Logic Masters Deutschland e.V.

At long last, a puzzle to match my name. This is another look at Yin Yang rules applied to funny topologies. If you enjoy this, and want to Yin Yang on a torus instead, you may enjoy this puzzle.

Next stop: the Klein Bottle! Anyway, thanks for playing, and have fun! Edit: Added a moat for taking notes. Huge thank you to ThePedallingPianist for the tutorial!

Rules:

Place the digits 1-6 in each row, column, and box.

Twisted Space: The grid is a Mobius Strip. The first and last columns wrap around, but undergo a twist, so that r1c1 is adjacent to r6c6, and r2c1 is adjacent to r5c6, etc. This is reflected in the coloring.

Yin and Yang: Shade some cells in the grid such that all shaded cells form an orthogonally connected set, and all unshaded cells form an orthogonally connected set. No 2x2 region of the grid may be entirely shaded or unshaded. This includes 2x2 regions that wrap around.

Sightline arrows: The digit in a cell with an arrow counts the total number of cells belonging to its yin or yang region in the direction the arrow points before reaching a cell of the opposite shading. This total includes arrow cell itself. If a cell has more than one arrow, its digit will be the sum of all cells counted this way (the arrow cell is only counted once in this case).

A sightline arrow that crosses the twisted edge of the grid diagonally will have its vertical component flipped as it twists. For example, if an arrow points southwest from r2c1, the next cell it sees will be r4c6, and it will be looking northwest from there.

Maze-Runner Circles: If the digit N appears in a cell with a circle, the shortest path of orthogonally connected cells through its Yin Yang region to any other instance of N with the same shading must be at least N cells, including both end-points.

Play here on SudokuPad