Here is a related discussion from combinatorics and more: http://gilkalai.wordpress.com/2009/06/29/test-your-intuition-6/#comment-2057 A very nice explanation by John Baez (in two installments) can be found here
http://golem.ph.utexas.edu/category/2006/10/knowledge_of_the_reasoned_fact.html#c005571
and here
http://golem.ph.utexas.edu/category/2006/10/knowledge_of_the_reasoned_fact.html#c005623
