The Puzzle Page is dedicated to bringing you the best puzzles collected from around the world along with original puzzles not seen anywhere else.

The staff at The Puzzle Page always enjoy seeing new puzzles and would love to hear from you. If you have a puzzle that's giving you problems, drop us a line -- we'd love to help.

## Friday, February 1, 2008

### The Missing Tile

Here's another favorite of mine. I think this one, above most other puzzles, can truly be described as a mind bender.

In the diagram below (click on the image to get a larger version) you see two figures made up from the same pieces. In the upper figure the colored pieces are arranged so that the area of the figure is (13 x 5) ÷ 2 = 32.5 tiles. In the lower figure, the same colored pieces have been rearranged so that the area of the figure is (13 x 5) ÷ 2 - 1 = 31.5 tiles (the -1 is for the missing tile above the number 8.)

This is not an optical illusion; the grid lines are there to help demonstrate that all the squares are uniform. Feel free to print out a copy of the picture, cut out the colored pieces in one of the figures and lay them out on top of the other figure to prove that they are indeed the same size.

How can it be possible to disect a polygon, rearrange the order of the pieces and end up with less (or more) space than was used before?