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# Knight swap puzzle

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Starting with a 4 x 3 board.

The object is to swap the white knights for black ones and vice versa in 16 moves.  Moving a knight one time counts as one move and alternating white and black knight moves is not required.

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Slightly confused here... like this?

Or like this?

akajake wrote:

Or like this?

That's the idea.  Nothing is captured, but you might have to solve this on a real board since you are not allowed to move the same color twice in a row.  I don't know if your solution is optimum or not when alternating moves is forced.

Thanks for trying.

wbport wrote:
akajake wrote:

Or like this?

That's the idea.  Nothing is captured, but you might have to solve this on a real board since you are not allowed to move the same color twice in a row.  I don't know if your solution is optimum or not when alternating moves is forced.

Thanks for trying.

Good puzzle, fun to do. And I thought I did alternate moves. Feel free to correct me or send me the solution if you want. Again, thanks for the brain teaser!

An isomorph is helpful in solving this puzzle.  Martin Gardner noted in "aha Insight" that the eight outside squares on a 3x3 board make up a closed knight's tour and his isomorph consisted of interlocking rings, but this model may be more helpful:

The six shaded squares are a closed knight tour as are the unshaded squares.  When unfolded into an isomorph there are two rings connected by the a2-c3 and c2-a3 links.  Each of the rings contain two knights of one color and one knight of the opposite color.

To solve this one knight each is swapped with the other ring while the other knights are repositioned within their original ring.  Moving a knight one time counts as one move and any knight can move at any time.

eliminate rotations and/or reflections in the final solution.

**Sorry, could not get the isomorph to display**

This puzzle appeared in "aha! Insight" by Martin Gardner in 1978 with an 18 move solution which was not revealed.  Two other readers and I found a 16 move solution which Mr. Gardner discussed in his Scientific American column in early 1978 or
1979, but I lost my copy of it.

Start with a1-c2-b3.  It takes two moves for any knight to go from one side to the other except that when c1 becomes open, the a4 knight zigzags to c1 in 3 moves.  When b1 opens up the Nc4 needs to get there but the Na3 needs to back up to c2 first.  The last two moves are c2-a3-c4 and Voila! it's completed.

Ignore all king moves, they are inserted to show how the solution works w/o a set.

How was my answer not correct? I see your solution, and I did the exact same thing without using the kings... In fewer moves too.

akajake wrote:

How was my answer not correct? I see your solution, and I did the exact same thing without using the kings... In fewer moves too.

It wasn't in fewer moves, though; your answer used 22 moves, vs. 16 moves used in wbport's solution. I think the point you missed is that the king moves (in the diagram from post #8) should be ignored completely, because they are not even a part of the sequence. The only reason for the king moves is that Chess.com's board editor requires them (so that Black and White alternate moves, as they must in standard chess). But since they aren't required for this puzzle, the actual solution given was:

Na1-c2, Nc2-a3, Nb4-c2, Nc2-a1, Nc1-a2, Na2-b4, Na4-c3, Nc3-a2, Na2-Nc1, Na3-c2, Nb1-c3, Nc3-a4, Nc4-a3, Na3-b1, Nc2-a3, Na3-c4  (which is only 16 knight moves).

cobra91: Exactly right.  I had intended in the 8th move of post #8 to move the Nb1 to a4, THEN drop the Na3 back to c2 to allow the c4N to get to b1, but those moves didn't interfere with each other and I let them stand.

This is as close as I can get to an isomorph:

a4-c3-a2-c1

b2-b1-b4-b3

c4-a3-c2-a1

One square vertical moves are allowed on any file but one square horizontal moves are allowed on the 1st and 3rd ranks only.  I'm using rooks instead of knights but label the squares as above.