Logic Masters Deutschland e.V.

"Oh I know! A deconstruction with overlapping regions!"

Many thanks to Vebby and Niverio for testing.

Rules:

Place the digits 1-9 in the grid such that digits do not repeat in any row, column, or region. Regions are 9 cells large, and contain the digits 1-9 once each, but their shapes and locations must be determined. Not every cell in the grid must contain a digit, but every clued cell must.

Within the grid there are two snakes, Snake A and Snake B (one cell wide orthogonally connected paths that do not branch or touch themselves, even diagonally). A digit in a circle indicates the number of surrounding cells in the 3x3 area centered at that cell that are part of Snake A, likewise with squares and Snake B. The snakes may touch each other freely, and may intersect. If two snakes intersect (i.e. they both have a cell in common), they must "cross". More formally, no two adjacent cells in the grid may belong to both Snake A and Snake B. Snakes may intersect at corners, or even at their heads or tails. All is fair play.

Every region is either entirely part of Snake A, or entirely part of Snake B. Cells that exist at intersections of Snake A and Snake B belong to two regions simultaneously.

Implications:

A consequence of these rules is that every cell with a circle, square, or given digit must belong to at least one of the two snakes. A second consequence is that because digits may not repeat in rows or columns, at least two cells in every column must not belong to either snake. These are two important insights necessary to make progress in the puzzle.

Examples:

Below is an example image as to how the snake rules may work. Yellow here is Snake A, blue is snake B, and green are intersections between A and B. Below shows several different ways the snakes could intersect with each other: at their heads or tails (marked by h and t, but may be interchangeable as orientation of the snakes do not matter), at corners, or pass through each other like an X. This example image does not show anything related to regions, though.

And below is an image of the puzzle. The screenshot of the puzzle below is a Penpa+ screenshot, in which diamonds represent a square and a circle in the same cell. In the CTC link, these diamonds are not there.

CTC link

Penpa+ link