Suppose you have a circle that is perfectly inscribed in a rectangle.
A smaller rectangle is placed on top of the first one, such that one corner is on the edge of the circle and the opposite corner matches a corner of the larger rectangle.

If the smaller rectangle is twice as long as it is high, how many of them will fit into of the larger one (without overlapping, of course)?

Combining what has already been said, there are 2 solutions: 2, and 50. This is taken from C.B.'s and wonshot's comments. Why are there two solutions? Because there are two ways this smaller rectangle can be. Its corner can touch the circle edge close to it, or it can touch the further edge of the circle where it is tangent to the rectangle.

Posted by Tristan on 2003-11-20 20:22:08