Logic Masters Deutschland e.V.

A Setting Saturdays prompt asked to combine X-sums and Thermometers. I had the idea to also bring negative numbers into the mix via Yin Yang. The rules are somewhat complex but I hope the example image helps clarifying it. If you should have any questions, feel free to ask in a comment. I am thanking IkeManga, NicoD, Donatello_86 and NEWS for testing and wish you joyful solving!

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:

Solve on Sudokupad