Remove Five Toothpicks, Leave Three Squares

Date: 09/16/2002 at 20:49:27
From: Cassie Bass
Subject: Math Puzzle

If you have six squares made up of toothpicks, how can you remove five 
toothpicks and leave three squares?

Date: 09/16/2002 at 23:31:37
From: Doctor Peterson
Subject: Re: Math Puzzle

Hi, Cassie.

You didn't say how many toothpicks you have or how they are arranged, 
but I'll suppose they are like this:

    _ _ _
   |_|_|_|
   |_|_|_|

This uses 17 toothpicks. When you remove 5, you'll have 12 of them to 
make 3 squares. That means you'll have 4 per square, so each toothpick 
has to be in exactly one of the squares, rather than seven of them 
being shared by two adjacent squares as in the original layout.

How could those three squares be arranged so they don't share any 
edges? Which toothpicks do you have to remove to do that?

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/