We Are All Arrows (6x6)
(Published on 30. August 2022, 12:31 by randomra)
Place the digits 1-6 into each cell in the grid so that each digit appears exactly once in each row, column and outlined region.
Digits on the given arrow must sum to the number in the attached circle.
EVERY cell should be a possible circled head of an arrow sum. (An arrow connects a sequence of distinct orthogonally or diagonally connected cells. Possible arrow examples for 3 cells: example F-puzzles link)
F-puzzles link
CTC link
Solution code: Row 1 (left to right) and column 5 (top to bottom), 12 digits long
Comments
on 26. September 2022, 12:09 by Rollo
Eine ganz tolle Idee!
on 22. September 2022, 16:49 by Samish
Excellent ! Great fun to solve, the use of the law of leftovers was very sweet. Idk if an 8x8 version could possibly be as good but it would surely make a great feature in ctc if it was.
@Samish -Thank you! 8x8 is in the works but not as pretty yet as this one. :) You probably need some kind of constraint like max 2-long arrows or anti-kropki.
on 17. September 2022, 01:16 by Niverio
It is ridiculous that this thing exists. One of the best 10 minute thoughts I have spent on any puzzle.
on 16. September 2022, 22:53 by randomra
Thank you for the lovely feedback!
on 16. September 2022, 13:56 by mathpesto
Wow! Upon reading the ruleset, I found it hard to believe this would be a 2-star difficulty, and was expecting something rather tedious. But now I can say this was a joy and such a clear, smooth solve path. Very much deserving of the 100% rating that is seldom given to puzzles of this difficulty. An absolutely brilliant construction. :)
@mathpesto - Thank you very much for the kind words! I'm glad the ruleset didn't stop you from trying the puzzle! :)
on 16. September 2022, 06:38 by thoughtbyte
Amazing discovery and setting here, this was immensely fun to work through, thanks @randomra!
on 14. September 2022, 16:32 by Phistomefel
Fun idea! Thank you, randomra! I am curious: Have you tried setting a Sudoku with this constraint on a regular 9x9 grid?
@Phistomefel - Thank you! Regular 9x9 would fail quickly. If you let 1 cell to not be an arrow, the start becomes interesting. https://i.imgur.com/JCLrKac.png
But there will be a lot of solutions as higher numbers will have almost full freedom as smaller ones will be highly connected to create the arrow lines. It might still worth to make this to feature the break-in.
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Reply: Thank you, I see. Some ideas work better (or at all) on smaller and/or irregular grids.
on 14. September 2022, 15:44 by Piatato
Alright, I had understood the rules after all. :-)
on 14. September 2022, 15:23 by Piatato
I think I must be misunderstanding the rules. How can the example be valid? Surely the 1s on the 6 arrow cannot be arrow circles?
on 14. September 2022, 00:07 by Agent
Great idea and very cool discovery!
on 13. September 2022, 22:11 by DiMono
Very interesting and fun logic. Congrats on your 100%!
on 1. September 2022, 04:07 by Aaronomys
Very fun and unique!
on 31. August 2022, 18:01 by Yawnus
Fantastic construction!
on 30. August 2022, 16:59 by Yoshi Baroshi
Very cool one! Loved the logic and the symmetry!
