Tag Archives: Futility Closet

The Two Errand Boys

This is another puzzle from the Futility Closet that was originally from Henry Dudeney’s Canterbury Puzzles.

“A country baker sent off his boy with a message to the butcher in the next village, and at the same time the butcher sent his boy to the baker. One ran faster than the other, and they were seen to pass at a spot 720 yards from the baker’s shop. Each stopped ten minutes at his destination and then started on the return journey, when it was found that they passed each other at a spot 400 yards from the butcher’s. How far apart are the two tradesmen’s shops? Of course each boy went at a uniform pace throughout.”

Answer.

See the Two Errand Boys for solutions.

Keyhole Problem

This is another problem from the Futility Closet website. It turned out to be pretty simple. The idea is to show the length of BC remains the same no matter where A is chosen on its arc of C1. 

(Update 7/1/2020) There is more to this problem than I realized, thanks to a revisit prompted by a question from Deb Jyoti Mitra.  See the revised Keyhole Problem.

Two Circles Puzzle

Another good source of problems is the Futility Closet site. This puzzle involved finding the line of maximal length passing through the intersection of two circles. I solved it before looking at the Futility Closet solution. Their solution of course was short, sweet, and elegant. Mine was more like the old adage of cracking a walnut with a sledge hammer. Still, I thought there were some unexplained parts to the elegant solution that justified the effort on mine. At least my solution provided an interesting, though convoluted, alternative. See the Two Circles Puzzle.

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