## Snakes and Mice

On a remote (imaginary) island, there are 11 snakes and a single mouse. As you’d expect, snakes eat the mice. But contrary to what you’d expect, when a snake eats a mouse, it turns into one.

The snakes live by only two rules:

1. Don’t get eaten.
2. Eat mice as long as rule #1 isn’t violated.

How many snakes and mice will there be left on the island?

10 snakes, 1 mouse.

If there were only a single snake and mouse, the snake could eat the mouse, then turn into one, leaving a single mouse.

If there were two snakes and a single mouse, rule 2 would keep either of the snakes from eating the mouse to avoid being eaten themselves.

With three snakes and one mouse, one of the snakes could eat a mouse and be safe as a mouse thanks to rule 2.

This pattern continues. With an even number of snakes, nothing happens. With an odd number of snakes, one snake can eat the mouse.

Thus, with 11 snakes, one snake would eat the mouse, turn into one and leave 10 snakes and 1 mouse.

Posted in Brain Teasers

3 Comments on "Snakes and Mice"

Ram says
April 25, 2018 @ 04:39

Wait, this is wrong. For the “odd #” explanation, you’re assuming the snake that turns into a mouse isn’t eaten because it was a snake, right? Then what about when there are two snakes and one mouse? One snake eats the mouse, and there are one snake and one mouse left, and the mouse won’t get eaten by the snake (because the mouse was a snake).

Besides, for 11 + 1, if this is your answer, you might as well say “One snake eats the mouse, leaving 10 + 1, and then nothing happens because the mouse was a snake.” Much shorter.

Something’s missing here.

Shabana sarguro says
May 18, 2018 @ 11:32

I don’t understand the question and the logic to the answer.

Tom says
March 5, 2019 @ 06:42

I think the answer should be no snakes and one mouse. “Snakes live by two rules; 1. Eat mice, 2. Don’t get eaten”. One snake eats the mouse, obeying rule one. It turns into a mouse. As it is no longer a snake the rules no longer apply to it. So another snake eats the mouse… and so on until all the snakes have eaten the remaining mouse that used to be a snake. When the last snake eats the (presumably huge) mouse that remains it turns into a mouse. Therefore no snakes left… just one mouse that used to be a snake that used to me a mouse that used to be a snake that used to be… etc