Thermal Equilibrium
(Published on 22. March 2024, 14:30 by Flinty)
Normal Sudoku rules apply.
Place the digits 1-9 so that they do not repeat in any row, column, or 3x3 box.
Positive/Negative Diagonals:
Digits may not repeat along the indicated diagonals.
Thermometers:
Digits on a thermometer strictly increase from the bulb to the tip.
The total value of all digits on each thermo is the same, and must be deduced by the solver.
To play this puzzle please click here: Play CTC
Hidden hints available below (may not work on all browsers/mobile).
Hint 1
There are leftovers from the Thermos in the corners, versus the sum of 45 in each row/column. These values are limited by the thermos and must sum to a multiple of 3. The easiest place to do some maths is the bottom left corner thermo.
Hint 2
There are a few ways to calculute the total value of each thermo, which we'll call 'n'. Perhaps the easiest logic to see: consider R9C2 and R9C3, if 'n' is 17, then those cells add to 6 (as 17x3 = 45+6). This doesn't work as you can't then make that thermo sum to 17. 18 has the same issues, 18x3 = 45+9 and if the high half of the thermo totals 9, how can the low half also be 9? :)
Solution code: All digits from Row 4
Comments
on 23. May 2024, 08:41 by ninjamunk
Enjoyed this very much!
I get the two star rating. But I think the break in and wrapping your head around the constraints is three stars worthy, but from their it's a two star puzzle.
on 1. April 2024, 10:32 by botteur
Loved it, and the hints were fantastic to check that I was on the right track but had missed one deduction.
on 31. March 2024, 23:37 by antiknight
Great puzzle!
on 23. March 2024, 13:58 by Franjo
Very nice puzzle! No need for any hint, I think - if you know Simon‘s secret… Thank you very much for sharing this lovely gem.
on 23. March 2024, 04:54 by silent_rob
Thanks for the great puzzle - I really enjoyed it! I managed to solve without the hints and was pleased that my instinct was close to your second hint. After the break-in it all solved so smoothly.
on 23. March 2024, 00:34 by VitP
i don't understand the given hints. i did it differently:
T = 4x45 - {C} + D = 9 S
working out min, max limits S to 2 values.
now work out thermo candidates. they are quite restricted.
iterate the min, max count - now only one value remains.
iterate the thermo candidates.
etc.
Flinty: Yes there are a few ways to work through it to calculate 'n' as you say it's restricted. Hopefully if people don't understand my hint they'll be able to make progress with yours. Thank you for sharing. :)
on 22. March 2024, 15:58 by goodcity
Always love grids with almost symmetry and a solve path far from being symmetric :).
on 22. March 2024, 15:47 by Caconym
Very cool break in and smooth solve from there
on 22. March 2024, 15:18 by sujoyku
Thank you for this wonderful puzzle, Flinty! I ended up reading the first hint, but then realised I had had the right idea, but made the reasoning overly complicated. The point where I knew the exact thermo-total was such a nice aha-moment. This is a gorgeous set-up and should be covered on CTC rather sooner than later!
Flinty: Don’t tell me, tell them (CTC) - haha. Thank you for the very kind words.
**
Thank you for your reply! You are right, Flinty, I rather should write an email to CTC recommending your puzzle.
Kind regards, sujoyku
