Circles cut from cardboard
Source: Canadian Mathematical Olympiad - 2009 - Problem 2.
May 4, 2011
rotationgeometry
Problem Statement
Two circles of different radii are cut out of cardboard. Each circle is subdivided into equal sectors. On each circle sectors are painted white and the other are painted black. The smaller circle is then placed on top of the larger circle, so that their centers coincide. Show that one can rotate the small circle so that the sectors on the two circles line up and at least sectors on the small circle lie over sectors of the same color on the big circle.