Question

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?

Answer 1

Answer:

1999 moves are required.

Step-by-step explanation:

Given is - In solving a jigsaw puzzle, a move consists of joining two clusters, including clusters of just one piece.

This means exactly $n-1$ moves are required to solve a jigsaw puzzle with n pieces.

Here, n = 2000

So, moves will be = $2000-1=1999$

Hence. 1999 moves are needed to solve the puzzle.

Answer 2

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.