## Multi-Way Skyscraper Sudoku

(Eingestellt am 18. September 2020, 16:00 Uhr von SudokuExplorer)

Inspiration for this puzzle comes from Qiu Yanzhe's stunning Extra Regions Skyscraper Sudoku and Lizzy01's lovely Rook Sudoku. I had plenty of fun creating this, I hope you also enjoy the logic! If you have a better name recommendation, do tell me.

Normal sudoku rules apply (each row, column and region contains the numbers 1 to 8).
Each digit represents a skyscraper of the given height. Higher skyscrapers block the view of lower skyscrapers.

The grey cells outside the grid are normal skyscraper clues (the number of visible skyscrapers in that row/column from that direction), and they form an extra region (that is, all outer clue values are different).

The green cells inside the grid are multi-way skyscraper clues. They tell you the total number of skyscrapers visible horizontally and vertically from that cell (in all directions). Not all green/inner clues are given. (See below example of a green multiway skyscraper clue)

In addition, the two cells next to the white dot are consecutive integers.

Example of a green multiway skyscraper clue (only the blue skyscrapers are visible from the green cell) with some normal skyscraper clues (on the outside):
You can try the below puzzle on Penpa+ or F-Puzzles. If anything is unclear, do write a comment below.

Lösungscode: Enter the 4th and 8th rows (left to right). (16 digits in total)

Zuletzt geändert am 9. November 2020, 23:30 Uhr

Gelöst von Voyager, cdwg2000, marcmees, Jesper, NikolaZ, StefanSch, Lizzy01, zorant, Skyler, Storm, CaneloC, Bobby, TimE, misko, polar, LucyH, Statistica, Mark Sweep
Komplette Liste

### Kommentare

am 29. März 2021, 20:42 Uhr von SudokuExplorer
@Mark Sweep: Thanks! I'm really pleased you enjoyed solving it :-)

Those who want to teleport and observe the landscape, may also want to try Mark's wonderful Panorama sudoku (id=0005RT).

am 29. März 2021, 15:41 Uhr von Mark Sweep
Great puzzle! Interestingly, I found the intial break-in relatively easy, but had more struggles mid-solve.

am 9. November 2020, 23:30 Uhr von SudokuExplorer

am 4. November 2020, 15:27 Uhr von SudokuExplorer
@Storm Thanks for trying it! I'm pleased you gave Lizzy01's puzzle a go. It needed more attention which the flood of puzzles didn't allow in the first place.

am 3. November 2020, 23:30 Uhr von Storm
Wonderful logic! Really enjoyed the concept.
Also thanks for the link to Lizzy01's puzzle :-)

Zuletzt geändert am 3. November 2020, 17:58 Uhr

am 3. November 2020, 17:42 Uhr von Skyler
Beautiful logic throughout the solve, from start to finish!
Thanks for the very enjoyable skyscraper :-D

---
Thanks for giving it a go and for your feedback. :-)
I'm glad it was an entertaining solve.

am 18. Oktober 2020, 13:10 Uhr von SudokuExplorer
@Lizzy01 Thanks for the kind feedback. I'm glad you enjoyed it after the tricky opening. :-)

am 17. Oktober 2020, 19:47 Uhr von Lizzy01
Very nice! Of course I just had to try this puzzle, after that introduction. It turned out a bit harder than I expected, given the hint of it being inspired by my puzzle, but once I found the break-in I could see the similarities, and a few more through the solve.

am 16. Oktober 2020, 19:23 Uhr von SudokuExplorer

am 16. Oktober 2020, 17:39 Uhr von SudokuExplorer
Yesterday I found a 6x6 puzzle by CHalb in 2011 on the portal that uses the same multi-way skyscraper clues. If you want to try that one, it has id=00015K

Zuletzt geändert am 20. September 2020, 16:51 Uhr

am 20. September 2020, 16:44 Uhr von SudokuExplorer
Anyone who does try this puzzle, do also give Lizzy01's very unique Rook sudoku (id=0003XE) a try. It only needs a few more solves and ratings to get its well-deserved rating.

Zuletzt geändert am 19. September 2020, 19:09 Uhr

am 19. September 2020, 13:30 Uhr von SudokuExplorer
@Voyager Thanks for testing and retesting the sudoku. :-) I'm glad it was an interesting challenge. The puzzle difficulty is either 3 or 4 stars depending on whether you spot the break-in and middle logic, so thanks for reassuring me. Being optimistic, I'm hoping most successful solvers will eventually spot the logic.

@cdwg2000 I'm sorry that you did not spot the logical route. I will some time in the future (maybe in a week after people have given it a go) add a hidden comment of my intended solution path. Thinking about the minimum/maximum number of visible skyscrapers in rows/columns is important along with some geometry.

@marcmees I'm glad you enjoyed the skyscraper sudoku. :-)
First understanding the property of the normal grey skyscraper clues (which are all different) is the key to starting and solving this puzzle.

Zuletzt geändert am 19. September 2020, 11:44 Uhr

am 19. September 2020, 11:43 Uhr von marcmees
needed a lot of thought on the outside skyscraper hints before hitting the right buttons - pure logic-
wonderful puzzle. thanks

am 19. September 2020, 11:15 Uhr von cdwg2000
It turned out that I missed the logical path, and I finally made it through repeated attempts. It's really a big problem!

Zuletzt geändert am 19. September 2020, 10:24 Uhr

am 19. September 2020, 10:17 Uhr von Voyager
I checked my solution threefold - imho this puzzle has exactly one solution and a logical solving path (i.e. I needed no T+E). But it is "close-knit" - a VERY carefully counting of the possibilities of seen scyscrapers was necessary for me while solving - but that's OK. After all an interesting puzzle. The designated difficulty of 3 stars is imho also OK.

am 18. September 2020, 23:24 Uhr von SudokuExplorer
Added new puzzle type tag, since I haven't yet found this type of skyscraper variant. If you are aware of a similar type, I would love to try it.

am 18. September 2020, 19:25 Uhr von SudokuExplorer
Renamed puzzle

am 18. September 2020, 18:49 Uhr von SudokuExplorer
I hope the above example makes it clear what the green multi-way skyscraper clues are. Remember that the normal grey skyscraper clues have to be different.

am 18. September 2020, 18:43 Uhr von SudokuExplorer
Added example of a multiway skyscraper clue

 Schwierigkeit: Bewertung: 96 % Gelöst: 18 mal Beobachtet: 1 mal ID: 0004C7

Lösungscode: