# Swapping knights

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?

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.

• 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. – Zandar Mar 5 '16 at 7:39
• Right you are - no idea how I missed that. As a result, we can make the solution more efficient. – Zerris Mar 5 '16 at 8:05

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