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Gear Rotation Puzzle

Place several gears into fixed sockets, build a connected reversing train, and turn the target through five deterministic gearboxes.

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How to use

  1. 1.Choose one candidate gear, then place it into a fixed socket; fill every socket before testing the train.
  2. 2.Use visible gear sizes and contact gaps to build one continuous path from the clockwise driver to the target.
  3. 3.Test the completed train, revise a recoverable failed layout, and solve all five gearboxes for exactly 1,000 points.

About Gear Rotation Puzzle

Gear Rotation Puzzle is a five-level construction game about ideal external spur gears. A clockwise driver is fixed on the left, a target gear waits on the right, and several empty sockets divide the space between them. Candidate gears have different tooth counts and matching visual sizes. Your job is to place every candidate into exactly one socket so the touching geometry creates a continuous, physically consistent path from driver to target.

This is not a one-question direction quiz. Each level is a small placement problem with three or four candidates, so a complete move is an assignment of several distinct gears to several sockets. Select a candidate from the rack and then choose a socket. Once a gear is on the board, its rack control is disabled; tap its occupied socket to return it before moving it elsewhere. That explicit pick-and-place loop prevents duplicate gears and works with touch, pointer, or keyboard controls.

The board calculates contacts from geometry rather than from a hidden answer list. Two ideal pitch circles create an edge only when the distance between their centers matches the sum of their radii within the game's small declared tolerance. A gear that looks close but does not reach its neighbor therefore remains disconnected. Filling every socket is necessary, but it is not sufficient: all placed gears must belong to the powered component and the target must be reachable from the driver.

Direction and ideal angular speed propagate through the resulting contact graph. Every external mesh reverses rotation. If one gear turns clockwise, each touching neighbor must turn counterclockwise, and its next neighbor returns clockwise. The signed speed rule is the incoming speed multiplied by the incoming tooth count, divided by the outgoing tooth count, and negated for the reversal. This means intermediate ratios telescope along a simple train.

An idler is useful because it contributes one more reversal and can bridge a physical gap. In the ideal end-to-end ratio, however, its own tooth count appears once in a numerator and once in a denominator, so it cancels. The final speed magnitude depends on the driver and target tooth counts. The number of external contacts determines whether the final direction matches or opposes the driver.

The solver uses breadth-first propagation, not a hard-coded solution comparison. It begins at the driver with signed speed plus one, visits every geometric neighbor, and assigns the expected opposite direction and tooth-count-adjusted speed. If a later path reaches an already assigned gear with a contradictory direction or speed, the layout has a conflict. An odd loop of external gears is the clearest example: returning to the starting side after an odd number of reversals asks one gear to rotate both ways. An even loop can remain consistent.

The target visibly starts turning only when the full placed graph is connected and conflict-free. Its board label reports clockwise or counterclockwise rotation, and the side ledger reports the ideal target-to-driver speed magnitude. Reduced-motion users receive the same direction and ratio state without depending on animation. The final completed level remains visible and rotating while every interaction is frozen, so the 1,000-point outcome matches the board rather than replacing it with an empty result.

Testing a correct train awards exactly 200 points and opens the next fixed gearbox. Five correct layouts produce exactly 1,000 points. There is no time bonus, random level, adaptive difficulty, hidden multiplier, or score penalty for exploring placements. A partially filled board cannot be submitted, and selecting, removing, or replacing candidates never counts as an error by itself.

One distinct failed full layout is recoverable. The feedback explains whether the target is disconnected, a gear is isolated, or a direction conflict exists. Submitting the identical assignment again is deduplicated and does not consume the remaining chance. A second different failed assignment closes the run. Restart returns to level one with an empty board, zero score, no failed signatures, and no held candidate.

Keyboard play covers the entire construction loop. Number keys 1 through 4 hold available candidate gears. Q, W, E, and T address sockets from left to right. Pressing a socket key with a held candidate places it; an occupied socket can be cleared when no candidate is held. Enter tests a completely filled train, and R restarts. Every pointer target is at least 44 pixels, with visible focus and held states.

The five levels are deterministic original fixtures. Their candidate radii, tooth counts, socket coordinates, driver dimensions, and target dimensions do not change between runs. Independent tests restate every level literally, complete the exact 200-to-1,000 route, recover from one failed train, deduplicate a repeated failure, trigger the second-failure deadlock, and freeze all terminal actions.

Reference tests separately cover ten published-rule examples: equal and unequal two-gear meshes, two- and three-stage trains, arbitrary idlers, speed increases, speed reductions, and direction parity. Additional geometric cases prove that an odd triangular contact graph conflicts, an even square stays consistent, and separated gears leave the target stopped. Expected signed speeds are literal test values rather than outputs generated from the production solver.

This game deliberately models only ideal same-module external spur gears for educational play. It is not engineering design software and must not be used to size a real transmission. It omits torque, power loss, tooth stress, backlash, profile interference, shaft alignment, lubrication, noise, wear, materials, safety factors, tolerances, and dynamic loads. The scope is shown beside the board and in the cited methodology.

Everything runs locally in the browser. No account, download, upload, API, remote model, random service, or hardware permission is required. The shared game shell adds Restart, best-score storage, keyboard guidance, and the double-Escape boss screen. For other connection puzzles, continue with Pipes Puzzle, Edge Match Puzzle, Connect the Numbers, or Rotating Picture Puzzle.

Methodology & sources

Five fixed levels place ideal same-module external spur gears at literal socket coordinates. Contact edges exist when center distance matches summed pitch radii within 0.75 game units. BFS starts the driver at signed speed +1 and propagates omega_neighbor = -omega_current * teeth_current / teeth_neighbor. Revisiting a node with a different direction or speed marks a parity/ratio conflict. A train succeeds only when every placed node and the target are connected with no conflict. Each success awards 200; full placement signatures dedupe failed submissions; two distinct failures deadlock.

Frequently asked questions

How do I play Gear Rotation Puzzle?
Select a numbered candidate and then a Q, W, E, or T socket. Fill every socket and test the train. Each valid external contact reverses direction, so the target must be connected without a direction conflict.
Does an idler gear change the final speed ratio?
In this ideal same-module external-gear model, an intermediate idler changes rotation direction but cancels from the end-to-end speed ratio. Driver and target tooth counts determine the final magnitude.
Does this game simulate a real gearbox?
No. It is a deterministic direction-and-ratio puzzle. It deliberately excludes torque, efficiency, backlash, deflection, tooth interference, lubrication, wear, and manufacturing tolerances.

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