Gear Train

A crank with 48 teeth sits at the head of a rail of five empty bays, and a box holds six loose gears of 8, 12, 16, 24 and 48 teeth. The order card asks for one thing: the hand must turn a stated number of times for one turn of the crank, and it must turn in a stated direction. The hand is fitted to whichever gear you put on last, so how many gears you use is entirely your decision — and that decision is the whole puzzle.

Two facts settle every board, and both are printed on the page rather than hidden. The speed comes from the first and last gear only: 48 teeth on the crank divided by the teeth on the last gear is the number of turns the hand makes, whatever sits between them. The direction comes from the count: meshed gears turn opposite ways, so every gear you add reverses the hand again. Count the gears including the crank — an odd train turns the hand the same way as the crank, an even one turns it the other way.

The catch is the frame. Every bay has its own clearance — the largest gear it will take — and the box is finite, so the gear the order needs at the end often cannot sit where the parity wants it. Working around that is the game, and each gear you fit or pull off costs a turn of the spanner.

Every board is built backwards from a machine that already works: the chain is laid first, the clearances are cut to accept it, the box is stocked to supply it, and only then is the order read off it. Then a solver walks every arrangement the box and the clearances allow — at most 720 of them — so the spanner budget is the shortest real answer plus five, and the number of working arrangements is counted 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. Read the order card first. It gives two numbers: how many turns the hand must make per turn of the crank, and which way it must turn. The crank always turns clockwise.
3. Work out the last gear. Divide the crank's 48 teeth by the turns asked for. Four turns needs a 12-tooth gear at the end; three turns needs 16; two needs 24; one needs 48; six needs 8.
4. Work out how many gears you need. Count the crank as one of them. An odd total turns the hand clockwise, an even total turns it anticlockwise. That tells you whether the last gear has to land on an odd-numbered bay or an even-numbered one.
5. Choose a gear with the left and right arrows. The cursor walks the six gears in the box, and each one shows its tooth count.
6. Press the up arrow to fit the chosen gear onto the next free bay. A gear larger than that bay's clearance will not go in, and asking costs nothing.
7. Press the down arrow to lift the gear nearest the hand back into the box. Esc and Z do the same. Every fit and every lift is one turn of the spanner.
8. Press Enter on a gear already on the rail to strip the rail back to it — that costs one spanner turn per gear removed, because the ones outboard of it have to come off first.
9. Watch the reading under the rail. It says what the hand does right now. Add one idler and watch the speed stay put while the direction flips: that is the rule the board is testing.

You can play entirely by pointer instead: click a gear in the box to fit it, click it again to strip the rail back to it, and click any bay to strip back to that bay.

How do you work out how many times the last gear in a gear train turns?

Divide the driving gear's tooth count by the last gear's tooth count. Two meshed gears carry the same teeth past the mesh, so a gear with half as many teeth must turn twice as often — and when you multiply that ratio along a chain, every gear in the middle appears once on the top and once on the bottom and cancels out. On this board the crank has 48 teeth, so a 12-tooth gear at the end turns four times per crank turn whether it is the second gear in the train or the fifth. That is why the gears in between are called idlers: they cost nothing and change nothing about the speed. The only thing they change is the direction.

Why does adding a gear in the middle flip the direction but not the speed?

Because a mesh is a reversal. Where two gears touch, their teeth move in the same direction at that point, which means the gears themselves turn opposite ways — so each extra mesh flips the answer again. A train of n gears has n − 1 meshes, so the last gear turns the same way as the first when n is odd and the other way when n is even. Nothing about that depends on tooth counts, which is exactly why an idler is such a useful part in a real gearbox: it is the cheapest way to correct a direction without touching the ratio. On this board it is also the move that gets you out of trouble, because it changes the parity without changing what the order asks for.

Is every board actually solvable?

Always, and by construction rather than by luck. The generator lays a working chain of gears down first, then cuts each bay's clearance so that it accepts the gear the chain put there, then stocks the box with exactly those gears plus spares — and only then reads the order off the finished machine. An order that no arrangement satisfies cannot be written, because no order is written that was not read off a machine that already works. A separate solver then checks it from scratch: it walks every sequence of gears the clearances allow, counts the ones that satisfy the order, and reports the shortest. That number is where the spanner budget comes from, so the budget is always achievable.

Why did my gear not go into the bay?

Because it is bigger than that bay's clearance, which is printed on the empty bay. A real gearbox has the same problem — a gear has to physically clear the case and its neighbours — and it is the constraint that makes this a puzzle rather than a division sum. Asking for a fit that will not go costs nothing, so it is safe to try. When the gear the order needs at the end will not clear the bay the parity wants it on, the answer is usually to change the count: add an idler earlier in the train so the last gear lands one bay further along.

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, no prizes.

Does it work offline?

Yes. Once the page has loaded once, the whole game — the board generator, the solver that proves the order can be filled, and the arithmetic that reads the rail — 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 gear, up fits it, down lifts one off, Enter strips the rail back to a gear already on it, and Esc empties nothing you did not ask it to. Every gear announces its tooth count, every bay announces its clearance and what is standing in it, and the reading is announced in words: how many turns the hand makes and which way it goes. Nothing on the board is carried by colour alone — a gear's size is written on it as a number, and its state is spelled out in words.

The crank is always 48 teeth and the box only ever holds gears of 8, 12, 16, 24 and 48, so every reading is a whole number of turns — no board will ever ask for two and a half. There are five bays, six gears, and answers run from two to five gears long. The spanner budget is the shortest real answer plus five, which is room for two mistakes and not enough for shuffling. This models the two things a gear train's ratio and direction actually depend on; it does not model centre distances, module, backlash or torque, so it is a way to learn the rule rather than a tool for designing a gearbox. There is no timer, no hint button, and no way to undo a spanner turn — reading the order before you touch the box is the whole of the skill.

Pipe Flow is the other spatial puzzle about making a path connect end to end, and Mirror Maze is the other one where a limited stock of parts has to be placed inside a frame that fights you. Balance Scale is the other machine here whose budget is derived from a solver rather than guessed, Unit Swap is the other game about exact conversions, and Ring Turn is the other one where moving a part carries its neighbours with it.

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