Please look at the nine dots in Figure 12-1. Your task is to connect the nine dots by four straight lines without lifting the pencil from the paper. It will likely help if you try the solution on a piece of paper before reading on and especially before turning to the solution (Figure 12-2).
Almost everybody who tries to solve this problem immediately adopts as part of his problem-solving approach an assumption that makes the solution impossible. The assumption is that the dots compose a square and that the solution ...