Ideal Gas Law
(Published on 3. September 2025, 16:45 by Tobias Brixner)
Puzzle link: Play on SudokuPad.
Rules: Normal Sudoku rules apply. Digits may not repeat within a cage. A cage represents a container filled with an ideal gas; its volume, V, is equal to the number of cells in the cage. A circle represents a pressure gauge; the digit in the circle is equal to the pressure, p, in the container to which it is connected by an arrow. The temperature, T, in a container is equal to the average of the digits in the container. The amount of substance, n, of the gas in a container is the same for each container. For each container independently, the ideal gas law is fulfilled such that the pressure multiplied with the volume is equal to the amount of substance multiplied with the ideal gas constant, R, and multiplied with the temperature, p V = n R T. The product n R must be determined by the solver. (You may think of this product as one global, unknown constant for the puzzle.)
Your feedback, ratings and comments are highly appreciated. Have fun!
Background: The ideal gas law relates thermodynamic quantities in an idealized model of a gas. While the derivation of this equation requires certain assumptions that are not generally fulfilled for real gases, the resulting equation is nevertheless a good approximation of many gases under many conditions. Thus, it is widely used in fundamental studies and practical applications. The equation in the puzzle rules is exactly the ideal gas law, with the only difference that in reality, all quantities have physical units (such as Kelvin for temperature), and in the puzzle we work only with numbers. Since in this puzzle, the amount of substance is the same for each container, it would have sufficed to replace n R with one unknown constant, such as x = n R, and write p V = x T as a condition because the actual values of R or n on their own do not matter here, but I wanted to keep the original physical equation in its known notation. The definition of volume in this puzzle is intuitive; the definition of temperature is meant to capture the actual physical definition of temperature as an average over particle energies, see my Sudoku Definition of Temperature for more information.
Example: The following image provides a fully solved example on a 4x4 grid. You may solve the example for yourself here on SudokuPad. Please note: Getting started with the 4x4 example is more complicated than with the regular 9x9 puzzle. Therefore, it is best to view the example primarily as an illustration of the rules and then move on to solving the 9x9 puzzle.
Solution code: All digits of row 8 (from left to right) followed by column 8 (from top to bottom) without spaces.
Comments
on 3. September 2025, 20:58 by sanabas
Another fun one
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Thanks a lot! - TB
on 3. September 2025, 18:14 by Tobias Brixner
There was an error in the solution code - I am sorry! This is now corrected.
on 3. September 2025, 17:55 by biorycbyd
The solution code set seems to be wrong.
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I am so sorry about that. It is now corrected. Thanks for playing! Please try again to enter the code. - TB
