lapisnev

Don't squeeze me, I fart

Things that make you go 🤌. Weird computer stuff. Artist and general creative type. Occasionally funny. Gentoo on main. I play rhythm games!

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porglezomp
@porglezomp

I solved this puzzle properly, by hand! It only took like four hours.

You know there's a simple algorithm for this puzzle: you just have to construct and solve a 54x54 linear system in ℤ₂! Each cell influences some subset of the other cells (and sets them to 1), so you make a column out of each cell to form a matrix 𝐀, as well as a vector for the solution 𝐛, and then solve 𝐀𝐱 + 𝐛 = 0 in ℤ₂.

More in-depth details below the cut, I'll explain all of that at least briefly for folks who don't know what those terms mean. And you won't see the solution unless you want to, if you want to try this method for yourself.


exerian
@exerian

this is literally my favorite thing about this website. the fact that both of you exist. the creator who builds insane puzzle. the genius that solves insane puzzle mathematically and shows their work.


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in reply to @lexyeevee's post:

i got this down to 5 lights before deciding it was dark enough for me.

do you even know if this is solveable? wait do you solve these by turning all the lights off or on. wait can you mathematically prove that any configuration of “chaos lights out” that’s solvable for all lights off is also always solvable for all lights on?

if it's "solvable to all lights off for any starting configuration", then solving to all lights off and repeating the solve path for "all lights on -> all lights off" gets you a solution for all lights on for any starting configuration

if it's "solvable to all lights off for some starting configuration", then no, even if you restrict yourself to:

  • every light affects itself
  • every light affects at most the 3x3 neighborhood centered on it

consider the 1x3 board where the lights affect (from left to right):

  • XX.
  • .XX
  • .XX

then you can solve, say, X.X to all lights off, but you can't solve it to all lights on

i remember how great i felt when i realized there was a reliable way to solve this puzzle. it made me feel like i had finally had some sort of clue on how to actually do it instead of aimlessly clicking everywhere and hoping i brute force my way into success.

you have taken this feeling away from me.

in reply to @porglezomp's post: