The Simple Proof of the Tetris Lamp
I recently read a similar case in Simon Singh's book <i>Fermat's Enigma</i> <a href="http://www.amazon.com/reader/0385493622?_encoding=UTF8&query=15" rel="nofollow">http://www.amazon.com/reader/0385493622?_encoding=UTF8&query...</a> about the 14-15 puzzle.  It was similarly unsolvable and provable the same way.<p>Interestingly, his account is rather different than that on wikipedia <a href="http://en.wikipedia.org/wiki/15_puzzle" rel="nofollow">http://en.wikipedia.org/wiki/15_puzzle</a>
Singh claims that Sam Lloyd created the puzzle, secretly proved it was impossible, and offered rewards to anyone who could solve it.