Comment by adamschwartz
3 days ago
Memorize which cells are white when the board first loads. Tap all of those in order without regard to the way the board changes as you go.
Edit: above tested for 5x5 rows&cols. For even boards it seems there’s a small end-game to repeat the process — something about parity I assume.
And you can do that at any board state, so if it starts with like 16 white squares you can make one or two greedy moves to minimize white squares, then do your memorize trick.
Yea that can shave a few moves off.
For fun you can also, for example, invert any board in N moves by tapping every cell straight across any row or column.
Interesting, and black magic as far as I'm concerned. How does that algorithm translate onto the Rubik's cube (which I evidently never learned to solve)?
Why does that work?
If you think of each button press as a matrix being added to the board state where only the row and column are set to 1, along with the commutative nature of the moves (order doesn't matter), then as long as the total number of "flips" from the cumulative matrices of moves is odd, then it will reset the board.
Mathematically I might say that the system's precomputed solution vector is readily apparent.
I think this only works with an odd grid size. With an even grid size you might have to do it twice.
What if there was only one white block on the grid?
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