POW #12: The Big Knight Switch

PROBLEM STATEMENT:

For POW 12, I am asked if four knight’s, (two black and two white) can

switch places, while perpendicular to each other, (meaning two black knights are

on one side of a 3×3 chess board with two white knights adjacent to them. They,

were feeling restless and decided to attempt to see if this were possible.

Keeping in mind the following guidelines:

No two pieces can occupy the same square

Knight’s can pass or jump over each other

The can only move two square forward and one to the right or one forward

and two to the right

Nothing is mentioned about proper turns, i.e. white first, then black,

then white.etc.

With those guidelines I was set to attempt to find if it were possible

for the knights to switch places with each other, following only the guidelines

above.

PROCESS:

In first approaching this POW, I reviewed for what it was exactly this

POW was asking for, making a clear mental image of the POW embed itself into my

mind. After carefully re-reading the POW and its guidelines, I had a somewhat

solid idea of how to approach it.

I first made a custom 3×3 chess board, and included the chess pieces

(two black and two white). I placed each in their appropriate sections and

proceeded to attempt to solve the problem. I calculated it to take each piece a

minimal of four moves to reach the other side of the board so I instantly knew I

would require 16 boxes for my diagram. But rather then going through that

process, I decided to take a much easier one, that being by simply drawing a 3×3

chess board with the chess pieces. After completing it, I began by simply

plotting the points and attempting to figure out the process through which I

would go through to solve this POW. I was quickly amazed when I found the answer

only minutes after originally starting. I re-tracked my steps and made the

diagram included. Since, I already knew, prior to starting, that each would

require four moves before reaching the other side, I traced the route each would

follow and devised a method in which the could move one after the other and not

interfere with each other which soon brought me to my conclusion.

SOLUTION:

The solution to POW 12, which is probable that is now evident is 16

moves which shows that they can do it, switching places that is. I know that

the least amount of moves or the smallest number of moves is 16 because it would

take each individual knight four moves to move to the other side of the board,

which means 4 multiplied by 4 is 16 moves total. The diagram I provided explains

how I reached this thoroughly through expression of art (lol).Using the

known fact of it taking a knight to move to the other side four moves is reason

enough for me to believe that 16 moves it the minimal amount of possible moves

totaled.

EXTENSIONS:

An extension to this weeks POW, would be to consider a POW in which you

were attempting to move or switch the places of four knight’s on a 8×8 or 4×4

chess board. To go in even further, consider the minimal moves, if possible, to

switch four bishops or rocks on a 6×6 chess board, if possible. To simplify

would be to merely increase the chessboard size for this weeks POW.

EVALUATION:

As a final evaluation for POW 12, I thought the overall thinking

required might have been somewhat of a decrease from other POW’s we’ve had. I

found this POW straight-forward and somewhat self-explanatory. I found it easy,

with little question.