Tuesday, 4 July 2017
Is Your Cat Cleverer Than You? Solution
DID you solve yesterday's puzzle? I must admit I really struggled with it although when I saw the answer I realised how it was all worked out. So here's the solution:
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?
In the previous post I explained that the way to solve this puzzle was to start with only a few doors, work out a strategy, and gradually increase the number of doors until there are seven of them. I showed how to solve the puzzle when there are only three doors.
Like many puzzles of this sort, the key to solving the problem is to be able to visualise it clearly. Below is a grid that shows what happens when there are four doors. Each column represents a door. If a cat is in the column, that means that there is a chance the cat could be behind that door. A door with an X means that I open that door. I’m going you show you how to use this grid to catch the cat.
On Day 1 there is a chance that the cat could be behind any of the doors, so there are cats in every column. I open door 2. If the cat is there, I win. Game over.
On Day 2 the cat can only be behind doors 2,3 and 4. This is because we have eliminated the chance that the cat was behind door 2 on Day 1. And if the cat was behind either doors 1, 3 or 4 on Day 1, by jumping one door left or right from these doors, the possible cat positions are now 2, 3 and 4.
On Day 2 I open door 3. If the cat is there, I win. Game over. I can delete this cat in the grid.
On Day 3 there are now only two possible positions where cats could be, doors 1 and 3. I open door 3, which means that on Day 4 there is only one possible position for the cat, door 2. By opening the doors in this order - 2,3,3,2 - I have a strategy that catches the cat in at most four days.
Once you play around with door order, you should - hopefully - eventually come to the right combination needed.
With 5 doors, the grid looks like the one below. If you worked out how to do it with 4 doors, it shouldn’t be too hard to extend the solution to 5. You can now catch the cat in 6 days: open doors 2,3,4,4,3,2 in order.
I am indebted to The Guardian newspaper for this puzzle.
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