Case 4 Pow 1 The Big Knight Switch

Problem Statement

Four knights, 2 white, and 2 black are sitting on a 3x3 chessboard. The knights were really bored, since they spent all of their time sitting on the chessboard doing nothing, so they decided to try switching places so that the white knights would end up where the black knights started our and the black knights would end up where the white knights started out. To do this, the knights had to follow the following rules:

- No two chess pieces can occupy the same square at the same time
- Knights can jump or pass over each other on the way to an empty square
- The knights can only move 2 squares up (or down, or left, or right) and 1 square to the left (or right, or up, or down.) The moving combinations must be 2 up or down and 1 to the left or right. Or, 2 to the left or right and 1 up or down. Example: They can't move 2 to the left and 1 to the left. They must always move in an "L" shape.
- No two pieces can switch spots at the same time
- The knights can only move one at a time
- They must stay within the 9 squares of their 3x3 chessboard

Process

To solve this POW I read over exactly what it was asking and what the rules to solving it were. The easiest method to solve it was by using "Draw-A-Picture." I started out with drawing a 3x3 square and marking the
positions on the board where the 2 white and 2 black knights were. To keep track of which knight was which, I named the uppermost left black knight Henry, or "H", the uppermost right black knight Julio, or "J", the bottom left white knight Timmy, or "T", and the bottom right white knight Nacho, or "N." TO start out, I drew a 3x3 square and drew the initials of the place where each knight was supposed to be. When I moved one knight, I drew an arrow to the spot where I wanted the knight to go, and then showed the moved knight in the 3x3 square, along with another arrow showing a different knight moving. To keep track of the various moves that the knights took, for every new move the knights took, I drew a new 3x3 square and I drew where the knights from the previous square moved (drawn by arrows) ended up.

Solution

The "Big" Questions

1. It is possible for the black and white knights to switch places on a 3x3 chessboard.

2.
For the solution to this POW I counted 16 moves for the black and white knights to switch places. I believe that my answer is the least number it would take for the knights to switch places, because I followed all of the rules and guidelines correctly, (No two chess pieces occupied any spot at the same given time, no two chess pieces switched into each others spot at the same time, the knights only moved one at a time, and they stayed within the 9 squares of the chessboard.) So, following all of the rules to this POW correctly, 16 moves would be the least number of moves it would take for the black and white knights to switch places. (Refer to the drawing on the next
page.)

3. It is possible.

Evaluation

I definitely considered POW 12 to be educationally worthwhile, because it made me think critically, and it taught me that the answer to a problem won't always be obvious, and that in order to figure it out, you need to look at the problem from different perspectives, and in different ways. POW 12: The Big Knight Switch was challenging, because if one move was incorrect, then it threw off all of the moves that were made after it, and therefore I had to do this problem several times through in order to get the solution.

Self-Assessment

For POW 12: The Big Knight Switch, I believe I deserve an E, because I am positive I found the correct solution by following all of the rules and guidelines to the problem correctly, and I understand the problem thoroughly.