Logic Masters Deutschland e.V.

Puzzle link: Play on SudokuPad.

Rules: Normal Sudoku rules apply.

A cage represents a chemical system. Its internal energy U is the sum of the digits in the cage and corresponds to the clue in the top left corner of the cage if given; its volume V is the number of cage cells; and its entropy S is the number of ways in which the locations of cells containing an odd digit could be arranged within the cage assuming there were no Sudoku restrictions. For the purpose of calculating entropy, the actual values of the odd digits are not relevant, i.e., they are considered to be indistinguishable. If a cage contains no odd digits, S = 1.

A red arrow indicates a reaction that converts the chemical system from which the arrow emerges (the reactant) to the chemical system into which the arrow points (the product). This reaction occurs at a constant temperature T, which is the digit in the cell next to the arrow labeled with T, and at a constant pressure p, where p = 1 in this puzzle.

The Gibbs energy G of a chemical system is G = U + pV - TS. The change of Gibbs energy from reactant to product, dG, is calculated as

dG = dU + p dV - T dS.

Here, “d” symbolizes the difference between product and reactant of the quantity following “d”, i.e., dG = G(product)-G(reactant), dU = U(product)-U(reactant), dV = V(product)-V(reactant), and dS = S(product)-S(reactant).

A reaction is spontaneous if and only if dG < 0. All reactions in this puzzle are spontaneous. The absolute magnitude of dG is the digit in the cell next to the arrow labeled with -dG.

Your feedback, ratings and comments are highly appreciated. Have fun!

Background: This puzzle incorporates the correct physical equation for the Gibbs energy and illustrates the conditions under which chemical reactions may occur spontaneously. Solving the puzzle requires a bit of arithmetic and evaluating inequalities, so if you don't enjoy that, choose a different puzzle. However, the solve path itself should be fairly linear with the given clues, so that for most of the time it should be clear where to look next during a solve.

If you want to familiarize yourself with the concept of entropy used here, you may want to look at my puzzle Entropy of Parity first because it introduced the definition.

Example: The following image provides a fully solved example on a 4x4 grid. You may solve the example for yourself here on SudokuPad.