[HN Gopher] Show HN: Lights Out: my 2D Rubik's Cube-like Game
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Show HN: Lights Out: my 2D Rubik's Cube-like Game
"Lights Out" is a mathematical puzzle that lives on an grid where
each cell of the grid is one of two colors: either red or white.
The goal is to eventually get all the cells in the grid to be red.
What's the catch? Clicking a cell will not only flip its color, but
also that of all cells sharing the same row or column as it. To
me, this game feels like playing with a Rubik's cube --- every time
you think you are fixing one cell, you mess up its neighbors!
There are many ways to arrive at a solution... some mathematical
(linear algebra, or combinatorics), others more logical,... and yet
others which are brute force. The title "Lights Out" comes from a
classic handheld game from 1997. The "rule" they follow for which-
cells-get-flipped-on-click is what I call "Adjacent." Additionally,
my mathematics teacher showed me this game following another
variant which I call "Same Row & Column," but on a bigger board. He
had worked out an algorithm for his version. I found the same
strategy before he revealed the answer, and I feel that the process
of discovering a solution is quite rewarding--it's fundamentally
related to computing on restrictive computer architectures. I
implemented this app with pretty basic TypeScript. It's been used
for some experiments to discover more general of strategies for
different click variants, board sizes, and even board dimensions!
It has also been the basis for the corresponding video produced
using the Python library _manim_. Try it out and let me know how
you do!
Author : raymondtana
Score : 70 points
Date : 2025-10-10 04:40 UTC (1 days ago)
(HTM) web link (raymondtana.github.io)
(TXT) w3m dump (raymondtana.github.io)
| kevindamm wrote:
| Enjoyable, after getting the hang of the "full rows/cols" variant
| it became like popping packing bubbles.. I kind of wanted to keep
| playing with the kaleidoscopic shapes you can make with the near-
| complete positions.
|
| I'd seen the "adjacent only" variant before but not the other
| two, I'm glad the default was one I hadn't seen or I might not
| have noticed there was a choice!
|
| Have you considered allowing the all-white state as a terminal
| state too? First time I completed it was with a detour to there
| (I know the text says make them red but my instincts went with
| the lights-out being to the color matching the background)
|
| Thanks for the diversion. On the 5x5 my scores went from ~100 to
| dozens (sometimes 8-10). On larger boards I'm not as consistent
| but also not as interested in path length.
| taeric wrote:
| Fun game, kudos!
|
| Calling it a 2d rubik's like makes me wonder if I should try to
| turn the code at the bottom of https://taeric.github.io/cube-
| permutations-1.html into a game.
| shiandow wrote:
| Once you figure out the trick to the row column puzzle it becomes
| trivial to solve, except that you need a steady hand.
| adamschwartz wrote:
| 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.
| rprenger wrote:
| 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.
| adamschwartz wrote:
| 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.
| o-o- wrote:
| 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)?
| patrickdavey wrote:
| Why does that work?
| primitivesuave wrote:
| 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.
| 0x1ceb00da wrote:
| What if there was only one white block on the grid?
| adamschwartz wrote:
| The game is initialized with a guaranteed solvable board:
|
| https://github.com/RaymondTana/Lights_Out/blob/31fe5e866c
| 45c...
| bradrn wrote:
| I'm pretty sure this case is solvable too. Click the
| white block, then click all the blocks which turned white
| after that. This flips each block twice (bringing them
| back to their original state), except for the original
| white block which was only flipped once.
| furyofantares wrote:
| I think this only works with an odd grid size. With an even
| grid size you might have to do it twice.
| owenpalmer wrote:
| I'm glad I got to play it for a bit before learning the trick.
| Quite a simple and clever puzzle!
| Carrok wrote:
| Not to be confused with the other grid based light flipping game,
| Lights Out, from 1995.
|
| https://en.wikipedia.org/wiki/Lights_Out_(game)
|
| Math article https://matroidunion.org/?p=2160
| acomjean wrote:
| Or 80s Merlin's Magic square game.
|
| https://en.wikipedia.org/wiki/Merlin_(console)
|
| Which was only 3x3. But red LEDs which were all the rage in
| handhelds in the 80s.
|
| When learning JavaScript I made a dupe of the Merlin game in
| JavaScript. It's really old but still seems to run. Lacks the
| depth of this game with its larger grid.
