Logic Masters Deutschland e.V.

Proof of concept of new (to me) metalogic

• Yin-Yang: Place either a 0 or a 1 in each cell such that all 0s are orthogonally connected, all 1s are orthogonally connected, and every 2x2 area contains both 0s and 1s.
• Fog: Some cells are hidden by "fog" meaning you cannot see their contents. Some fog may be removed when a digit is correctly filled. Digits can be logically deduced, no guessing is needed.
• Minimality: The puzzle has a unique solution when all the fog has been cleared, but removing any given digit would make the puzzle nonunique.

Play in SudokuPad

Hint: three lemmas about Yin-Yang puzzles in general