Ring puzzles explained: from Chinese rings to rotate rings games

What counts as a ring puzzle

The label covers a lot of ground. There are metal puzzles made of interlocked rings that you pull apart, jewellery-style puzzle rings built from several linked bands, and the digital games in which rings sit on a board and fly away when you free them. What they share is a rule of dependency: one ring holds another, so you cannot move the second until the first has let go.

That single idea is why ring puzzles feel like logic rather than reflexes. You are never asked to be quick. You are asked to work out which ring is really free and what that frees next.

The Chinese rings puzzle, or baguenaudier

The Chinese rings puzzle goes by several other names, including baguenaudier, Cardano's rings and the devil's needle. It is a loop that has to be disentangled from a sequence of rings on interlinked pillars. The loop can be string or a rigid piece of metal.

Its true origin is unclear. A tradition credits the Chinese general Zhuge Liang in the second or third century, but that rests on an unnamed source. The earliest firm references are from the early sixteenth century: Yang Shen mentions a puzzle of nine linked rings, and Luca Pacioli's 1509 book De Viribus Quantitatis mentions it too. Both treat it as already well known. French peasants later used the mechanism as a lock, which is where the name baguenaudier comes from in the popular story.

Why the maths is famous

The rings in the classic puzzle can only come off in a strict order, and the number of moves needed grows quickly: it roughly doubles with every ring you add, so a nine-ring version takes a few hundred moves. The nineteenth-century mathematician Édouard Lucas, who also invented the Tower of Hanoi, found an elegant way to solve it using binary numbers and Gray codes, the same kind of method he used for his own puzzle.

That is the lesson of the whole genre. A puzzle that looks like a tangle is really a sequence, and once you see the sequence the tangle falls apart.

How rotate-the-rings games work

The digital version swaps pillars for clamps. In Ring Twist, each open ring has a gap cut into its band, and most rings carry a clamp, a short stem with a block on the end that wraps around the band of a neighbour. A clamp grips as long as the neighbour's band runs through it. Turn that neighbour until its gap reaches the clamp and the clamp lets go.

The dependency rule is the same one as in the old metal puzzle. A ring cannot turn while its own clamp grips another ring, so every board is a small chain of dependencies. Rings at the ends of a chain spin freely, the ones in the middle wait, and closed rings, solid circles with no gap, leave only when everything their clamps grip has gone. When a ring is held by nothing and holds nothing, it lifts off the board and flies away.

Ring TwistTurn the rings, slide the gaps, set them all freePlay now

What the digital version changes

A physical puzzle punishes a mistake with a tangle you have to undo by hand. The browser version removes that cost. In Ring Twist every turn can be turned back, undo and restart are free, and a bulb hint shows a good next turn. Every one of its 200 levels is generated for the game and checked by a solver before it ships, so a way through always exists and you cannot trap yourself.

What it keeps is the thinking. Boards grow from two rings to twenty-one, on hexagonal clusters and square grids, with closed rings from level 6. A single long turn can sweep a gap over several clamps and free several rings at once, and stars are counted in turns, so the fewer gestures you need, the better. If you want to try it, it runs in the browser on desktop, phone or tablet with no download.

Frequently asked questions

Guides & tips

• Ring Twist - Rotate Rings game guide: how to free every ring in as few turns as possible

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• Ring Twist — Turn the rings, slide the gaps, set them all free