Thermal Signatures
(Published on 12. May 2025, 01:13 by 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)
Solution code: Column 2, from top to bottom with a dash (-) to indicate region borders (grid edges don't need to be entered)
Comments
on 13. December 2025, 05:06 by 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...)
on 2. November 2025, 02:00 by 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
on 22. August 2025, 13:52 by Agent
Very cool!
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Many thanks for sharing Agent, glad you had fun with it! :D
on 10. June 2025, 08:46 by oskode
Perfection!
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Ah, you're too kind, thank you so much! Glad you enjoyed the puzzle like that :D
on 9. June 2025, 10:27 by 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
on 21. May 2025, 19:05 by 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
on 13. May 2025, 14:00 by 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
on 12. May 2025, 20:39 by 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)
on 12. May 2025, 17:41 by 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!
