On a $3\times3$ grid we have:
with $8$ moves needed to swap the red and blue knights.
What is the minimum numbers of moves to swap the knights on a $4\times4$ grid?
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2 Answers
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It will take:
20 moves to swap the knights
This can be done as follows:
All credit goes to @klm123 for demonstrating a good way to visualize this in a similar puzzle.
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1$\begingroup$ You seem to be missing some connections - B2 to C4 and D3, and C3 to A2 and B1. This does actually put opposite-coloured squares in reach of B2 and C3. $\endgroup$– ZandarMar 5, 2016 at 7:39
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$\begingroup$ Right you are - no idea how I missed that. As a result, we can make the solution more efficient. $\endgroup$– ZerrisMar 5, 2016 at 8:05
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I believe it is, in chess terms,
20 half moves, or 10 move pairs.
In algebraic notation:
1. N3b2 N2c3 2. Na1 Nc1 3. Nb3 Nbd3 4. Ncb4 Nc2 5. N1d2 Nd4 6. Nb1 Nd2 7. Na3 Ncb1 8. Nbc4 Nac3 9. Ndb2 Nc2 10. Na4 Nd1
