Controversial FOW
(Published on 6. January 2026, 18:00 by galium_odoratum)
I was initially unsure whether to publish this puzzle, but ultimately decided it was worth sharing. While solving Fog of War puzzles, there was one recurring thought I kept coming back to, and this puzzle is built around that idea. To avoid potential frustration: if you find yourself stuck or suspect the puzzle is broken, please read the hint/explanation below. With this hint, the puzzle is probably a 2.5 difficulty, without it I cannot really estimate the difficulty.
Normal Sudoku rules apply.
Renban: Each pink Renban line contains a set of consecutive digits in any order, without repeats.
German Whisper: Adjacent digits on a green line must differ by at least 5. Digits cannot repeat on a green line.
Killer Cages: Digits in cages must sum to the number in the top-left corner and cannot repeat. Cages cannot overlap and always consist of orthogonally connected cells.
Grey Square: The grey square contains an even number.
Yellow cells: Some cells have a yellow background. This is purely cosmetic and has no rules attached to it.
Dynamic Fog: Placing a correct digit, might clear some fog somewhere. No guessing is required!
Play on SudokuPad
Hint/explanation:
The initial idea for this kind of reasoning came from thinking about the classic Sum and Product puzzle by Hans Freudenthal, when I read the typical “no guessing is required” statement in FOW puzzles. In this puzzle, conclusions are drawn not only from what is explicitly stated, but also from what would otherwise force ambiguity.
The rules cearly state that this puzzle is guaranteed to be solvable without guessing. That guarantee is itself part of the logic. If, at some point, several interpretations appear possible, but only one of them allows a logically forced continuation, then that interpretation can be deduced as correct.
In particular, some structures hidden by fog (such as cages) may allow multiple theoretical configurations. However, if only one configuration leads to an unambiguous placement while all others would require guessing or branching, then those other possibilities can be ruled out. Proceeding in this way is technically not guessing, but logical elimination based on the global solvability promise of the puzzle. In other words: if the puzzle needs to be constructed in a certain way (cage size/total or whisper length) to allow continuation without guessing at specific points during the solve, then it is constructed that way, since no guessing is required.
To avoid accidental guessing, each digit directly deduced by using this logic is highlighted yellow.
I fully understand that this is not what the “no guessing” rule is usually meant to be used for. However, it is a logical consequence/potential caveat of the rule as stated. I am also aware that this type of reasoning might seem unintuitive or unsatisfying, thus the name of the puzzle. I do not want to cause any fruststration and I am sorry if I did.
Solution code: Row 6
Comments
on 8. January 2026, 23:10 by annaeinachin
It took me a while to understand the logic. Quite surprising and refreshing to see how this logic turns up differently all through out the puzzle.
It was though but very fun for me. Thank you!
on 8. January 2026, 18:49 by CitrusGremlin
Puzzle is not for me but I'm glad it exists.
on 8. January 2026, 13:40 by galium_odoratum
Thank you for all your feedback, I appriciate it a lot! I agree that the whisper deduction is the weakest and depending too heavily on the interpretation of the rule. Thus I've made some really small changes:
-Added one whisper cell
-Added one whisper rule (no repeats on a green line)
on 8. January 2026, 03:36 by sanabas
Guessing is required for one deduction. Rest of it makes sense by its own rules, and it is an interesting idea. If guessing wasn't required, then removing all the fog should leave constraints that force a unique solution, but that's not the case. Pinged you on disc in the puzzle discussion channel.
on 7. January 2026, 19:55 by jwsinclair
Enjoyed this :). I also like that you made it absolutely clear to solvers that this puzzle is unconventional in its approach to logic. (To anyone who's complaining: what did you expect?)
There's also some really good logic here, even (if not especially) in the more conventional steps.
on 7. January 2026, 05:02 by illegel
Surprisingly smooth solving process, even though I was unsure a few times if my assumptions about the fog were correct. However the thought of the uniqueness is fresh and interesting. I do think people will more find the merit of this puzzle if it is posted on April 1st lol.
on 7. January 2026, 01:14 by dzamie
I came back and re-did it properly. It's a pretty good puzzle, and I do think it would be cool to see more of this variant, once one thing gets a bit more ironed-out that I'll elaborate on in a hidden comment.
on 6. January 2026, 21:32 by Myfyr MJ
Sorry I did not enjoy that at all. It was pretty much 100% bifurcation unfortunately.
-that is fine, thank you for your honest feedback and for giving it a try anyway. there is a logical solving path without bifurcation, if you are interested, dm me on discord. galium
DM sent!
on 6. January 2026, 18:57 by Myfyr MJ
Sorry I did not enjoy that at all. It was pretty much 100% bifurcation unfortunately.
on 6. January 2026, 18:35 by VitP
i am sorry, but your logic is invalid.
you are using definitions of logic that are NOT universally accepted, and definitely not in use in the vast number of puzzles on this site.
nothing wrong with using your own version of definitions and logic. but then you need to EXPLICITLY state those things as PART of the rules, not a "hint if you need it".
furthermore, there are TYPES of logic that are generally not considered acceptable here, such as applying uniqueness to solve a puzzle, and that is what you are doing, at LEAST.
notwithstanding the above, but it IS correlated, using "cage clue is in top left" is NOT a sufficient rule, because it IS ambiguous for some cage geometries. one CORRECT version is "cage clue is in LEFTMOST cell of TOP row". that's the way language works.
-I agree that the interpretation used here is unusual and not part of the standard Fog of War toolkit. However, unusual does not mean invalid. This platform is open to a wide range of puzzle styles, and constructors cannot always be expected to follow all established customs, especially when deliberately experimenting with the form.
The reasoning used does not rely on uniqueness or selective assumptions, but on a global guarantee stated in the rules and which is applied consistently throughout the solve. Regarding rule wording, I accept that some formulations (such as cage clue placement) could be made more explicit to avoid edge-case ambiguity. That said, even under alternative cage geometries, the logical structure of the solution path remains unchanged. Thank you for giving it a try anyway :) galium
