Friday, August 5, 2011

Banach's Match Box Problem

A poetry collection by Susan Case (see also 5 July 2011 posting)  -- The Scottish Cafe (Slapering Hole Press, 2002) -- celebrates the lives and minds of a group of mathematicians in Poland during World War II. Its observations and insights add a new dimension to the important story of the Scottish Book to which it refers -- a book in which the mathematicians reorded their problems and solutions. First published in a mimeographed edition in 1957 by Stanislaw Ulam, The Scottish book: mathematics from the Scottish Café (Birkhäuser, 1981) may now be seen and searched at GoogleBooks.  Case's collection includes statements of two of the Scottish Book's problems:  here, below, is "problem 193" -- which I offer as a "found poem."  A photo of its Scottish Book solution follows.

     problem 193
           May 31, 1941

     the Banach Match Box Problem

     A certain mathematican always carries two boxes of matches,
     one in his right pocket and one in his left pocket.  He picks
     a box at random to light his pipe.  Initially the boxes each
     have N matches.  When he finds the first box empty, what is
     the distribution of the number of matches in the other box?

The Scottish Book provides this solution:

Click on image to enlarge.

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