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For those looking for a definitive proof, you can set up the puzzle initial conditions, and the flips that each button makes as a set of linear equations. These linear equations can then be put together to make a matrix equation with unknown coefficients representing the button presses needed to solve the puzzle. You can then prove that some of the button states cannot be reached.
The simpler more intuitive way to prove this is to look at what buttons get affected by what button presses. If you spend long enough staring at it, you might eventually notice that the: Top left, middle left, middle right, and bottom right buttons are coupled. That is, all other button states on the board can be individually controlled except these four. There is no button press that affects one of those four buttons and not the other three. That is to say, all button presses either affect: none, two, or all four of those four coupled buttons mentioned. The only way to solve this puzzle, then, is if, of those four coupled buttons, all are the same colour or two are the same colour when the rest of the puzzle is the same colour.
It is pretty easy to get the puzzle into a state where all other buttons are the same colour. If you do this, you'll notice that of the four coupled buttons, only an odd number are the same colour. There is no way to change an odd number of colours in those four coupled buttons, and therefore the puzzle cannot be solved.
I've got my cheeky paper with the proof on it, but I imagine with this info anybody else could reproduce these results.
https://youtu.be/Yh3XtURX3jE
If you are able to correct your program to figure out how he actually solves it, please do let us know the solution. I'd like to solve the bomb.
so he faked it
1. Empirically moe*4 has exhaustively shown no combinations work.
2. Theoretically it can be shown that of the nine buttons, four cannot be controlled independently (no combination of presses changes only that button) and of those four coupled buttons their values can only be changed in pairs. Since 3 of those 4 buttons have the same color (at the beginning and no matter what you do) the puzzle cannot be solved.
So I would draw 1 of two conclusions, either they cheated their way to completing the puzzle, one way or the other, and found then triggered that audio - or fantastically recreated the Morty/Trover voice to say the words they did in the video.
I'm leaning toward the cheating though, whereas the last bit of subtitles still reference breaking the door down.
If it is the first, that would suggest there is a way to complete the puzzle. Sounds like Roilland's voice to me though, not an emulation of it.
More likely there was a state early in production where you could solve it, then they changed it to be unsolvable, probably related to the achievement. So the audio file stayed, but the solution didn't.
Should've listened to Trover all along.