The Duck and the Fox


I got this problem from Rustan Leino, who got it from Koen Claessen.

I solved it and wrote up my solution.


A duck is in circular pond. The duck wants to swim ashore, because it wants to fly off and this particular duck is unable to start flying from the water. There's also a fox, on the shore. The fox wants to eat the duck, but this particular fox can't swim, so it can only hope to catch the duck when the duck reaches the shore. The fox can run four times faster than the duck can swim. Is there always a way for the duck to escape?

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