3x3=4x4
(Published on 4. June 2022, 14:39 by filuta)
This was originally planned to be an example puzzle for a bigger one, but since it is not clear when or whether I will finish it, I decided to publish this one separately (and I also feel it deserves its own page anyway). Big thanks to the CTC discord server users Piatato, SpeedyBozar and henrypijames for their test solves and feedback.
Enjoy the puzzle, I will be happy to read your comments.
-fill in the grid with digits 1 to 4 with no repeats in any row or column,
-draw four - potentially partially or completely overlapping - orthogonally connected areas (of size 4) each containing digits 1 to 4 once each such that each cell is a part of some area,
-digits on an arrow sum to the digit in the corresponding circle where each digit (both on an arrow and in a circle) is considered multiplied by the number of areas it belongs to.
Example:
In the spirit of the puzzle I prepared a 2x2 example puzzle (with digits 1-3 and three areas) - the grid in the middle shows the digits of the solution with corner marks showing the number of areas containing the corresponding cell - the arrow works since 3x2=1x3+3x1, the grids on the right then show the areas. You can solve the example here (but it's not ... ehm ... very challenging).
Links to the main puzzle:
penpa+ link (extended version with four grids)
ctc app link
f-puzzles link
Solution code: Row 1, then row 2, then row 3 (just 9 digits, no commas or spaces). Then for each horizontal domino write the number of areas that contain both cells in that domino, first row 1, then row 2, then row 3 (6 digits, no commas or spaces). The final code is therefore 15 digits (for the example puzzle the code would be 233121).
Comments
on 12. May 2024, 23:52 by Styku
Very fun and unusual ruleset. Not that hard or I got lucky :)
on 27. December 2023, 22:55 by wisty
Awesome puzzle! Such a beautiful concept - really hard at first but not necessarily a very long solve either, just one that requires specific insights. I'm sure the 8x8 puzzle will be a whole different beast though xD
on 5. October 2023, 14:00 by wullemuus
Amazing how many combinations are possible with 4 digits ... . The real irritation was the fact that there was no ending in the CTC app visible and so I tried to find other solutions ... . but now I will try the 8x8 variant as well.
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Yeah, it's a very old link.
on 8. September 2023, 15:10 by xtfnfhvzzw
I can't understand what is the mean of domino
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by a domino I mean a pair of orthogonally adjacent cells
on 7. April 2023, 10:48 by Yann
Wow, 9 cells that, tangled in arrows, delivered an amazing solution path. I think this ruleset has a lot of potential, but I still don't know whether I will solve 8x8=9x9, maybe you could record a solution walkthrough to that puzzle, because I would love to see its solution. In every case, thank you for this puzzle filuta, it's a stunning example of how hard a small puzzle can be .
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Happy to hear you liked my puzzle, in fact it is my plan for this year to make solve videos for several of my puzzles including 8x8=9x9, so if you are interested, I will let you know when it's finished.
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Thank you very much !
on 15. August 2022, 22:01 by PrimeWeasel
Cool
on 27. July 2022, 03:38 by Samish
A surgical strike to my brain is the analogy that come to my mind. There were more steps in my solving path than cells in this grid. Astonishing puzzle, really glad I didn't give up !
on 22. July 2022, 20:43 by DiMono
Fascinating concept for a puzzle. Glad I got to solve it.
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Thanks, 8x8=9x9 is certainly my project over the summer.
on 14. July 2022, 16:50 by DiMono
Can a cell be part of 0 areas for an arrow value of 0?
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No, each cell is a part of some area.
on 10. June 2022, 21:36 by Elliptical
Good luck setting a 9x9. I'm looking forward to solving such a beast.
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Thank you. (and btw, if you're up for a real challenge, I just posted one yeaterday)
on 6. June 2022, 07:24 by Prutsbeest
It's amazing to see how difficult a 3x3 puzzle can be, yet very enjoyable! Setting a 9x9 puzzle will be quite a challenge though :-)
Thanks, filuta!
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Thanks a lot, Prutsbeest!
on 5. June 2022, 13:02 by filuta
added tag
on 5. June 2022, 11:57 by filuta
increased difficulty
on 5. June 2022, 02:15 by henrypijames
Man, I had such a hard time with this puzzle - difficulty >4 stars despite its size. Don't think I'll be torturing myself with a full-size version. :D
on 4. June 2022, 15:46 by kolot
Very clever puzzle and very beautiful logic. I was scared after reading the first two paragraphs, but it wasn’t really monstrously hard; but a 9x9 version of this might be really scary. :-)
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Thanks, yeah, it is scary to set also. I hope to find ebough courage (and time) at some point.
on 4. June 2022, 15:09 by Piatato
Never before or after have I spent so much time or felt so proud about solving such a tiny puzzle!
