Today Phil taught me a new puzzle:
There is a circular pond of radius 1. At the center of the pond sits a duck; at the edge, a fox. The duck wants to reach the edge of the pond and fly away. The fox, who is perfectly logical, wants to catch the duck, and is capable of moving at a speed of 1 around the circle (though of course, if moving won't bring it any closer to the duck, the fox will just sit still). Question: what is the slowest speed the duck can take and still make it to the edge of the pond without being caught? How should the duck get there (i.e., move in a straight line, go in spirals, etc)?
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