Which way did the bicycle go?

Yesterday, we talked about Sherlock Holmes Adventure of the Priory School, in which Holmes deduces the direction of a bike’s travel by examining the depth of the impression left by each wheel.

Sherlock Holmes deduces the direction of bike travel

Careful observers have been howling ever since at Doyle’s obvious error. Unless you’re cycling in a circle, the rear wheel will always follow and obliterate the track of the front wheel, no matter which way the bike was going. You can’t tell which direction the bike was going just from the depth of the tracks.

In the story, it turns out Holmes made a lucky guess and cracked the case. But can you figure out the direction of bike travel by examining the tracks? It turns out you can. Mathematician George Hart discusses this puzzle in his Mathematical Impressions blog. You can watch his discussion in the Youtube video below, as well. And isn’t that Red Line model bike pretty cool?

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