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Problem of the Day #401: The Duck and The Fox April 23, 2012

Posted by Saketh in : potd , add a comment

A number of different versions of the following classic puzzle exist:

A duck, pursued by a fox, escapes to the center of a perfectly circular pond. The fox cannot swim, and the duck cannot take flight from the water. The fox is $k$ times faster than the duck. Assuming the fox pursues an optimal strategy, how can the duck reach the edge of the pond and fly away without being eaten?

First, find a strategy by which the duck can escape if $k=4$. Then, determine the smallest value of $k$ such that it is impossible for the duck to escape.