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Traveling on a Train

Two travelers, starting at the same time from the same point, travel in opposite directions round a circular railway.  Trains start each way every 15 minutes, the easterly ones going round in 3 hours, the westerly in 2.  How many trains did each traveler meet on their circuit, not counting trains met at the terminus itself?

A Tangled Tale, Lewis Carroll, 1885

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"Traveling on a Train," Convergence (March 2007)