# Mexican Hats

## Recommended Week

Year 1 : All Weeks

James Marshall

## Problem 1

Four Mexican bandits are arrested and placed in two separate cells, one bandit in isolation, and the other three bandits together. The governor of the gaol decides to play a game with the prisoners, and offers to free them if they can solve his puzzle. He gets the prisoners to line up facing the wall, then a guard enters each cell and places a hat on each prisoner. The governor tells the prisoners that two of them are wearing black hats and two are wearing white ones... if one of them can correctly identify the colour of their hat he will be set free, but if he is wrong, his sentence will double. Each prisoner can only see the other prisoners in front of him, and cannot see through the wall. After five minutes one of the prisoners correctly announces the colour of his hat.

Which prisoner was released?

A:) || (:B (:C (:D

Version with answers (available for CS staff only)

## Problem 2

On another occassion, five bandits are arrested, and placed in two separate cells. The governer plays the same game, isolating one bandit, and getting the other four bandits in the other cell to face the wall. This time he puts three black hats and two white on them.

Which prisoner would you rather be to have the greatest chance of being released?

A:) || (:B (:C (:D (:E

Version with answers (available for CS staff only)