Answer to the first puzzle

It's convenient to put a single number in the center of a square to indicate its size. For example, the blue square in the lower right is a 3 by 3 square, so we can label it 3.

All we really know is the relative sizes of the squares. If the small squares are designated as being 1 unit by 1 unit, then the sizes are given below.

8 5
1 1 3
2

Note that the sizes of the squares form the sequence

These are the first few numbers in the Fibonacci sequence. Leonardo of Piza (also called Fibonacci) included a problem on rabbits relating to this sequence in a book he wrote about eight hundred years ago. Each number in the sequence is the sum of the preceeding two. So the next few numbers are 13, 21, 34, and 55. The Fibonacci sequence has become very important in mathematics and science over the last few hundred years because it naturally occurs in so many places.

You can see how this square dissection puzzle could be extended to have more of the Fibonacci sequence by continually attaching squares to the long side of the rectangle.

On to Puzzle 2.

1999. This page may be printed for classroom use.
David E. Joyce

Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610

The address of this file is http://aleph0.clarku.edu/~djoye/puzzles/square1.html