Rotae: Ring Puzzle

Rotae is a calm, thinky puzzle about turning rings. Beads sit on circles that cross each other. Where two rings meet, the bead belongs to both, so every turn also moves something somewhere else. Drag along a ring to turn it, and arrange the beads to match the goal. • 216 levels in 12 chapters. Start with two rings and ten beads; rings, layers, colours and moves grow step by step until the last chapter: a 3×3×3 cube flattened onto the plane, with nine nested rings and 54 beads. • Every level has a target move count. Solve it within the target for three stars. • Nested-ring chapters show a cube laid flat: turning a ring is turning a layer. • Formula demos show how a commutator moves just a few beads and puts everything else back, so you can use it yourself. • Three looks, switch any time: Plain, Astrolabe (heavy cast bronze) and Movement (the gears of a skeleton watch). • Undo and restart. Stuck? Auto-solve shows the way (it unlocks the next level but earns no stars). • Local leaderboard: your ten fastest times on every level. • In English, Simplified and Traditional Chinese, Japanese, Korean, Spanish, French and German. No ads, no account, no data collected, and it works offline. The math behind it: each ring turn is a permutation, and together they form a permutation group. The formulas in the game are commutators, X·Y·X⁻¹·Y⁻¹. You don't need to know any of that to play.