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Treebeard's Stumper
3 Apr 98

April Fools' Gold

Snow in the local mountains on April 1 was something unexpected, and so is this classic stumper. The top figure has as area of 8x8 = 64 squares. Cut the figure along the lines into four pieces, and reassemble them as shown in the bottom figure. The same four pieces now have an area of 5x13 = 65 squares, one more than we started with. Here's an easy way to get rich. Just copy the top figure onto a sheet of gold, cut and reassemble, and then sell the extra square! Can this be right, or is it just April Fools' Gold?

If that's too easy, then the advanced stumper is to explain the connection with Fibonacci numbers: 3,5,8,13,...

Answer


last modified .

Marc Kummel / mkummel@rain.org