Waterfall Sudoku
(Published on 1. May 2021, 08:29 by XDuncan)
Sudoku rules apply.
The numbers above the puzzle represent the value of streams. Streams fall straight down until they encounter a number less than the stream. When ever a stream encounters a number less than the value of the stream, the value of the cell is subtracted for the stream. If the value of the cell is equal to the stream, the stream is terminated. The remaining value of the stream is divided in half and continues to both bottom corners of the cell. If a cell is against the very edge of a puzzle, all of the remaining stream is directed to the inside corner of the cell. If a stream encounters a cell that would split it to have uneven streams that number is not allowed. When two streams intersect their values add. All streams must be terminated before they reach the bottom.
Anti-knight: numbers cannot appear in the same 3x3 area.
example:
puzzle:
https://f-puzzles.com/?id=ye63k5k8
Solution code: column 5 followed by row 4.
Comments
on 26. June 2024, 21:12 by StefanSch
@FischmitFahrrad: In welcher Spalte ist denn der Fehler, so dass das Wasser nicht gestoppt wird?
Ich habe eine "Lösung", in der die erste Spalte nicht aufgeht, aber das ist offenbar nicht die gesuchte Lösung.
Mit der Anti-King-Regel (aus dem Link) gibt es auch vollständige Lösungen ohne Fehler:
123456789
748219563
695387142
814695237
279138654
536724918
482961375
367542891
951873426
on 18. January 2024, 02:15 by FischmitFahrrad
Really like the rule set, so I did put quite some time into this solve. The puzzle has some really nice logic in the beginning (but definitely not 3*, because of the complexitiy of the rules I'd even say 5*).
Unfortunately the puzzle is broken with one stream leaving the grid at the bottom.
on 7. December 2023, 22:10 by hepcecob
GET ON MY LEVEL N00BZ!!! 2.5 years unsolved.
The real rule is anti-king (not anti knight). The example ignores this. The rules also don't really make it clear that the waterfalls, when join, they add up. Ontop of this there is another mistake in the example, where the 2 and 4 combine in to the 6 (top right corner), and go ontop of the 4, it should've moved moved left with the 2.
on 8. November 2023, 15:53 by NGeorgescu
I tried a brute-force solution using python, and (if I understand the rules correctly) did not get a working solution. It's basically a standard sudoku solver but you just add an additional check that it satisfies the waterfall condition, so if you're using a backtracking algorithm then the possible boards at each step has this additional filter.
on 10. February 2023, 12:35 by AstralSky
Basing on my understanding, I have reached the first 4 rows like this:
123456789
?8?219??3
4953??162
???6?5?3?
and all waterfalls fulfilled but puzzle still get a lot solutions.
So, either puzzle is broken or the rules need to be further specified.
on 10. February 2023, 11:30 by AstralSky
The ruleset means, If stream value > cell value, subtract cell value from it and their difference must be even in order to split streams into two equal parts.(Unless on col 1&9 because they don't require a even distribution of stream). Split that number in half and those halves go to their adjacent columns and streams converge if met.(Unless in column 1&9). If stream value = cell value stream is absorbed and terminates. If stream value ＜ cell value stream just skip the cell and go to next until finally meeting the ＞ or
= circumstances.
if that's so how's this 3 stars though.
There seem to be a million cases how the streams would be splitting to keep going. I can't find a way to handle those cases.. I liked the idea though it seems to be overcomplex.
Some hints and clarification on anti knight part(whether it exist) appreciated.
on 31. August 2021, 23:57 by uvo_mod
Label "Online Solving Tool" ergänzt.
on 1. May 2021, 23:09 by DanMeehan
I'm unclear as to how to derive the value of the stream. Maybe if you go through the calculations for them using some columns in the example?
Thanks!
on 1. May 2021, 12:08 by SKORP17
Ich verstehe weder die Regeln noch das Beispiel
on 1. May 2021, 09:37 by XDuncan
added example
on 1. May 2021, 08:39 by XDuncan
clarified rules
on 1. May 2021, 08:29 by XDuncan
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