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I am looking for a reference (book or article) that poses a problem that seems to be a classic, in that I've heard it posed many times, but that I've never seen written anywhere: that of the possibility of a man in a circular pen with a lion, each with some maximum speed, avoiding capture by that lion.

References to pursuit problems in general would also be appreciated, and the original source of this problem.

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Since you're asking for a reference, perhaps this will do?

Wolfram Mathworld says the problem was listed by Rado in 1925. The reference is on the problem description page, here.

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Here is a book on this type of problem

http://press.princeton.edu/titles/8371.html

it is also briefly mentioned in his other book "Euler's Fabulous Formula".

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    $\begingroup$ The book is Chases and escapes: the mathematics of pursuit and evasion by Paul J. Nahin. Google Books Preview $\endgroup$ – ShreevatsaR Oct 14 '10 at 8:37
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The book is Coffee in Memphis by Bollobas. It's the first problem, and there are loads more :

http://www.amazon.com/Art-Mathematics-Coffee-Time-Memphis/dp/0521693950

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