A river is a snake path of orthogonally connected cells starting next to a cage; the digit in that cage sets the length of the river. The number in the top-left corner of a cage sets the sum of the digits along the river. Rivers must decline in digit value from one direction to the other, starting from the cage. Rivers must not include cages. Rivers may touch themselves orthogonally, and rivers may overlap.
Summary: Rivers act as 'reverse thermometer arrows', with the controlling cage setting the length and total. Including the controlling cage, cages must not be in any river.
Rules Example
I hope you enjoy the puzzle and I am eager to hear how you go!
Solution code: Row 2, Row 4
on 22. November 2021, 17:28 by jez9999
Took me 2 days and lots of re-visits to solve this. Required very heavy levels of bifurcation on several occasions. Perhaps too much to be a very satisfying puzzle.
on 16. October 2021, 14:38 by salty-horse
Fun puzzle. I ended up not tracing four of the rivers, so I wonder if I missed an easier solution.