Brain Pickings

The Disappearing Bicyclist: A Vintage Puzzle to Tickle Your Brain

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“Which boy has vanished? Where did he go?”

Chess player Sam Loyd (1841-1911) had a knack for mind-bending puzzles, which his New York Times obituary described as “a real gift… for the fantastic in mathematical science.” Among his most famous feats was a vanishment puzzle titled Get Off the Earth. It depicted a rectangular background, topped with a circular card — the “world” — which could be rotated. Along the rim of the circle sit 13 Chinese men. When the world is oriented with the large arrow pointing to the North East, you could count 13 men. But when you turned the Earth slightly so that the arrow pointed to the North West, there were suddenly only 12 men.

This decidedly less racist version of the puzzle, known as The Disappearing Bicyclist, offers the same intentional discombobulation:

Turn the disc so the arrow points to A — and count 13 boys. Then move the arrow to B — and there are only 12 boys in view.

Which boy has vanished? Where did he go?

The genius of Loyd’s puzzle? Each of the many bodyparts — arms, legs, heads, flags — has tiny slivers missing. When the disc rotates, these slices get ever so slightly rearranged, so that each boy gains a part from his neighbor — a clever puzzle, certainly, but also a playfully poetic reminder that our perception of reality is but a function of our angle, and that everything is connected to everything else.

Find more such delightful discombobulators in The Universal Book of Mathematics: From Abracadabra to Zeno’s Paradoxes and the 1959 Loyd original Mathematical Puzzles of Sam Loyd.

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