# Some Fun Problems.

- 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.

- 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?

- Try to turn all
the lights on.

- Try this slide puzzle.

You can find more fun problems
in the page of module on Puzzles of
the Math Explorers Club.