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© Copyright 2002, Jim Loy
Here is a famous puzzle by Sam Loyd. The picture is
made up of a rectangular background piece of cardboard or paper. On top of that
is a circular world. Part of each Chinaman is on each piece of cardboard. We
start with the picture on the left, with the arrow pointing in the direction
marked N.E., and count 13 Chinamen. Then we rotate the Earth, so the arrow
points in the direction marked N.W., and count 12 Chinamen. Where did the 13th
Chinaman go?
Well, there never were 13 Chinamen. There were many parts of Chinamen, arms, legs, bodies, heads, and swords. And each had tiny slivers missing. Then when the Earth was rotated, these pieces were slightly rearranged. In particular, each of the 12 Chinamen gained a sliver of a Chinaman from his neighbor. For example, at the lower left, there are two Chinamen next to each other. The top one is missing a foot. When the Earth is rotated, he gains a foot from his neighbor on the right. That neighbor gains two feet (he lost one) and one small piece of a leg, etc.
This is a particularly good example of a vanishing puzzle. See The Extra Square, which is a vanishing puzzle in reverse.