The foil. Often lumped in with the others, but nothing here is linked: every single move is topologically trivial. The jailer is a rule, and the sentence is exponential.
mode
5 steel rings sit on a brass bar. At any moment at most TWO of them are willing to move: ring 1, always — and the ring just past the first ring still on the bar. Start simple: click ring 1 and lift it off.
11111Moves: 0 · shortest from here: 21full solve minimum for 5 rings: 21
Step 1 of 4 — Two willing rings
Every state sits on one long path — the Gray code numbers your position. ● you · ● all off (goal, position 0) · ● all on (start, position 21)
This puzzle looks like it belongs to the ring-and-string family, but it is a deliberate impostor: at no point is anything linked with anything else. Every individual move is easy — ring 1 always toggles freely, and at most one other ring is ever movable. The difficulty is that there are exponentially many of these easy moves, and the rule forces them into one exact order.
Watch the teal dot on the path below the controls: each move slides it one step, never more. That is the whole game — a very long corridor with no shortcuts.
References: L. Pacioli, De Viribus Quantitatis (c. 1500) · Wikipedia, "Baguenaudier".