Definition of Temperature
(Published on 4. May 2024, 10:23 by Tobias Brixner)
Puzzle link: Play on CTC SudokuPad.
Rules: Normal Sudoku rules apply. No digit may repeat within a cage. The temperature of a cage is given by the average of its digits. Orthogonally touching cages must have the same temperature. An orange line acts as thermometer with its bulb in the lower-temperature cage. Along a thermometer, digits increase from the bulb end, and the middle cell contains the temperature difference between the connected cages.
Background: The zeroth law of thermodynamics states that if two thermodynamic systems are both in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. As a consequence, their temperatures are the same. This is reflected in the rules by requiring that all orthogonally touching cages must have the same temperature. In 2019, temperature was formally (re)defined in terms of statistical thermodynamics, where temperature is in essence proportional to the average kinetic energy of the particles in the system. This is reflected in the title of the puzzle and in the rules when interpreting the digits in a cage as kinetic particle energies. The middle cell of a thermometer in the puzzle behaves like a thermocouple that measures temperature differences.
Solution code: All digits of row 8 (from left to right) followed by column 4 (from top to bottom) without spaces.
Comments
on 11. August 2025, 13:26 by MathGuy_12
Fantastic puzzle concept! Loved it from start to finish, an excellent approachable showcase, makes me want to set a puzzle with this constraint myself!
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Thank you so much! I am happy that you enjoyed it. - TB
on 9. July 2025, 21:46 by sockerbecca
This was a very interesting concept! Quite math-y. It took me a little while to get the hang of the thermometers vs the thermocouples, but then it was smooth!
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Many thanks! - TB
on 3. May 2025, 19:20 by Scarlet Manuka
Very interesting mechanic with the cage averages. Not too hard and lots of fun!
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Glad you liked it! And many thanks for playing and commenting one year after this puzzle's release. - TB
on 5. May 2024, 15:34 by DanishDynamite
Tough but nice!
