In solving a jigsaw puzzle, a move consists of joining two clusters, including clusters of just one piece. What is the minimum number of moves required to complete a two-thousand piece jigsaw puzzle that is separated into individual pieces?

Solution: As always, try to find a way of looking at the problem that makes the solution simple. In this problem, regardless of the current state of the puzzle, a move consists of combining two clusters into a single cluster. Therefore every move reduces the number of clusters by 1. Since we begin with 2000 clusters (the single pieces) and end with 1 cluster, we need / [2000-1=/boxed{1999}/] moves to complete the puzzle.