[This is a back-issue of one of this site’s newsletters]
If you’ve been reading for a while, you might remember this puzzle: Can you find a rectangle whose area equals its perimeter?
For example, a 6 x 3 rectangle has a perimeter of 18 units, and the area is 18 square units. The same number!
“Everyone” knows that 3×3 + 4×4 = 5×5. This little factoid, and other Pythagorean triplets, can be the basis of a nice set of puzzles. Here’s the first. If you draw a 5×5 square on graph paper, how can you cut it up (following the lines on the graph paper) so that the pieces can be rearranged to form a 3×3 square and a 4×4 square?
This is not so hard to do. Here’s one possible solution :