Ken's Puzzle of the Week

Swapping Knights Again

W     B
B     W
W     B
B     W

Place four white and four black chess knights on a 4x4 board as shown.  Using standard knight moves, swap the positions (black for white.)  Moves do not need to alternate in color, and at no time may a knight be under attack from the opposite color.

For ease of comparing solutions, use this labeling of the board for declaring moves.
+--+--+--+--+
| A| B| C| D|
+--+--+--+--+
| E| F| G| H|
+--+--+--+--+
| I| J| K| L|
+--+--+--+--+
| M| N| O| P|
+--+--+--+--+
Warmup: Try the puzzle with only the corner knights first - start with just white knights on A & P, black on D & M, then swap.

Source: Original.  Similar to previous knight-swapping puzzles.


Solutions were received from Kirk Bresniker, who sent an 800+ move computer-solved solution.  But the puzzle can be solved with 34 moves.  It helps to remap the board to a different graph like the one below.  Kirk reran his analysis and found no better than 34 moves.  My solution is below, and Kirk's list of twenty such solutions follows that.

My 34-move solution is below, each line alternating colors:

L-N, E-C, D-F-L, M-F,
H-B-K, I-B,
F-O,
K-D, B-K-M,
O-I, C-E,
P-J-H, A-J,
I-G,
H-B, J-H-O,
G-P, N-G-A, L-N-G, E-C-J,
O-F-L, B-K-E,
J-H, G-I

Kirk's twenty 34-move solutions.  They are all very similar to each other and some differ only in order of moves:
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-B J-A L-C M-F F-O D-F B-K O-H F-O N-L K-M E-K C-E K-D O-I
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-B J-A L-C M-F F-O D-F B-K O-I F-O N-L K-M E-K C-E K-D O-H
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-H K-B B-I F-D N-E E-K C-E K-M
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-H K-B B-I F-D N-E L-F C-L F-M
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-H K-B B-I F-M C-E E-K K-D N-E
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-H K-B B-I F-M C-E L-F F-D N-L
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-H K-B B-I F-M N-E E-K C-E K-D
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-H K-B B-I F-M N-E E-K K-D C-E
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-H K-B B-I F-M N-E L-F C-L F-D
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-H K-B B-I F-M N-E L-F F-D C-L
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-H K-B F-M N-E L-F F-D C-L B-I
A-G E-K H-J L-F J-C G-N I-G F-O N-L G-N K-B B-H C-E P-G H-J O-H G-I J-P 
H-J I-O J-A E-C M-K K-B D-K O-F B-I K-B F-M N-E L-F F-D C-L B-H
E-K I-G M-F H-J F-O K-B D-K L-F J-C B-H G-N K-B B-I N-E E-K C-E F-L K-M 
E-K K-D I-B A-G L-C G-N P-G C-J N-L G-N B-I J-A N-E H-J O-H J-P
E-K K-D I-B A-G L-C G-N P-G C-J N-L G-N B-I J-P N-E H-J O-H J-A B-H G-N 
K-B B-I N-E E-K C-E F-L K-M E-K K-D I-B A-G L-C G-N P-G C-J N-L
E-K K-D I-B A-G L-C G-N P-G C-J N-L G-N B-I J-P N-E I-G O-I G-A E-K I-G 
M-F H-J F-O K-B D-K L-F J-C B-H G-N K-B B-I N-E E-K C-E F-L K-M
E-N K-E E-C I-B B-K F-M N-G K-D O-F H-B B-K C-J F-L G-I K-E J-H A-G E-C 
I-O G-I H-B P-G C-J L-C G-N J-P C-J J-A B-H M-K N-L K-E D-K L-F
E-N K-E E-C I-B B-K F-M N-G K-D O-F H-B B-K C-J F-L J-H K-E G-I A-G E-C 
I-O G-I H-B P-G C-J L-C G-N J-P C-J J-A B-H M-K N-L K-E D-K L-F
E-N K-E E-C I-B B-K F-M N-G K-D O-F H-B B-K C-J J-H G-I K-E F-L E-K I-G 
M-F H-J F-O K-B D-K L-F J-C B-H G-N K-B B-I N-E E-K C-E F-L K-M
G-N B-I J-A N-E I-G O-I G-P E-K I-G M-F H-J F-O K-B D-K L-F J-C B-H G-N 
K-B B-I N-E E-K C-E F-L K-M E-K K-D I-B A-G L-C G-N P-G C-J N-L
J-P C-J J-A B-H M-K N-L K-E D-K L-F E-N K-E E-C I-B B-K F-M N-G K-D O-F 
H-B B-K C-J F-L J-H G-I K-E J-P C-J J-A B-H M-K N-L K-E D-K L-F

Mail to Ken

My 34-move solution is below, each line alternating colors:

L-N, E-C, D-F-L, M-F,
H-B-K, I-B,
F-O,
K-D, B-K-M,
O-I, C-E,
P-J-H, A-J,
I-G,
H-B, J-H-O,
G-P, N-G-A, L-N-G, E-C-J,
O-F-L, B-K-E,
J-H, G-I