Ten Chairs, Four Walls, an Equal Number on Each
A rectangular dance hall has four walls. Place exactly ten chairs along them so that every one of the four walls has the same number of chairs standing against it. No cutting chairs in half, no trick furniture — just careful use of geometry.
Reveal the answer
Yes, it's possible: a chair set exactly on a corner counts toward both walls that meet there. Put a chair on two opposite corners and space the rest along the walls, and every wall can show exactly 3 chairs using only 10 chairs in total (4 walls x 3 = 12, minus the 2 corner chairs that each get counted twice = 10). It's Problem 20, 'Ten Chairs,' in Boris Kordemsky's The Moscow Puzzles (1956), the best-selling puzzle book ever published in the Soviet Union.
— Boris A. Kordemsky, The Moscow Puzzles: 359 Mathematical Recreations — Problem 20, 'Ten Chairs'; first published as Matematicheskaya Smekalka, 1956
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