Get Off the Earth!

I absolutely love this geometric puzzle, which I first discovered when reading a book by Martin Gardner. Martin Gardner, in turn, had been introduced to me by my husband David. Martin Gardner was a long-time contributor to Scientific American; he wrote about mathematic and scientific curiosities. Such things were fun for my husband, and myself. I hope you’ll enjoy this puzzle as much as we did!

Sam Loyd was a chess player and puzzle creator at the turn of the 20th century. Some of his puzzles, such as Get Off the Earth, were sold as novelty items. Count the number of Chinamen on the puzzle above. You’ll see the arrow is pointed to “NE” on the globe. Then rotate the arrow to “NW” and one of the Chinamen has disappeared. Where did he go?

You can recreate this puzzle by printing and cutting out the two pictures below and assembling them with a brad.

This is a type of vanishing puzzle. Parts of the 13 original Chinamen have been cunningly redistributed so that there are only 12 when you rotate the circle. It helps understand this if you take some playdough and create 13 worms. Then distribute parts of the 13th worm over the remaining 12 worms.

Here are some other examples vanishing puzzles using the same principle.

One practical application of a vanishing puzzle might occur to you when the airport clerk says you have too many pieces of luggage. “You’ll have to pay an additional $200 for that 5th piece of luggage…unless you can divide its contents among the other 4.”