Alice has painted a cat on a white disk such that the left eye of the cat is exactly on the center of the disk. Inspired by it, Bob grabbed a white disk of the same size and sat down to paint on it a cat exactly same as Alice's. But after he finished, he noticed that the cat has the exact same size and shape, but he has got the position wrong; its left eye is not at the center. Now he plans to cut the disk into pieces and reassemble them, so that he can get the cat's left eye at the center of the new disk, but he doesn't want to change the shape or size of the cat or the disk. How can he do that with making the fewest possible pieces?
Source: Mathematical Miniatures, by Savchev and Andreescu.
Answer
One (non-straight) cut:
Place Alice's disk on top of Bob's such that the cats match up. Cut off the part of Bob's disk that lies outside Alice's. The cut makes a circular arc that has the same distance between the endpoints as the part of the original perimeter that lies on the piece with the cat on it. Since the two circular arcs also have the same radius (and span less than 180° of the perimeter), you can move the cut-off lune to the other side of the main piece, and the two pieces now cover Alice's disk perfectly.
(Or a different image by Carl Löndahl: https://nup.pw/YK9cjY.png)
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