Mountain killer sudoku
(Published on 3. February 2023, 07:24 by Nylimb)
Normal sudoku rules apply: Fill the grid with digits from 1 to 9, so that every row, column, and 3x3 box contains each of the 9 digits exactly once.
In addition, there is a mountain hidden in the grid. Its peak is at the 9 in the central box. The mountain consists of all cells which can be reached from the peak by repeatedly moving from a cell to an orthogonally adjacent cell containing a smaller digit. (See example below.)
Each cage, indicated by the dotted lines, shows the sum of the mountain cells in the cage. Digits cannot repeat in a cage, whether they're in the mountain or not.
The cells separated by the black dot are in a 1 to 2 ratio.
You can solve this in Penpa or in the CTC-app.
Note: Without the kropki dot, this puzzle would have multiple solutions; adding the dot was the best way that I found to make the solution unique. At the time, I didn't know if a puzzle like this could be made with just the killer cage constraints. I now know that it can, but I haven't been able to create a 'nice' puzzle like that.
If you want to solve an easier puzzle of this type first, try Introduction to mountain sudoku. And if you like this puzzle, you might also like my other mountain sudokus.
Solution code: Row 1 and row 9.
Comments
on 19. March 2023, 02:01 by SimplePurpleFrog
Great logical flow, thank you.
on 8. March 2023, 04:32 by mnasti2
I stared at this for a while when it first came out without the foggiest idea how to start. But after solving your “Mountain view sudoku” I had the insight and confidence to come back. Fun puzzle and constraint, thanks!
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@mnasti2: I'm glad you liked it. In hindsight, I should have published an easier one first.
on 24. February 2023, 08:10 by NIGHTCRAULER
Great puzzle, came here from the intro mountain puzzle and enjoyed this one even more. Challenging but intuitive and rewarding. Was almost entirely solved before getting stuck longer than I'd like to admit because I forgot digits cannot repeat in cages lmao. Thanks for setting :)
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@NIGHTCRAULER (28/2/2023): Thanks. Yes, the "no repeats in cages" rule is needed for this, and even with that the kropki dot (or something else) is needed. As I mentioned, it is possible to make a mountain killer puzzle with just cages, although not necessarily a nice one. One thing I still don't know is whether or not knowing the complete structure of the mountain can give a unique solution.
P.S. (6/3/2023): Now I know; even just knowing the shape of the mountain can be enough. See puzzle # 000D6O.
on 20. February 2023, 01:10 by Nylimb
Added link to introductory puzzle.
on 16. February 2023, 05:54 by wisty
This puzzle is so much fun! The break-in is a perfect blend of understanding the constraint and elegant box logic. Boxes 2 and 8 were where I looked next, and the logic there was fascinating! Really nice job constructing this so it is smooth and also everything resolves.
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@wisty: I'm glad you enjoyed it. I designed some of the logic, but some just sort of happened, and I had fun discovering it while solving several versions of the puzzle before choosing this one.
on 13. February 2023, 08:24 by Allagem
What a creative and intriguing concept! This puzzle sounded interesting right the very first time I read it back when it was first posted, but I had to give up twice because I couldn't figure out how to start. Your recent mountain puzzle made me come back and try one more time... I finally had the epiphany I needed on how to start restricting some things and get my first foothold in this mountain :^) Once you start, the rest of the solve was smooth as butter and very fun to discover. Love this concept! I think you could easily turn it into a series if you wanted to (You could use real mountain names! :D)
The very first move on this puzzle is by far the hardest and I think a number of people (including myself the first 2 times) probably skipped over this puzzle after not finding anything in the first few minutes. To generate interest in the concept, might I suggest an introductory mountain puzzle where the peak of the mountain is given? If the first move or two is clearer, people are more likely to get hooked on the idea ;)
@Allagem (13/2/2023): Thanks for the suggestion. I'll see if I can come up with a nice introductory puzzle.
@Allagem(19/2/2023): I've published "Introduction to mountain sudoku" https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=000D0H. The solver still has to figure out where the peak is, but it's easier than in my earlier puzzles.
on 12. February 2023, 23:02 by Nylimb
Added link to Mountain sandwich sudoku.
on 3. February 2023, 18:01 by Nylimb
Minor edit.
on 3. February 2023, 16:34 by Nylimb
Changed example.
on 3. February 2023, 16:25 by MonsieurTRISTE
If you play Minecraft, then the mountain rule could be explained easily: Pour a bucket of water on the peak, and the water will spread onto exactly all mountain cells.
on 3. February 2023, 09:34 by Shotguntemplar
I don't understand this ruleset
@Shotguntemplar: I've changed the example to show a path from the peak to another cell, and added some black dots. Does that help?
