9x9 Chaos Constructions: X-Sums and Arrows
(Published on 19. June 2021, 19:51 by abed hawila)
This puzzle is inspired by two recent excellent puzzles created by SudokuExplorer, which gave me some new ideas to make the puzzle more enjoyable, and hope you enjoy it.
For some extra puzzles do check out SudokuExplorer’s puzzle: 6x6 Chaos Constructions: X-Sums and 7x7 Chaos Constructions: X-Sums.
Rules:
1. Divide the grid into nine regions, each containing nine cells. These regions must be orthogonally connected. In addition, no 2x2 area belongs to the same region.
2. Each row, column, and region contains the digits 1 to 9.
3. A clue outside the grid indicates that the first X cells in the row/column from that direction are in the same region, where X is the digit in the first cell from that direction. Moreover, the next cell (the (X+1)th cell) is part of a different region.
4. A numerical clue is the sum of the digits in those X cells. If the sum is not given, it is indicated by a question mark (?). Not all outside clues are necessarily given.
5. Arrow rules apply. Digits along an arrow sum to the digit in its circle or capsule. A capsule designates a two-digit number.
6. Outside Arrow clues also act as X-sum clues.
7. Digits along an arrow belong to the same region, while arrow circle belongs to another one.
As always, your feedback and comments are appreciated and highly valuable.
Below is a 5x5 example puzzle. You can try it on Penpa+ .
Links to play the main puzzle: f-puzzle link or Penpa+ link
Solution code: Enter the 5th row of and the 5th column of the puzzle. For each boundary edge within the row/column, enter the capital letter I. For example, the third row in the 5x5 example is 24I3I5I1 whilst the third column is 5I4I31I2.
Comments
on 10. July 2024, 23:11 by StephenR
Lovely stuff, thanks. Smooth start and then it got a little stickier in parts.
on 19. May 2022, 22:03 by Piatato
Very nice and enjoyable!
on 22. March 2022, 17:10 by Mody
Schöner Einstieg und dann ging es ebenso schön und logisch weiter.
Nice entrance and then it continued just as nicely and logically
on 2. February 2022, 23:21 by abed hawila
updated puzzle tags
on 22. June 2021, 20:30 by VykkDraygo
Finally got it done. My issue was just messing up pencil marks. Repeatedly. At least once, I had the regions correctly (and logically) deduced, but an earlier error in pencil marks lead to a contradiction. It was worth the effort though. Lovely puzzle! I especially enjoyed the break in.
*** Glad you loved it, yeah in this puzzle type a wrong pencil mark costs a lot, unfortunately. But I am happy you managed to finish it at the end.
on 22. June 2021, 14:07 by Statistica
Klasse!
*** Thank you :)
on 21. June 2021, 11:32 by abed hawila
Changed Penpa link to fix the automatic Answer check.
on 21. June 2021, 08:56 by PixelPlucker
Great puzzle! I really enjoy construction puzzles and there was some very clever, subtle logic in this one that made it well worth learning the rules. :)
***Thank you PixelPlucker, glad to hear this :)
on 20. June 2021, 23:52 by Vebby
Superb puzzle, so much fun! Thanks Abed!
*** Thanks Vebby, glad you had fun ;)
on 20. June 2021, 16:19 by Playmaker6174
What an absolute treat! There're lots of brilliant logics and funny moments throughout the solve :)
Apparently haven't got new idea for my puzzle collection but this puzzle surely put a smile on my face ;)
***Thank you Playmaker6174, don't be upset, solving more puzzle would definitely give you some interesting ideas to create new ones, will be waiting your next one ;)
on 20. June 2021, 15:40 by Jesper
Thanks for another fun chaos construction! And I learned again that I should read the rules properly before starting - at least those that are written in bold :-). I will post a 9x9 puzzle based on your 'classic' rules (without arrows, etc.) in the next few days. So if you feel like it, have a go at that.
*** Thank you Jesper, glad you had fun. Waiting for your puzzle for sure ;)
on 20. June 2021, 10:25 by henrypijames
Penpa check didn't work for me (neither automatic or manual) even though my solution was correct.
Edit: It only works when the outside arrow clues are left blank.
Reply: Thank you for solving the puzzle, actually, this is the first puzzle that I create using penpa, I hope this wasn't a big concern and try to modify it.
on 20. June 2021, 08:10 by henrypijames
Ouch! I broke the puzzle repeatedly until I realized that I'd misread "Not all outside clues are necessarily given" as the opposite...
on 20. June 2021, 04:35 by cdwg2000
Very nice,I stupidly misunderstood the rules. Until I figured out the rules, I started to solve them smoothly (every step is in accordance with the rules and logic). I have to say that the introduction of the "22" restriction is very good. This is a regional division. Very good idea, thanks abed hawila！
***Thank you cdwg2000. Glad you made your way through it after a slight misunderstanding at the start of the solve. I was worried about the number of rules, but seems working so far ;)
on 20. June 2021, 02:23 by Storm
There are quite a few rules to get one's head around, but it was well worth doing. Amazing logic!
***Thank you Storm. Glad to hear this ;)
on 20. June 2021, 01:41 by SudokuExplorer
@cdwg2000: How did you deduce the value in R2C1?
Btw R2C1 tells how many of the first few cells in row 2 that are part of the same region.
The logic regarding R3C1 is fine.
on 20. June 2021, 01:11 by SudokuExplorer
Wonderful puzzle with a lot of fun logic! The no 2x2 rule was very handy throughout the solve. I would say that it started fairly easy, then got trickier to finalise the regions again with some interesting and fun logic. Thanks Abed for revisiting this idea, it was very entertaining! :-)
*** Thank you so much SudokuExplorer, I was waiting for your valuable feedback, especially after getting used to this type. Also, I am very grateful to you because you encouraged me to re-consider creating a 9x9 grid after creating your puzzles. I am glad you had fun solving it ;)
on 20. June 2021, 01:08 by VykkDraygo
I had actually thought of combining outside arrows with the chaos construction idea as well, but don't have the skill to construct it. Obviously, I like the idea of outside arrow clues. I think there is some interesting potential with them, especially when combined with other outside clues. I'm going to give this go, but it might take a while. Looks tough!
**You can do it for both solving this one and setting a one that satisfies you. Looks tough but it is not once you wrap your head around the rules. if you get stuck at some point, just post a hidden comment and I'll be happy to help ;)
on 19. June 2021, 21:22 by abed hawila
changed the example.
on 19. June 2021, 20:35 by dandbdi
In the example, the top right outside arrow sum "9" isn't an X-sum clue (which should be 6). Is it a mistake, or does rule 6 only mean that outside arrow clues act as a "?" clue?
**Thank you for pointing it out, yeah there is an error in the example, I will change it.
