Ring Turn

Thirty-six numbered tokens sit in three concentric rings — twenty round the outside, twelve inside that, four in the middle — and each ring counts 1 upwards from its own corner when it is home. The rings are stacked like turntables, so turning one carries every ring inside it round with it: the outer ring moves all three, the middle ring moves two, the centre ring moves only itself. That single rule is what stops this being three separate dials. Every ring prints how far round it has been turned, both ways, so the puzzle is arithmetic rather than eyeballing — and the turn budget is the shortest possible route plus exactly four, a number worked out by searching all 960 arrangements rather than guessed.

It runs entirely on your device: 0 network requests, works offline. No ads, no account, nothing to buy, and no betting, money or prizes of any kind.

1. Focus the board — click it, or press Tab until it is focused.
2. Choose a ring with the up and down arrows. The chosen ring is drawn with a heavier edge and marked ▸ in its own control row underneath the board.
3. Turn it with the left and right arrows — anticlockwise and clockwise, one slot per press. Enter also turns it clockwise and Shift anticlockwise, and the ↺ and ↻ buttons in each control row do the same thing with a mouse or a finger.
4. Read the offsets. Each control row says how far its ring is from home and what the two routes cost, like 6 of 20 clockwise from home — 6 back or 14 on. Those three numbers are the whole state of the puzzle.
5. Remember what moves with what. Turning the outer ring changes all three offsets by one, so the middle and centre numbers you are aiming at are the ones they will read after you have fixed the outer ring, not the ones they read now.
6. Get every ring to 0 before the turns run out. The tokens read 1, 2, 3 … clockwise from each ring's dashed home corner when you are there.

How do you solve a puzzle where turning one ring moves the others too?

Work from the outside in, and do the arithmetic before you touch anything. The outer ring is the only one nothing else can move, so fix it first: send it back by its offset, or on by the ring's size minus its offset, whichever is fewer turns. Then — and this is the step people skip — recompute the inner offsets, because those turns dragged the inner rings by the same amount. A middle ring reading 2 after you take the outer ring back 10 reads 2 − 10 = −8, which on a twelve-slot ring is 4. Fix that one next, recompute the centre, fix the centre. That route always finishes, and on this board it is never more than four turns off the best possible, which is exactly the slack the budget gives you. The shortcut worth learning: because turning a ring is just adding to a residue, you can add the whole plan up on paper before you make a single move.

Why does turning the outer ring the long way round sometimes cost less?

Because the ring sizes do not divide one another. Twenty and twelve share only a factor of four, so going all the way round the outer ring the long way — say 10 on instead of 10 back — leaves the middle ring somewhere completely different from where the short way left it: twenty steps is eight steps on a twelve-slot ring, not none. Now and then those eight steps land the middle ring nearer home than the short route did, and the detour more than pays for itself. On 44 of the 960 arrangements the obvious outside-in route is beaten this way — 32 of them by two turns and 12 by four — which is why the game finds the true minimum with a search rather than trusting the sum.

Why does the centre ring move on every single turn?

Because every ring is stacked on the ones outside it, so whichever ring you turn, the centre goes with it. That gives you a free check on your own arithmetic: the number of turns you have made always has the same odd or even as the centre ring's offset. If the centre reads an odd number and you have made an even number of turns, you have miscounted somewhere. It also means a board whose centre is one step out can never be finished in an even number of turns, however clever the route.

Where does the turn budget come from?

From a search, not from a guess. The only thing that matters about the board is how far each ring has been turned, so the whole puzzle has 20 × 12 × 4 = 960 possible arrangements — small enough to walk all of them by breadth-first search from the solved position when the page loads. That gives the exact shortest route from any board. The budget is that number plus four, and the four is measured too: it is the largest amount by which the plain outside-in route can ever exceed the best possible, anywhere in the puzzle. So a correct plan always fits inside the budget, and turning rings at random never does.

Can a board ever be impossible?

No, twice over. The board is dealt by starting from the solved position and applying real rotations to it, so the reverse of what the generator did always solves it. And the three moves between them reach every one of the 960 arrangements, so there is nothing to be stranded in even in principle. Boards are also rejected unless they are at least eight turns from home, because a two-turn board is not a puzzle.

Is there any money, betting or in-app purchase in this?

None, and there never will be. No currency, nothing to buy, no hints to unlock for a fee, and no prizes of any kind. The only number the game keeps is how many turns you used.

Does it work offline?

Yes. Once the page has loaded once, the whole game — the board, the generator and the search that proves what the shortest route is — is on your device. No server is involved in play at any point.

Can I play it with a keyboard or a screen reader?

Both. Arrows choose a ring and turn it, Enter and Shift turn it as well. Every tile announces its ring, its slot, its number and whether it is the home corner; every control row announces its ring's offset and both routes home as a sentence. The chosen ring is marked with a heavier edge and a ▸, and each home corner carries a dashed edge and the word home, so nothing on the board depends on telling two colours apart.

A six-by-six board: rings of 20, 12 and 4 slots, one selected at a time, and 960 arrangements in all. Dealt boards run from 8 to 16 turns from home, so budgets run from 12 to 20. There is no timer and no penalty for thinking — only turns are counted, and a turn is only ever one slot of one ring. The tokens themselves never change, and no ring is ever reordered: the only thing a board can differ in is how far round each of its three rings has been turned.

Shape Shift is the other puzzle here that is really counting in a modulus — there it is how many times to press each tile, here it is how far round each ring has gone. Slide Fifteen is the other ordering puzzle in this family, and Light Grid is the one where the moves cancel instead of stacking.

Bookmark this page (Ctrl+D, or ⌘D on Mac) or install the app — it works offline the next time you need it.