Squares in Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A $2$ by $3$ rectangle contains $8$ squares. Can you see how?

2 by 3 rectangle

A $3$ by $4$ rectangle contains $20$ squares. Can you see how?

3 by 4 rectangle

A $4$ by $6$ rectangle contains $50$ squares. Can you see how?

4 by 6 rectangle


What size rectangle contains exactly $100$ squares?

Is there more than one?
Can you find them all?
Can you prove that there are no more?

A poster of this problem can be found here.
 

Published July 2006,August 2006.