Sunday Times Teaser 2503 – No Title

by Danny Roth

Published September 12 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?