Some Fun Problems.

1. In the middle of the ocean there is a small island where everybody is part of this strange religion. One of the rules the people with this religion have to follow is the following : if you ever find out that you have blue eyes, you have to kill yourself that day at midnight. Because of this rule, people never talk about other people eyes and there are no mirrors in the island. So they can all live happily without knowing what the color of their own eyes is. They do see other people eyes, moreover, they all meet every day at noon where they have the chance to look at each other. One day, a foreigner comes to the island and at the noon meeting he tells everybody: "at  least one of you has blue eyes". The questions is what happens in the island thereafter. Assume, for example, that in the island there are 100 people with blue eyes and 100 people with brown eyes. Another important assumptions is that everybody in the island is a perfect logician.
   
   
2. Suppose we have a cube of cheese. This cube is divided into 27 small cubes of cheese, so it looks like a Rubik cube (3 x 3 x 3). There is this little mouse who wants to eat the whole cube of cheese. He starts eating the cube in the center, and then has to continue eating adjacent cubes. (Two cubes are adjacent if they share a face.) Can the mouse eat the whole cube of cheese?
   
   
3. Try to turn all the lights on.
   
   
4. Try this slide puzzle.