Broken Tap
(Published on 9. September 2021, 03:00 by Xailran)
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. No negative river constraints.
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. There is no negative constraint.
In this specific puzzle, rivers must have at least one solution but may have more. Blame the Broken Tap!
Rules Example
I hope you enjoy the puzzle and I am eager to hear how you go!
Solution code: Column 5, row 9. No characters other than numbers
Comments
on 17. April 2022, 07:28 by Xailran
Added possibility of multiple rivers to the description.
on 8. February 2022, 08:11 by Droi
I love this puzzle type but I'm not sure how you can be happy with two possible solutions for the rivers, I almost ignored the solution specifically because I thought it must be deterministic.
Response from Xailran: Sorry, haven't been active on LMD lately! Good idea, I've now added a line to the description along these lines.
At the very least it should be mentioned in the rules that rivers might have multiple possible paths.
on 22. November 2021, 19:37 by jez9999
Not too tricky to get through, but required some work all the way along. Flowed nicely! Highly enjoyable.
on 20. October 2021, 02:39 by Jax-El
So am I doing something wrong with the solution code? After I put in the single digit answer I thought was correct, it gave me an error. Then I tried every number from 1-9 and none worked. I am on mobile.
Response from Xailran: Hi Jax-El. I just checked the solution code, and it should be fine. Make sure you enter both the correct column and the correct row. Should be 18 digits all together
Response from Jax-El: Ohhhh. Maybe I was unfamiliar with Solution Codes in LogicMasters. I entered and it worked. Thank you!
on 10. September 2021, 16:16 by SudokuExplorer
A fun puzzle with potential, thanks :-)
on 10. September 2021, 10:32 by marcmees
Nice but due to the minimalistic construction most clues had a well defined sum path. How would this sort of puzzle relate with more but harder to find sum clues?
Response from Xailran: Thanks Marcmees! I have a few ideas still bouncing around for further River Sudoku puzzles, and you've just added one to the list. The main challenge is that since cages can't be included in rivers, even if the rivers are very ambiguous, more cages restrict the rivers on their own. Downstream comes close to almost being brute-forced for some rivers, and I want to avoid forcing deep explorations of the rivers; makes the difficulty feel artificial to me.
on 10. September 2021, 06:01 by 10feet
The logic on this was quite amazing. I thought I was going through it pretty well, but ran into a trap of my own making. It took me all day trying to figure out where I went wrong with the 19 cage only to discover finally my mistake was on the 10 cage.
on 9. September 2021, 18:31 by rmahus
I understand how the name of the puzzle relates to its content. But the first time I read Broken Trap which also makes sense because you start out pretty trapped but then you manage to escape so the trap is broken.
It was quite complex but all the deductions felt logical.
Excellent puzzle.
on 9. September 2021, 04:18 by bob
What a coincidence...this puzzle popped up and I had just finished your first river puzzle a few days ago so the ruleset was fresh in my mind. I don't think I've ever been the first solver before. Thanks for fun puzzle, looking forward to more
