Chilly Sums
(Published on 26. April 2026, 16:27 by sujoyku)
Rules:
- Normal sudoku rules apply, i.e. each row, column and 3x3 region has to contain the digits from 1 to 9 once each.
- 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.
The value of a cell that contains the digit X equals X if the cell is unshaded and -X if the cell is shaded.
- Thermometers: Values along a thermometer must strictly increase from the bulb end.
- Signed X-sums: If the first value X seen from a clue outside the grid is positive, the respective clue indicates the sum of the first X values in the respective row or column. If the first value X seen from an outside clue is negative, the respective clue indicates the subtraction of the first |X| values in the respective row or column. In other words: If the first value X is negative, all values that are part of the X-sum get multiplied by -1.
Example: The image shows a few valid signed X-sum combinations where yellow (=unshaded) indicates positive and blue (=shaded) negative values. The (-9)-clue is satisfied because 4+(-7)+(-8)+2=6-15=-9. The 11-clue is obtained by adding the first 3 values with opposite signs, so 3+(-1)+9=12-1=11. The 13-clue is satisfied because the first value is negative and 9-8+7+6+5-4-3+2-1=29-16=13.
Here you can solve the puzzle online:
Solution code: Digits in Row 5 from left to right (9 digits in total)
Comments
on 6. May 2026, 07:56 by MysticMan
I love the way in which negative numbers and Yin Yang can bend the rules. Lovely puzzle!
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Thank you for your comment, MysticMan! I am glad that you enjoyed the variant.
Kind regards, sujoyku
on 30. April 2026, 22:36 by mse326
I have to agree with Henry that there is a better way to word. More problematic however is that the rules in the link don't include the clarifying text, and frankly without it I think the wording is wrong. Without it the first cell in a negative strain would still be negative so in the example the 3 in the 11 clue would be -3-1-(-9)=5. And many, like me, just open the link and read the rules there. I spent 2 hours completely stuck until I came back here and saw the way I'm supposed to do it. Then it only took 30 minutes. So the rules in the link need to be changed to at least have the clarifying text
on 30. April 2026, 16:17 by henrypijames
I think a better description for the outside clue would be: sum of same-color cells (as the first cell), minus sum of opposite-color cells, within the first X cells from the clue's side.
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Thank you for your comment, henrypijames! This is indeed equivalent to my rules wording.
Kind regards, sujoyku
on 27. April 2026, 23:54 by harwiltz
This was awesome!!! This is an interesting site... I had an easier time solving this than some 2* puzzles I played recently. Still think this one was tricky, yet smooth.
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Thank you for your comment, harwiltz! I am glad you had a smooth solve. Regarding what you mention about difficulty: I have often experienced the same. Sometimes I felt I got "lucky" by spotting the right things at exactly the right moments.
Kind regards, sujoyku
on 27. April 2026, 17:22 by Chaka
Absolutely lovely YY puzzle featuring a very interesting rule setup! I found it to be a bit more difficult than 3* (maybe 3,5*) because of the new (?!) mixed X-Sums rule which I haven't seen before. Thanks a lot for creating and sharing with us! <3
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You are much welcome, Chaka, thank you for commenting! I am glad that you liked this YY construction. I also very much agree with your assessment of difficulty, which is why I initially uploaded it at 4*. When being in doubt, I try to err at the higher end of the difficulty scale. :)
Kind regards, sujoyku
on 27. April 2026, 14:57 by Exigus
Fantastic. Thanks!
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Thank you, Exigus! I am glad that you enjoyed the puzzle.
Kind regards, sujoyku
on 27. April 2026, 12:20 by Franjo
Vielen Dank für das tolle Puzzle! Ich glaube, das funktioniert auch mit der normalen X-Sums-Regel: am Rand steht die Summe der ersten X WERTE, wobei X die erste ZIFFER ist. (Man müsste nur das eine oder andere Vorzeichen bei den Randvorgaben ändern.)
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Vielen Dank für deinen Kommentar, Franjo! Es freut mich, dass Dir das Rätsel gefallen hat. Du hast natürlich vollkommen Recht. Die Wahl der Vorzeichen ist eine Konvention. Meine Idee war, dass es einen Unterschied machen sollte, ob die "Summe" mit einem positiven oder negativen Wert X beginnt.
Herzliche Grüße, sujoyku
on 27. April 2026, 09:59 by Snookerfan
Very nice! Lovely interactions between the rules. Thanks
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You are much welcome, Snookerfan, thank you for your comment! I am glad that you liked the interactions of the different variants.
Kind regards, sujoyku
on 26. April 2026, 23:11 by BG03
Have rated this 3* difficulty and 5* for quality. A nice YY twist to thermos and some interesting logic on the way to the solution. It takes some crunching to fully absorb the implications of YY but not as difficult to work out as implied by the 4* difficulty as it stands right now. Also think it is better than 90% as it stands right now. Thank you for sharing.
Edit: NVM my rating dropped the puzzle to 3* difficulty
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Thank you for your comment, BG03! I am glad that you liked the puzzle. Considering difficulty: After the testing feedback, I thought it was somewhere between 3 and 4 stars and since the ruleset is somewhat complex in its own right, I decided to upload it at 4. I am happy to see that people find it closer to 3*.
Kind regards, sujoyku
on 26. April 2026, 20:14 by mihel111
Very nice YY. Thank you Sujoyku.
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Thank you for your comment, mihel111! I am glad that you enjoyed the puzzle.
Kind regards, sujoyku
