The Big Knight Switch

P.O.W. #2
The Big Knight Switch
Problem Statement
One day 2 white chess knights and 2 black chess knights were on a chess board, which is 3x3 squares. The knights decided to try to switch places, like the white knights would end up where the black knights started out and the black knights would end up where the white knights started out.
The rules are:
Each ‘move’ consists of two squares in 1 direction and then 1 square in a perpendicular direction.
They have to stay within the nine squares of their board
There are 4 questions that you must answer also:
Can they do it?
If so, what is the least number of moves it will take them to switch?
How do you know this number is the least?
If it is not possible, explain why not.
The board looks like this:

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 a picture of a 3x3 chess/checkerboard. 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 labeled on the top and bottom of the chess/checkerboard where each knight started out, because when I first started out I forgot where each knight began. 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.
Key:
B=Black
B1=Black Knight 1
B2=Black Knight 2
W=White
W1=White Knight 1
W2=White Knight 2
Move #1
B1

B2

W1

W2
Move #2

B2

W1
B1
W2 Move #3

B2

W1

B1
W2
Move #4
W1

B2

B1
W2
Move #5
W1

B2

B1
W2
Move #6
W1
W2

B2

B1

Move #7
W1
W2

B1
B2
Move #8
W1
W2
B1

B2
Move #9
W1

B1

W2

B2
Move #10

B1

W1
W2
B2
Move #11

B1

W2

W1
B2
Move #12
W2

B1

W1
B2
Move #13
W2

B1

W1
B2
Move #14
W2
B2

B1

W1

Move #15
W2
B2

W1
B1
Move #16
W2
B2
W1

B1

Solution
I. It is possible for the black and white knights to switch places on a 3x3 chessboard.
II. 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, 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.
III. It is possible.
Self-Assessment
I definitely considered this P.O.W. to be really hard, 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.