Club409

The best damn waste of time!

Game on

mwinter
Total posts: 4227
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: 4227
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: 2283
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: 4227
(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: 2283
Yup, it's sufficient for one to just move back and forth.
Drew
Total posts: 4895
semi-related but i had a dream last night that i was sitting around with some math professor or something and we're looking at a problem and i come up with a way to solve it and he's like "pfft yeah if you want to brute force it that way" and there was a little bit of superiority in it so i decided to take offense so i'm like ok look mr ivory tower we don't all have time to wait around for for the math muse to share an elegant solution with us sometimes you just find a way that you know will work and you grind it out, do you know how much of this world was built by brute force how about i brute force you right now, and then i was like hmm that might've been an overreaction but at that point i was in too deep so i kept acting indignant
Shawn
Total posts: 1298
Sounds like the beginnings of a porn plot. Brute Force!
mwinter
Total posts: 4227
Bruce Force storms the Ivory Tower, clothes torn, chest glistening, and muscles rippling.
He overpowers the math muse and gives a clinic on Grinding It Out.
Everybody claps.
Drew
Total posts: 4895
And then he finds $5
Shawn
Total posts: 1298
$5 is $5