by Dave Youngs
This month's Puzzle Corner activity is a fascinating visual paradox with mathematical origins. The puzzle consists of a disk that rotates within a circle on a separate sheet. The two pieces, when put together, picture a ringed planet circled by astronauts. With the disk in its initial position (inside arrow to A), 15 astronauts surround the planet. When it is rotated to the second position (inside arrow to B), one astronaut disappears! Rotating the disk back to its original position restores the missing astronaut. The challenge in this puzzle is to explain how this "disappearing act" works. **
While linear disappearing puzzles were common in the late nineteenth century, it took the genius of Sam Loyd, America's premier puzzlist, to invent the first circular ones. In 1896, Loyd received a patent for what would prove to be his most successful puzzle, Get Off the Earth. This puzzle consisted of a card with a disk attached showing 13 warriors ringing the disk. When the disk was rotated, one of the warriors disappeared, leaving only 12. Two questions were printed on most versions of the puzzle: "Which one has vanished?" and "Where did he go?" Over ten million copies of the puzzle were sold, mostly as advertising premiums. This puzzle was so popular it broke the shackles of Madison Avenue and entered the political arena -the Republican Party gave away thousands of copies in McKinley's successful bid for the presidency in 1897.
To make the circular puzzle, students need some scissors, a copy of one disk from the first worksheet and the circle from the second worksheet. After carefully cutting out the disk (planet), they center it within the circle (rings), lining up the arrow on the disk with the A on the circle. Fifteen astronauts surround the planet. When the disk is rotated so that the arrow points to the B, there are only 14 astronauts, leaving students to ponder the fate of the missing astronaut.
If students are careful, they can use a paper fastener to attach the disk to the circle on the second worksheet. The centers of the disk and circle are marked to allow this, but any misalignment will seriously detract from the puzzle's effectiveness.
I hope you and your students find this puzzle as fascinating as I do. It will certainly exercise you mental facilities as you ponder how it works.
For better print quality, please use the following images:
**Hint: You might try measuring the astronauts and finding their average heights when there are 14 and when there are 15.