Logic Masters Deutschland e.V.

The Border Kiss

Rules:

Normal Sudoku rules apply.

Regions: Divide the grid into four distinct regions. Each region is orthogonally connected and touches each of the other three regions orthogonally (shares at least one edge). No 2×2 block may be entirely within one region. The four regions do not all have different sizes (at least two regions are the same size).

Paths: Draw two different orthogonally connected, non-branching paths through cells. Each path connects two circled cells (pairings are deduced by the solver). The paths may not touch or overlap except that they share exactly one cell, marked by the green dot.

Path types: One path is a parity changer: any two orthogonally adjacent cells connected by this path contain digits of opposite parity. The other path is a consecutive path: any two orthogonally adjacent cells connected by this path contain consecutive digits.

Circle clues: A digit in a circle equals the number of times the path using that circle crosses the border of the circle’s own region.

Red dots: A red dot between two adjacent cells means no path segment (of either path) crosses the edge between those cells.

Squares: A digit N in a square means the digit N appears exactly N times within that square’s region.

Cages: Digits in a cage sum to the value in its top-left corner and do not repeat within a cage. If a cage is labeled EVEN, then the cage sum is even.

German Whispers: Adjacent digits on the green line differ by at least 5.

Arrow-count cells: A digit in a cell with arrows equals the total number of cells containing any part of either path in the indicated arrow directions, counting from that cell to the grid edge; include the clue cell if it contains a path segment.

Kropki: Cells joined by a white dot are consecutive. Cells joined by a black dot labeled N are in a ratio of 1:N.

Diagonal sums: Numbers outside the grid on a diagonal indicate the sum of the first 7 cells along that diagonal from the grid edge.

Outside region-run clues: A number N outside a row/column means the first N cells from that side are in the same region, and the (N+1)th cell is in a different region.

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Happy solving!