I’m not sure I’ve ever seen a puzzle with a selectively-negative constraint like this. The grid is marked like a 9x9 checkerboard, and only on shaded cells, there’s a “local global” constraint, so if a shaded cell is not marked as minimum nor as maximum, that’s important information.
Rules:
Normal Sudoku rules apply.
There are additional regions marked in blue. Each also contains the digits 1 through 9.
Every other cell is colored a shade of red, like an oversized checkerboard. Colored cells containing a digit greater than all orthogonal neighbors are red, with arrowheads pointing out. Colored cells containing a digit less than all orthogonal neighbors are pink, with arrowheads pointing in. Colored cells without arrowheads are neither greater than nor less than all orthogonal neighbors.
Estimated difficulty: 2 out of 5
Solve on SudokuPad