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3x4 Knight Swap (Posted on 2010-02-13) Difficulty: 3 of 5
Eight white chess knights are placed on a 3x4 chessboard, four along the top row and four along the bottom, which are labeled as P, Q, R, S, T, U, V and W, as shown in the figure.

Exchange the positions of P and T, Q and U, R and V, and S and W in minimum possible number of moves.

P Q R S
T U V W


Let the squares be identified from 1 through 12 being read from left to right down.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Move Regimes | Comment 1 of 6
With no pieces on the board but either P or Q, each has 4 regimes to get to its mirrored position:

P[1] -- {7,9}
P[2] -- {10, 8, 2, 9}
P[3] -- {10, 3, 5, 11, 2, 9}
P[4] -- {10, 3, 12, 6, 4, 11, 2, 9}

Q[1] -- {8, 10}
Q[2] -- {9, 7, 1, 10}
Q[3] -- {11, 5, 3, 10}
Q[4] -- {11, 4, 6 12, 3,  10}

The other pieces have regimes which are transmutaions of either P or Q.

I am having some difficulty in working through these.  Maybe there is however enough information in the set of moves which I have offered to calculate the required moves without "playing"the game.

Edited on February 15, 2010, 7:35 pm
  Posted by brianjn on 2010-02-14 02:52:17

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