|
| https://www.aramcomjean.com/magic_squares.html
| noduerme wrote:
| Amazing. I had one of these, and playing your version just
| took me back to the frustration I had figuring out that game
| when I was 7 years old.
| hatthew wrote:
| A straightforward solution for larger puzzles: if you click on
| the four corners of a rectangle, you flip those corners while
| leaving the rest of the rows/columns the way they started. So
| after you pick the low hanging fruit at the start, find any
| rectangle with 3 or 4 white corners, and then click on all 4
| corners of that rectangle. If this leaves you with a just one
| white in each row and column, it's easy and doesn't require
| memorization to click each of those whites to get to the solved
| state.
| hackernj wrote:
| Years ago, I developed a 2D Rubik's Cube game for my son, in
| order to learn JavaScript:
| https://www.thelyonsfamily.us/games/FlipYourLid/
|
| As far as I know, my son is the only person who plays it. :-)
| throwawayk7h wrote:
| There are two significant ways in which this differs from a
| Rubik's cube.
|
| 1. It's abelian. Moves can be done in any order, to the same
| result.
|
| 2. there's a simple algo to solve this. Working from top to
| bottom, left to right: click the first white cell, then click the
| cell below it. (Then there's a simple endgame at the end once the
| bottom row is reached.)
| raymondtana wrote:
| Hi everyone, I'm the OP and wanted to share a few comments that
| might come as spoilers. So read with caution!
|
| 1. _The default game has a simple winning strategy_ : the app
| begins with a 5x5 board under the "Same Row & Column" variant.
| Some here have already figured out how to get all reds: [Memorize
| all the white squares on the board at some fixed moment, and
| click those cells in any order.] Some of the info below helps see
| why.
|
| 2. _The game is always winnable_ : the app is set up to secretly
| begin with all reds and then perform many random clicks to mess
| it up; it's always reversible.
|
| 3. _The order of clicks doesn 't matter_: the click actions
| commute.
|
| 4. _Every click is self-inverse_ : clicking a cell twice under
| any variant leads to the same board as before.
|
| 5. _A winning strategy need only list out which cells to click
| once_ : Because of the properties of commutativity and self-
| inverse, any winning strategy could be freely shuffled in order
| and have any duplicate clicks cancel out, leading to a strategy
| of cells meant to be clicked just once---the rest ignored.
|
| 6. Suppose "n" is odd and play the "Same Row & Column" variant.
| Then, the n-by-n board is solvable by the strategy of "click all
| the cells that were white." But when "n" is even, then this
| strategy fails on the n-by-n board. However, there indeed is
| another strategy that solves those systematically.
|
| 7. Very little is known about the other variants, nor about other
| sizes and dimensions of boards. And it is not true in general
| that any random pattern of white-and-red can be turned into all-
| reds. Try to find a good heuristic for separating out winnable
| vs. unwinnable boards!
|
| 8. I did forget to mention other versions of Lights Out besides
| the handheld game. Other physical games and video games used the
| 5x5 "Adjacent" variant, too.
|
| Bonus Questions:
|
| 1. Can you think of an interesting clicking-rule variant that
| would _not_ be commutative?
|
| 2. Can you come up with the winning strategy for winning n-by-n
| boards when n is even under the "Same Row & Column" variant?
|
| 3. Can you figure out any winning strategy for the other
| variants? I haven't found any good way to proceed without just
| memorizing the solutions.
|
| Thanks for the comments!
| rossant wrote:
| Among the 2^n configurations, how many are solvable?
| hoqqanen wrote:
| I loved that handheld as a kid! I was discovering how powerful
| vibecoding was last year and used this exact game to show some
| friends
| https://drive.google.com/file/d/1jVLpVfUWDkdgImLo45VDtroB-EZ...
|
| One other variant that I've made in the past is cells have N
| states which increment and cycle mod N.
| onedognight wrote:
| Here's my solution: clicking four boxes that form the corners of
| a rectangle will flip them leaving the rest of the board
| unchanged. Using this move you can find sets of rectangle corners
| with more white than red and just click them. This will converge
| to a solution. If you can find a symmetric board where all
| rectangle corners have equal red and white then this method would
| fail. I haven't found one yet.
|
| EDIT: I found some positions where this technique cannot be
| directly applied.
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