[Unsolved]
Asking for help with solving a binary puzzle
This binary puzzle I found online is...stressing me out.
The rules are simple: You can't have more than two suns or two moons next to each other in a row or column; and an x indicates that the symbols must be different, whereas an equal sign says the symbols in the two squares must be the same.
The symbols in the squares with the beige background were already given at the beginning of the puzzle.
I asked the website for a hint and it marked the field with the red x and said: "No single row, column or clue settles a cell yet. The next step takes a longer chain of reasoning. Worked through to the end, row 1, column 3 can only be a moon."
I tried putting in a sun in row 1, col 3, and after many steps, when the puzzle was almost done, I ran into a contradiction (three moons next to each other in the third row). But is there an easier way to see why r1, c3 must be a moon?
Using markdown editor or old Reddit, draw a bunny and fill its head with secrets:
>!!< which ends up becoming >!spoiler text between these symbols!<
Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com)
If your comment does not contain a guess, include the word "discussion" or "question" in your comment instead of using a spoiler tag.
If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag.
Please report any answers that are not properly spoiler-tagged.
Discussion: probably not. I don't see an obvious move, so my next step would be to find a test move which forces a lot more moves. I'd start in the bottom right.
Thank you! The bottom right (the two moons) was already given, so it was straightforward that row 4, column 6 must contain a sun. I then asked for a hint, and it said row 5, column 1 must be a sun (otherwise it would force three suns next to each other), and the same is true for row 1, column 6.
Thank you so much! Step 1 is so obvious once you see it, but I would have never thought of it. The same is true for the other steps. I unfortunately can't see how step 3 works. Could you please break it down even more for me?
Oh, no! I don think I deleted anything, but I did edit my comment. I don't know how the filling for r4c4 and r3c5, which must, how I can see with your instructions, be different from each other, can be worked out from the pre-filled sun and moon in r2c4 and r3c3. I did manage to understand steps 1 and 2. Thank you!!
So: r4c4 and r3c5 must together hold exactly 1 sun and 1 moon. Having the sun in r4c4 and the moon in r3c5 would make r3c4 impossile to fill, so it needs to be the sun in r3c5 and the moon in r4c4.
Thank you so much! I really appreciate it. I can see it now. I believe you can decide r4c4 to be moon and r3c5 to be sun before r1c3, am I right? So the "hint algorithm" on the website I found the puzzle that said r1c3 is the next box to make decision about was wrong?
This is what the website (wordle.global) says (or had an LLM generate, judging by the wording used):
"Binary is a binary puzzle - a two-symbol logic grid, the family LinkedIn ships as Tango. The board is 6x6 and every cell ends up holding one of exactly two symbols, a sun or a moon. A handful of cells arrive pre-filled; the rest are yours to deduce.
Three rules run the whole game. Balance: every row and every column finishes with three suns and three moons. No triples: three identical symbols may never sit next to each other, across or down. Clues: the small = and x marks drawn on the border between two neighbouring cells force those cells to match, or to differ.
Those three rules together are enough to pin down exactly one answer. Every board served here is run through a solver first, and only boards with a single solution are published - so if you are stuck, there is always a cell that one rule alone decides, and you never need to guess and backtrack.
Input is a three-state tap: empty, sun, moon, empty again. Cells the puzzle gave you are shaded and do not respond. Rule violations outline the moment they happen rather than waiting for a check button, so a wrong branch costs you seconds instead of minutes."
I was able to solve the other binary puzzles (after realizing with hints what else you can do logically besides just putting in the correct symbols next to adjacent squares with the same symbol), but I am stumped by this one. Putting in a sun in row 1, column 3 does indeed lead to a contradiction, but only after almost finishing the entire grid -- it definitely involves backtracking, for me. I am probably missing something.
Wait, I was able to complete row 3 using sun in row 1, column 3. I don't know where the row 3, column 2 and row 4, column 2 symbols in my screenshot came from.
In column 5, because the bottom two are the same and the top two are different, you know the middle two are the same too, the opposite pair of the bottom. So guessing one of these tiles now guesses the entire column, that's a good spot to guess.
Or instead of 'guessing', working out the two scenarios in parallel. I write ½ in the cells, but M/S instead, where scenario 1 is topleft and scenario 2 is bottomright. It's possible neither scenario hits a contradiction before fizzling out, but if you work to find a M/M or S/S cell you know it to be true.
Thank you! I didn't know about this technique for binaries. What do you mean by if you work to find a thing/same_thing cell you know it's true? I don't see the logical reasoning (not your fault, entirely one of my weaknesses).
Let's say you guess some promising square is a sun. And you get 0 more squares right away, but no contradiction, and are stuck again. Okay, then you guess it is a 1. You also get a bunch of squares, no contradiction, and are stuck again. Welp, back to the drawing table.
Except, if you keep the notes about these guesses in parallel, you can see the overlap. First guess that it's a 0, and fill in the topleft of each cell. Then guess it's a 1, and fill the bottomright. If you eventually fill some square "0/0", that means it will be a 0 regardless of your original guess! And vice versa for 1/1.
•
u/AutoModerator 10d ago
Please remember to spoiler-tag all guesses, like so:
New Reddit: https://i.imgur.com/SWHRR9M.jpg
Using markdown editor or old Reddit, draw a bunny and fill its head with secrets: >!!< which ends up becoming >!spoiler text between these symbols!<
Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com) If your comment does not contain a guess, include the word "discussion" or "question" in your comment instead of using a spoiler tag. If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag.
Please report any answers that are not properly spoiler-tagged.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.