29 August 2018
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From The Sunday Times, 12th September 2010 [link]
George has placed two vertical mirrors touching each other, with an angle between them. He has also placed a small cube between the mirrors and counted how many images there are of it in the mirrors. (For example, if the mirrors had 90 degrees between them, there would be three images). He wrote down two whole numbers – the angle between the mirrors, in degrees, and the number of images of the cube. When Martha saw the two numbers, she commented that their product, appropriately, was a perfect cube.
What was the angle between the mirrors?
Note: After much discussion of this puzzle, regular solvers of The Sunday Times Teaser puzzles have decided that the puzzle is flawed, and there is not enough information given to arrive at a unique solution. Nevertheless the puzzle has some interesting aspects to it.