Find the River
(Published on 28. November 2025, 15:56 by Schorsch)
Normal Sudoku rules apply.
Each box in the grid has a height value equal to 10 times its center digit. Each cell in the grid has a height value equal to its digit + its boxes’ height.
A hidden river flows throughout the grid. The river consists of a single stream starting at the cell with the biggest height value and ending at the cell with the lowest height value. The river visits every box.
After visiting a cell, the river continues downhill to the orthogonal or diagonal neighbour with the lowest height value. If none of the neighbouring cells have a lower height value than the current cell, the river instead ends in a sink.
Have Fun!
Play on Sudokupad
Solution code: Digits from column 1, top to bottom
Comments
on 4. December 2025, 03:32 by EFlatMinor
Beautiful puzzle!
Looked impenetrable at first. Solving your other (lovely) river puzzles was a big help in getting started
on 29. November 2025, 08:26 by Justalilguy
Beautiful puzzle! Very carefully placed clues that make for an amazingly satisfying solve. Well done.
> Thanks! Glad you enjoyed the solve.
on 28. November 2025, 21:01 by kasperd
There are some aspects of the rules I find unclear.
It says the river starts at the biggest value and ends at the smallest value. Does that refer to the biggest and smallest value on the river or the biggest and smallest value in the entire grid?
Moreover the rules don't specify if values will be unique throughout the grid. And if values are not guaranteed to be unique, how will the river move when duplicated values are encountered?
> Hi! The river starts and ends on the most extreme height values in the entire grid. Height values do not necessarily have to be unique. The edge case where a river cell has two lowest neighbour could allow the river to split, but that is not possible in this puzzle.
on 28. November 2025, 16:03 by Schorsch
Clarified german rules
on 28. November 2025, 15:59 by Schorsch
This a hard puzzle. If you're new to the river rule set, feel free to check out my previous river puzzles for a (slightly) more approachable introduction to the constraint.
Previous puzzle in the series: https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=000IWR
