Thermal Signatures
(Eingestellt am 12. Mai 2025, 01:13 Uhr von Kafkapharnaum)
Big thanks to chrisj50 for testing, as well as to henrypijames for helping clarify the issue of Thermo uniqueness (see rules).
RULES
Irregular 9x9 Sudoku rules apply: Place the digits 1 to 9 once in each row, column, and irregular region.
CHAOS CONSTRUCTION
Divide the grid into nine regions of nine orthogonally connected cells each. Each region must have a unique Region Number, defined as the digit in its top-leftmost cell (top before left). The Region Numbers must be the digits 1 to 9 with no repeats.
THERMO ARROWS
The grid contains hidden, non-crossing, non-overlapping thermometers. A cell with one or two arrows points toward the bulb, tip, or both ends of the same hidden thermo, located n cells away in the given direction(s), where n is the digit in the arrow’s cell. Different cells may point to the same thermo.
– A bulb’s cell digit is also the Region Number of that region, and each thermo is fully contained within its region.
– Digits along thermometers continuously increase from bulb to tip.
– Thermometers may be of any length from 1 to 9 cells, are not restricted in content other than the bulb, and can move diagonally.
– Thermo uniqueness: in the finished grid, for each thermo, assume the most direct route between bulb and tip (eg. if a 1 can connect to an adjacent 9 tip, assume a two cell thermo, even if it could pick up any other adjacent digit to make it a longer thermo).
Play the puzzle on Sudokupad
Play the puzzle on Penpa (With green inner edges required for the solution check)
Lösungscode: Column 2, from top to bottom with a dash (-) to indicate region borders (grid edges don't need to be entered)
Kommentare
am 19. Januar 2026, 17:49 Uhr von skuntsel
This is a ridiculously clever puzzle. It is Insane that it resolves at all. Very elegant and intricate solve path, off to a simple start, but getting seriously hard in the mid-solve. One of the best resolution of top-right corner and lower-left afterwards that felt just astonishing. Also, you must have profound and in-depth experience with irregular sudoku to try out this puzzle. All in all, this is definitely among the plethora of the best puzzles I’ve ever solved. Stunning construction, Kafkapharnaum! Take a bow!
Also, as a side note I’ve taught myself not to presume anything not explicitly specified by the rules, so probably went on a more difficult solve path after all. As well, there is no need for an arrow in r9c9 (that I missed because of an overlapping x on top of it) and the puzzle perfectly resolves without it, although with more difficulty.
As well, after having contemplated the puzzle for some time it feels that there must be another rule added, that not all bulbs and tips are necessarily referenced by the arrows, which allows for a more intriguing solve path that still resolves, leaving ambiguity in row 1 and column 1 straight until the very end, that’s how I solved it. Were I to assume that every bulb and tip is referenced, I would’ve solved the puzzle much faster and I would’ve skipped the very beautiful irregular sudoku part. Many things revolve themselves basing on uniqueness, which I didn’t use as this was not explicitly stated. It feels like I didn’t give out any information to warrant hiding this comment, but think it was necessary to expose that.
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Thank you so much for the (very) kind words and for the detailed feedback! Lots of good points you are making, and it seems that we are very much alike with regards to interpretations of rules hehe
As you probably saw or guessed, this puzzle attracted quite a bit of comments regarding the rules, which I think is to be expected for any puzzle that has not only 'invisible' elements to be discovered, but the nature of which is also floaty. One element was deliberate on my part though -- that to not specify too much about the arrows and the region headers; and in fact, if you feel like taking all of this even further, you can try next bodemeister's 'Thermal Doppelgangers', which pretty much took this concept to its limits. If you had fun with my puzzle here, you are guaranteed to have a blast with that other one, but be ready for some discovery-type deductions hehe ;-)
am 13. Dezember 2025, 05:06 Uhr von Piatato
How did I miss this beauty? Creative ruleset and a very enjoyable solve!
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Thanks a lot for the kind words, much appreciated! Glad you enjoyed that one -- and if you're still up for some 'doppelgangering', you might be interested in bodemeister's 'Thermal Doppelgangers', which is based on this invisible thermo ruleset, here, but in Doppelganger format (though I can't comment on it as I have yet to solve it myself...)
am 2. November 2025, 02:00 Uhr von Chilly
very nice construction - smooth all the way :)
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Thanks a lot for the kind words, glad you enjoyed! And well done in finding it smooth all the way -- if I were to replay it myself after some time has passed, I'm not sure it'd be a ride without hiccups for me haha XD
am 22. August 2025, 13:52 Uhr von Agent
Very cool!
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Many thanks for sharing Agent, glad you had fun with it! :D
am 10. Juni 2025, 08:46 Uhr von oskode
Perfection!
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Ah, you're too kind, thank you so much! Glad you enjoyed the puzzle like that :D
am 9. Juni 2025, 10:27 Uhr von MagnusJosefsson
Very fun puzzle, enjoyed it a lot!
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Thank you for sharing, much appreciated – very happy to hear you enjoyed the puzzle! :D
am 21. Mai 2025, 19:05 Uhr von earthpuzzles
Enjoyed this foray into invisible thermometers! The region numbers constraint led to some fun mid-solve debates between my “just enter the number, it’ll be fine” brain and my “every step must be completely logical and clear” brain. Thanks!
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Haha, thanks for the solve and this feedback! It's really interesting to see the various reactions to this one, as even I was a bit taken aback at first at how it turned out, but I'm really thrilled to see the reactions to its... unusualness, for lack of a better term :D
am 13. Mai 2025, 14:00 Uhr von wullemuus
Enjoyable construction! Invisible thermos sound more frightening as they were in fact due to the clever placed arrows and the restrictions they implicate ;-) I wasn't sure if any region number has to contain a bulb or only vice versa, but this didn't matter. Could we expect this ruleset in a next level puzzle?
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Happy to hear you enjoyed, and thanks for the perspicacious feedback! As indeed, it was originally meant to be an easier puzzle, but as it became clear that it would be hard to set, I just went and committed to a hard puzzle. And as for your question, it's a yes and no I think; I'm still playing with the Region Number bulbs idea, but not invisible thermos. Basically I'm really, really trying to set a minimalistic puzzle like bode, but I just can't do it! XD
am 12. Mai 2025, 20:39 Uhr von marcmees
Q: I assume the most direct route may go diagonally as well?
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Hi marcmees -- indeed, they can (I will update the text as soon as I have a second)
am 12. Mai 2025, 17:41 Uhr von chrisj50
I enjoyed my test solve of this - an interesting twist on the CC ruleset with some very satisfying ‘aha’ moments in the middle! I’d recommend colouring those regions and pen-marking the tips/bulbs of the invisible thermos
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Thanks a lot again for testing Chris, much appreciated as always, and I'm glad you had fun with it!
