You are probably familiar with these little tile slide puzzles with 15 tiles that slide around in a 4 x 4 grid. The object is to slide the tiles around so that the tiles marked 1 through 15 are arranged in numerical order. The card that comes with the puzzle shows a number of different ways to arrange the numbers, including arranging the tiles in reverse numerical order. In this episode of Numberphile we learned why this particular arrangement is impossible.
