The Big Knight Switch

The Big Knight Switch

Problem Statement: Two black and two white knights were on four corners of a 3x3 chess board perpendicularly. One day the black and white knights were all feeling bored and decided to try to switch each other places, so they would end up ton the opposite place. They can move to the left or right two squares and then down or up one square. However, they could only move one at a time within the 3x3 board and no two knights could occupy the same space at the same time.

Process: I started the process by drawing a 3x3 chessboard on a piece of binder paper and placing two black and two white cubes on their starting positions. Every time I tried to move the cubes in random orders, I would get stuck when one black and one white cube on the right places and the other two were just repeating the their same route. Then I used the circle method to move the cubes in a route of circle. However, it confused me even more. So then I just used hand drawing to solve the puzzle, and it worked!

Solution:

The total number of moves is 16. Many students got this number, too! After many times of trying, I determined that the smallest number of moves is 16 because it would take each individual black/white knight four moves to move to the switched space. That is the only way or solution for the four knights to switch place with those rules.

Extensions:

Three red and three gold plants were placed perpendicular to each other in a garden. One afternoon the master decided to switch the plants, so the red plants are on one side of 5x5 chessboard liked garden with three gold knight adjacent to them. Because the master was too old, so he could only move one plant at a time. He could move to the left or right three squares and then down or up two squares. Can old master do it?

Evaluation: