### PROBLEM I had a somewhat solid idea

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PROBLEM STATEMENT:For POW 12, I am asked if four knight’s, (two black and two white) canswitch places, while perpendicular to each other, (meaning two black knights areon 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 squareKnight’s can pass or jump over each otherThe can only move two square forward and one to the right or one forward and two to the rightNothing 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 possiblefor the knights to switch places with each other, following only the guidelinesabove.PROCESS:In first approaching this POW, I reviewed for what it was exactly thisPOW was asking for, making a clear mental image of the POW embed itself into mymind. After carefully re-reading the POW and its guidelines, I had a somewhatsolid 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 andproceeded to attempt to solve the problem.

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I calculated it to take each piece aminimal of four moves to reach the other side of the board so I instantly knew Iwould require 16 boxes for my diagram. But rather then going through thatprocess, I decided to take a much easier one, that being by simply drawing a 3x3chess board with the chess pieces. After completing it, I began by simplyplotting the points and attempting to figure out the process through which Iwould go through to solve this POW. I was quickly amazed when I found the answeronly minutes after originally starting.

I re-tracked my steps and made thediagram included. Since, I already knew, prior to starting, that each wouldrequire four moves before reaching the other side, I traced the route each wouldfollow and devised a method in which the could move one after the other and notinterfere with each other which soon brought me to my conclusion.SOLUTION:The solution to POW 12, which is probable that is now evident is 16moves which shows that they can do it, switching places that is. I know thatthe least amount of moves or the smallest number of moves is 16 because it wouldtake 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 explainshow I reached this thoroughly through expression of art (lol).Using theknown fact of it taking a knight to move to the other side four moves is reasonenough for me to believe that 16 moves it the minimal amount of possible movestotaled.EXTENSIONS:An extension to this weeks POW, would be to consider a POW in which youwere attempting to move or switch the places of four knight’s on a 8×8 or 4x4chess board. To go in even further, consider the minimal moves, if possible, toswitch four bishops or rocks on a 6×6 chess board, if possible.

To simplifywould be to merely increase the chessboard size for this weeks POW.EVALUATION:As a final evaluation for POW 12, I thought the overall thinkingrequired might have been somewhat of a decrease from other POW’s we’ve had. Ifound this POW straight-forward and somewhat self-explanatory. I found it easy,with little question.Category: English