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The puzzle seems simple enough. It is only a few squares and you only have four knights (the knights move in an “L” shape, like in regular chess). The goal is also straightforward: swap the positions of the black and white knights.

enter image description here

Clarification 1: Every time a knight moves, it must move into an empty square.

Clarification 2: The knight moves do not have to alternate in color.

Attribution: JUNE HUH, COMBINATORICS, AND THE STRANGE ALLURE OF CHESS KNIGHT PROBLEMS

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    $\begingroup$ I feel like all knights swap problems is the same after you make the connectivity graph 🤔 $\endgroup$
    – justhalf
    Commented Jul 20 at 5:25
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    $\begingroup$ @justhalf In a sense yes, but making the step to the connectivity graph is non-trivial. If you know this technique then all knight swap problems can be solved with it. If you don't know it knight swap problems can be quite hard. $\endgroup$
    – quarague
    Commented Jul 21 at 11:31
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    $\begingroup$ @quarague yea, so the so-called variations of knight problems most of them have the same solution, which is to convert it to connectivity graph and trivial from there. There are some knight move puzzles which are still not trivial after converting, those are interesting. $\endgroup$
    – justhalf
    Commented Jul 21 at 11:35

1 Answer 1

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Here is my solution with 40 moves. (last step should be 3+2+3=8) enter image description here We represent the movement of the knights in a graph, where each knight can only move to adjacent nodes. Then we see that in order for the positions for the knights to swap, we must use the "waiting station" at position 9 to pluck out the white pieces and place them to the right positions with respect to the black knights.

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    $\begingroup$ This would be 40 moves. The last 3+2+2=7 should be 3+2+3=8. You had a B at 6 and B at 8 and they must go to 7 and 9. That's 2 moves for the one at 6, and 3 moves for the one at 8. $\endgroup$
    – causative
    Commented Jul 22 at 3:14
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    $\begingroup$ edited answer, thanks for the catch! $\endgroup$
    – lnx
    Commented Jul 22 at 6:44

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