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A Shade of Parity Thermos

(Published on 5. July 2025, 06:18 by PhysicistFromFunen)



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I recently solved some absolutely stellar yin yang puzzles and thought to try out how the shading might fit with parity thermometers. Well, in this puzzle, digits on parity thermometers must not only obey the usual ruleset but their parity must also follow the shading!

Rules

Normal sudoku rules apply.

Yin Yang:
Shade some cells such that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2x2 area is fully shaded or fully unshaded.

Shaded Parity Thermometers:
Thermometers see only one parity. Blue ones see even digits, orange ones see odd digits.
On a thermometer, digits of the seen parity must strictly increase from the bulb end and must also be strictly dominant. Digits of the unseen parity are unaffected by the thermometer.
Additionally, on each thermometer, all digits in shaded cells belong to the same parity, while all digits in unshaded cells belong to the other parity. This applies separately, i.e. even digits might only go in shaded cells on one thermo but in unshaded cells on another thermo.
Bulb-to-tip examples (bold digits are shaded):
Valid blue thermo: 2-5-6-1-8
Valid orange thermo: 3-4-5-4-7-9
Valid orange thermo: 7-9
Invalid of either colour: 1-2-3-4 (no majority)

Play on SudokuPad!

Solution code: Box 1, in reading order. 9 digits no spaces.

Last changed on on 6. July 2025, 07:14

Solved by Doc Liu, Piff, Jesper, SKORP17, Joyofrandomness, PippoForte, sehringdipity, palpot, gnidan, VitP, Dentones, jkuo7, blueberrypug, SparklePuzzle, WvdWest, Baklin, Exigus, mcs131313, whtshername, tgstar, Thebodfather, dogfarts, Nemefish, Asphodel
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Comments

on 19. July 2025, 04:36 by Nemefish
The break in was a bit of a struggle. If you are stuck look below

The corner thermos in box 1 and box 3 are important and help with a large swath of the perimeter.

on 7. July 2025, 22:20 by Exigus
Very nice puzzle. Seems quite hard at first but once you poke it a bit it opens up. Thanks!

on 6. July 2025, 07:14 by PhysicistFromFunen
Changed the estimated difficulty level.

Last changed on 6. July 2025, 07:37

on 6. July 2025, 00:48 by VitP
this one is definitely level 4.
you need to be an expert BOTH at yin-yang AND parity thermos to even get started, and that gives you virtually nothing.
there is basically NO information to even try the yin-yang.

AND THEN there is the ADMINISTRATIVE problem that you need TWO TYPES of colouring, i.e. the available notation is insufficient.

HOWEVER, i AM a fan of both genres, so i did massive bifurcation until i found the simple pattern that leads to a fast solve.

SPOILER/HINT: it is the two puny thermos in the corners. didn't see that coming.

thanks to PfF for another stellar puzzle.

—- PFF:
Thank you for the comment - I definitely see your points!
Regarding the double colouring, I found that using light and dark grey for parity did not obstruct the clarity of the yin yang. But I appreciate that that may well just be an effect of setter’s glasses and that I am a sucker for colouring puzzles ;)

Difficulty:3
Rating:89 %
Solved:24 times
Observed:1 times
ID:000O2S

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