Club409

The best damn waste of time!

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mwinter
Total posts: 4203
So clearly there's some sneaky reason that the knight can be there after being moved 8 times.

Also it talks about a legal game history, not just legal Knight moves.. so presumably the black knights have to be moving around and end up back in their starting position.. or something similar.
mwinter
Total posts: 4203
Ok I got it. SPOILER ALERT

White Knight on the Right takes 8 moves to kill the queen:
[ [ 1, 2 ], [ -2, 1 ], [ 2, 1 ], [ -2, 1 ], [ -2, 1 ], [ 1, -2 ], [ -2, 1 ], [ 1, 2 ] ]
While White Knight on the Left takes 5 moves to get to the other Knight's starting position:
[ [ 1, 2 ], [ 2, 1 ], [ 2, 1 ], [ 1, -2 ], [ -1, -2 ] ]
acelxix
Total posts: 2265
I had brute forced it too (albeit in excel) and found out it's not possible with the left knight.  If you read the latest article, one quick way to make that determination is to realize that when a knight moves, he always changes from black to white, or vice versa.  So, since the starting square and ending square are different colors, it's not possible for the left knight to capture the queen in an even number of moves, therefore it has to be the right knight.  Once you make that realization, it's a simple puzzle to solve. :)  Fun/challenging puzzles though!
mwinter
Total posts: 4203
(Updated 5/1/2020 8:07 AM)
I guess the only remaining gotcha could be making sure the black knight(s) can move around the board in such a way that they're back in starting the position(s) in the right number of moves to match the end state (also without occupying a square that the white knights need for their paths), but I feel like the interesting part of the puzzle is solved so I'm not going to pursue those details :)

My guess is either black knight just oscillates and that's enough.
acelxix
Total posts: 2265
Yup, it's sufficient for one to just move back and forth.