Your mission is to find the cat by opening the correct door. Each day you can open only one door. If the cat is there, you win. You are officially smarter than a cat. If the cat is not there, the door closes, and you must wait until the next day before you can open a door again.
If the cat was always to sit behind the same door, you would be able to find it in at most seven days, by opening each door in turn. But this mischievous moggy is restless. Every night it moves one door either to the left or to the right.
How many days do you now need to make sure you can catch the cat?
Before you start take note, the seven doors are in a line, so if the cat is behind the first or the last door, it has only one option for where it can move during the night. Otherwise, each night it decides randomly whether to move to the left or to the right.
This puzzle is purrfectly fiendish. At first it may appear impossible to find your furtive feline. But if you begin by trying the puzzle with a smaller number of doors, you will hopefully be able to work out the correct strategy.
I'll give you the answer tomorrow. Let me know if you solve it before then, so if you are still puzzling, don't look at the comments quite yet! I would welcome any comments, of course, even if they are to tell me to get a life and stop doing cat puzzles!
Below are a couple of hints, so don't look if you want to solve the puzzle all on your own.
I’ll get you started. If there were only THREE doors, then it is possible to catch the cat in two days:
Day 1: open the middle door.
Day 2: open the middle door.
This strategy guarantees you will get the cat, since if it is not behind the middle door on Day 1, then it must be behind either of the end doors. And if it is behind either of the end doors on Day 1, then in both cases it will move to behind the middle door on Day 2. Caught!
If there are FOUR doors, it is possible to catch the cat in four days. But now it’s up to you to work out how.
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