Regular Sudoku's constraint is simple: each digit appears exactly once in each row, column, and box. Rock Paper Scissors Sudoku carries that constraint but adds the game's nontransitive rule — Rock beats Scissors, Scissors beats Paper, Paper beats Rock — as an additional condition that governs how the three gestures can be placed relative to each other.
The result is a puzzle that requires you to track two independent constraint systems simultaneously. The placement logic from Sudoku still applies. The beat-relationship logic from RPS applies as an additional filter on every valid placement. A cell that looks correct under the Sudoku rules may violate the RPS adjacency rules. A cell that satisfies the beat-relationship requirements may break the row or column uniqueness constraint.
The overlap between these two systems produces puzzles that are solvable but not through either logic alone. You have to hold both simultaneously, which is a different kind of constraint satisfaction problem than standard Sudoku presents.
The game is available in graduated difficulty settings. Beginner boards give you enough starting placements that the RPS logic is mostly confirmatory. Advanced boards require you to use the beat-relationship constraints actively to eliminate possibilities that pure Sudoku logic would leave open.