Chaos Construction: Regional Skyscrapers
(Published on 14. April 2022, 11:51 by MagnusJosefsson)
In the grid you must place nine orthogonally connected irregular regions.
Every row, column, and region must contain the digits 1 to 9 once each.
Each digit in the grid is also a "skyscraper" whose height is the digit in that cell. Taller skyscrapers obscure the view of smaller ones.
Numbers outside the grid indicate the number of different regions that are visible looking along that row or column (i.e. how many different regions the visible skyscrapers along that row or column belong to).
An arrow in a cell indicates that the number of different regions visible from that point along the indicated direction is exactly equal to the digit in the cell.
All possible arrows are given.
Example:
The puzzle:
Link for solving online:
Penpa+ (Solution check requires green edges around regions as well as digits in the cells)
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Solution code: Row 5 followed by column 5.
Comments
on 24. March 2024, 08:57 by by81996672
It's really a great puzzle. There were several times when I had reached the final part, but for some reason, I ended up making mistakes. I also tried several times but couldn't find where the problem was. Perhaps due to habitual thinking, it wasn't until later that I realized something and verified my guess at the R4C2 in the example question. If I could take a closer look at the example question, I should know that all the arrows are given, only referring to the cells that already have arrows.
on 20. February 2024, 22:57 by zzw
That was wild! A real brain melter. Awesome puzzle, thanks!
on 20. February 2024, 22:55 by Myxo
Wow, incredible and very hard puzzle!
on 23. November 2023, 17:43 by Playmaker6174
It's such a monumental moment that I finally revisited this one as the 'second official' 2000th solve on this site, and what a wonderful puzzle this was!
So many cool and intricate deductions throughout (especially the use of the negative constraint) but hell there're also so many traps as well, including one that almost got me to a wrong route. Thanks for this great treat! ;)
on 25. August 2023, 09:09 by Christounet
Wow wow wow !! I have had this one on the workbench for quite a while now. The various implications of the negative constraint make it such a hard puzzle to scan ! It is so easy to forget about a possible configuration of skyscrapers. So satisfying and beautiful. Thanks a lot !!
on 16. November 2022, 17:14 by zwooz19
Holy moly, what a battle that was. A wrong assumption in the bottom row from minute 2 of the solve added many many hours of retrying the puzzle. Thank you for such a fantastic puzzle!
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Thanks a lot, I'm really glad you liked it! /Magnus
on 4. November 2022, 14:40 by peacherwu2
I think this is the hardest sukodu puzzle I ever solved. So tricky that I broke it numerous times and have to come back again and again.
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Thanks for solving and well done for sticking with it and persevering! /Magnus
on 29. July 2022, 06:44 by sugardude
The best puzzle i've ever seen in my life.
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Thanks you so much for solving and for the lovely feedback :) ! /Magnus
on 14. July 2022, 21:23 by Agent
This was a phenomenal puzzle. I'm glad
I decided to attempt it despite some scary comments, because the logic is absolutely wonderful. The puzzle is very challenging but fair all the way through. Hats off!
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Thank you very much Agent, I'm glad you enjoyed it! /Magnus
on 11. July 2022, 14:51 by udukos
The negative restriction was quite powerful. I wish I had observed that sooner. Thanks for another brilliant puzzle, Magnus!
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You're welcome, thanks for solving udukos! /Magnus
on 21. June 2022, 20:26 by PixelPlucker
Very satisfyingly intricate and a proper challenge! It made for an excellent evening project (took me 4+ hours as well). Thanks Magnus!
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Thank you PixelPlucker, I am very glad you liked it! /Magnus
on 9. June 2022, 23:25 by Niverio
Wonderful. Extremely difficult yet very rewarding!
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Thank you very much Niverio and well done! /Magnus
on 21. May 2022, 00:44 by harrison
Wow! That was so difficult, but rewarding when I finally finished! Major props on constructing this
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Thank you harrison and well done! /Magnus
on 8. May 2022, 20:04 by XYX
It seems like there are 2 solutions(here I mean the region is not unique), There is a pair of 7 which can goes to both region. Really excellent puzzle!
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Thank you XYX! Check the clues outside the grid, I think you will find that one of them disambiguates which 7 goes to which region :). /Magnus
on 21. April 2022, 21:07 by KNT
2 attempts over 3 days and finally came out the other end. This might be the single hardest puzzle I've ever done on this site. Amazing at every step.
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Thank you KNT, and well done for finishing the puzzle! /Magnus
on 20. April 2022, 14:34 by polar
What a brilliant (& challenging) puzzle - thank you :)
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Thank you very much polar, I am really glad you liked it! /Magnus
on 18. April 2022, 04:16 by TotallyNormalCat
Recently I've been wondering if it was still possible for a sudoku to be so difficult that it would take me 4h+. The answer is yes.
Great puzzle
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Thank you for solving and for your nice comment! Btw, I've added a video link in a hidden comment showing my intended solution path if you want to compare :) /Magnus
on 16. April 2022, 22:22 by henrypijames
Difficulty 6/5 stars - seriously, if this puzzle had taken me half as long as it has, I would've rated it 5 stars. Incredibly, incredibly hard region division, none of the early deduction constituted a breakthrough (AKA break-in). Mid- and lategane just as tough, broke it a few times, was on the verge of giving it up, but came through in the end - by the skin of my teeth.
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Thanks for solving and well done for finishing the puzzle! I knew it was difficult but didn't expect it to be quite *that* hard for a solver of your caliber :). Anyway, I've uploaded a video of the intented path in a hidden comment if you want to see if there was something we did differently. /Magnus
on 15. April 2022, 12:08 by Jesper
Great puzzle, requiring some interesting and unusual logic!
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Thank you Jesper! /Magnus
on 15. April 2022, 01:26 by marcmees
very nice CC with rewarding solve. thanks.
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Thank you Marc, glad you liked it! /Magnus
on 15. April 2022, 00:32 by Dandelo
But I don't agree about the example. Of course it's much easier, but it's also a nice puzzle. I'd suggest to publish such good examples as separate puzzles, since they're much more than explanation of the rules.
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Interesting. Yes, maybe I should have then. My own thinking was that the example was a little bit boring as there was quite little region geometry and its solution path relied so much on the arrow clues/negative restrictions. /Magnus
on 15. April 2022, 00:01 by Dandelo
Very nice and very hard.
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Thanks Dandelo! Yeah, this is probably one of my harder puzzles, undoubtedly a genuine 5 stars difficulty. /Magnus
on 14. April 2022, 20:54 by Vebby
Great puzzle! Consistently challenging, almost every deduction requires careful consideration. Very satisfying to complete it. Thanks Magnus! :)
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Thank you very much Vebby, and well done for solving it! /Magnus
on 14. April 2022, 13:44 by Dandelo
Wenn ein Gebiet in einer Zeile oder Spalte zwei Segmente hat, die beide gesehen werden, werden die ein- oder zweimal gezählt?
If an area has two segments in a row or column that are both seen, are they counted once or twice?
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It is only counted once. /Magnus
on 14. April 2022, 11:45 by MagnusJosefsson
I am very pleased with how this puzzle turned out, I hope you will want to give it a try. It is however quite challenging, with a lot of region geometry, combinations of clue types, and negative restrictions. Please don't hesitate to write a hidden comment if you get stuck or need a small hint.
While it does not have the beauty (and perhaps worse flow) than the main puzzle, the example puzzle can provide good practice to get familiar with the ruleset.
Good luck!
