If this puzzle reminds you of a Rubik's cube that is not a coincidence. The mathematical structure of both puzzles is essentially the same. The moves in both puzzles form a non-abelian group, which is the source of the challenge. See http://web.mit.edu/sp.268/www/rubik.pdf
In fact, a fun meta-puzzle is to find a three-dimensional analog to this two-dimensional puzzle.
It might be helpful to note that the moves form a group, but the puzzle itself is the group action of this group on the cubes/squares/pieces.
In this context it reveals the usefulness of commutators, which are moves of the form ABA'B', where A and B are some sequence of moves and ' denotes inverse.
In general A and B aren't commutative, but with respect to a subset of the pieces, the actions of A and B are effectively commutative, so ABA'B' will do nothing to those pieces. Which means you can get some simple permutation control over the remaining (usually much smaller) pieces of the puzzle.
My first thought was the same, “ah it’s just a group puzzle like a rubik’s”. In my case, understanding the math doesn’t make up for me being completely useless in solving it.
Fun. I have a blog I wrote years ago that had fun seeing a Rubik's cube as permutations. I can see how that could map somewhat to this. I should pick that back up.
With both, a key can be learning how to "swap" two pieces without modifying the others around them - once you have that worked out, you basically can solve it even if not in the most efficient manner possible.
Never heard of Quixo, thanks for sharing. My domain name was picked randomly a decade ago among the remaining short-ish names -- being similar in name is a coincidence.
> (draw at optimal play on a 5x5 board, win for first player on smaller boards)
Somewhat relatedly, I keep wondering how board size affects the game of chess in particular.
It seems that a 1x8 board definitely leads to a stalemate (because the pawns in front of the kings would block each other), but at some point adding new columns (with the relevant pieces) makes the game impossible to exhaustively search, and at least plausibly introduces the ability for one of the players (presumably white) to win with perfect play.
That ability for a winning strategy to emerge just beyond our ability to compute is somehow tantalising.
Without changing the rules somewhat, it appears that the odds change dramatically enough to make easy wins for one of the players on such smaller boards. Hence, variants include some weird stuff.
Agreed, I thought I had it cracked when I noticed that I just needed to get the spacing right on Easy, but man the difficulty is a cliff going into medium.
EDIT: Oh Ok, Medium isn't that hard either, much harder than easy though, just figuring out the last "row" is to toothsome part.
There’s a Japan-only game for the Sega Game Gear called Kinetic Connection that plays similarly but involves rearranging a scrambled picture rather than moving colored blocks into a pattern.
“Game 3” is the mode that rotates rows and columns like a Rubik’s Cube.
There are probably earlier examples, but that’s the one that I’m familiar with. I imagine a clever person could adapt it into a simple word game as well. Old computer and console games are a gold mine for ideas for simple puzzle games.
I was developing a similar game in Unity but decided to go further and add portals, rotations, splitting and other mechanics. Unfortunately, I have never managed to polish it (those 20% that take 80% of time, duh). I hope one day someone will implement something similar.
For the easy and medium, it seems like you can work outwards from the top left corner, solving progressively larger squares. 1×1, 2×2, etc. Once one of those squares is correct, you never have to touch the rows or columns in that square again.
Probably not a perfectly efficient strategy but it makes it easier to think about.
Same as you, but I took 90% on the time only on the last line, the first three are solved use basic swipe of two squares, as in a beginner cube method.
Wow. Back in high school (~2011) I made this game as an ios app. I remember I published a video on YouTube and a few months later I found a copy on the App Store. Maybe it was just a coincidence. Unfortunately I don’t find my video on YouTube anymore, can it be that YouTube deletes old videos ?
While I don't suffer from red-green colorblindness, it does actually hurt my eyes. One might consider offering a color switcher since as best I can tell they just need to be different from one another for the puzzle to work
Anyway, if you happened to peek at the illustration of the POC (used contrasting light / dark colours, plus patterns and softened letters of corresponding "inversion" [0]), do you think it is an improvement?
Author of the game also updated the contrast [1], so now it is light blue versus slightly darker violet, but still with same default (usually black) text colour [1]. Do you like it better? Or would you prefer classical black versus white or something in this lines?
Sure, and my response was to provide simple POC to try some alternative hopefully more accessible appearance on top of live version for folks with colour vision troubles and potentially for the author as well.
group theory aside, the elegance of sliding implementation is such that it feels like just humming along playing with Turing tapes that can act on each other in some nice smooth way; that's not to say it's a precisely accurate analogy, more that it just feels nice in some intuitive CS / math sort of way
the other was that found it easiest to move to known state and then solve, like an intermediate canonical isomorph instead of solving directly as human without machine group theory super rotators
heres a non-constructive solution for the medium puzzle. the commutator of a row move a and a column move b (defined [a,b]=aba^-1b^-1). is a three cycle. it is not hard two see that any three cycle is conjugate to either a commutator or a product of two commutators [a,b]*[-a,b]. the three cycles generate the alternating group, which is maximal in Sn. but the group action also contains a 4 cycle, which is not in the alternating group. so the action must be all of Sn.
Would it make sense to increase the difficulty more gradually? And independent of each other? Like size, number of colors, degrees of freedom, individually, instead if just easy medium hard, with presets?
That was my initial idea (if you peek at the code, you’ll see it’s simple to create a 2-color + hard-mode). But it turns out that hard is quite hard, even with just 2-colors. So I picked 3 instead of 4 levels.
I was finding this hard then wanted to see how long it would take to solve just quickly sliding randomly. Turns out very quick! If the number of moves was limited this wouldn't work
I liked it. Very reminiscent of a rubik's cube. I found it's easier to make solid stripes and manipulate from there instead of going for the checkerboard right away.
Any hints on how to solve even the easy one? I did map out what a sequence like right->down->left->up does, but feels like I'm still missing a step at least.
That's not a coincidence. The mathematical structure of both puzzles is essentially the same. The moves in both puzzles form a non-abelian group, which is the source of the challenge. See http://web.mit.edu/sp.268/www/rubik.pdf
I cloned the github repository, but I have no idea how to install/start/generate the website. So I can't hack into it. Could you provide explanation, please?
In fact, a fun meta-puzzle is to find a three-dimensional analog to this two-dimensional puzzle.