Gearworks · Food for Thought
In Gearworks, you don't just build machines, you build arguments in force, multiplying small advantages until their product is exactly the number on the screen.
Every day, Gearworks presents you with a number. It sits there, unblinking, in the puzzle header: Target ×12 · 3 slots, or Target ×36 · 4 slots, or Target ×8 · 2 slots. Your job is to fill those slots from a bank of parts, building a chain of simple machines whose combined mechanical advantage matches that target precisely. The bank always holds one working combination plus a few distractors, and the chain grows from two slots to four over a six-puzzle run. Not close. Not approximately. Exactly. The game will tell you if you've overshot, undershot, or hit the mark. Only the last one lets you move on.1
This is the core loop of Gearworks: compose machines, multiply their advantages, and aim for precision. It sounds simple, but it's deceptively deep. You're not just stacking parts; you're reasoning about multiplication in the physical world. A lever here, a gear there, a pulley system you've never tried before, each contributes a factor, and the product of all those factors is your answer.2
The satisfaction comes from that moment when the numbers align. You've arranged a lever with an effort arm twice as long as the load arm (that's a 2× advantage), connected it to a gear train where a 20-tooth driven gear turns on a 10-tooth driver (another 2×), and finished with a pulley supporting the load on three rope segments (3×). The chain's total is 2 × 2 × 3 = 12. If the target is 12, you've won. If it's 8 or 18, you've failed. The game's engine compares your chain's mechanical advantage to the target with a floating-point-safe tolerance, and the result is binary: an exact hit wins, anything else fails and sends you back to the bank.3
What are you chaining together? Gearworks uses four of the classical simple machines, each with its own formula for mechanical advantage. These aren't arbitrary rules the game invented; they're the textbook definitions of how force multipliers work in an ideal, frictionless world.1
The lever is the most intuitive. Place a fulcrum under a beam, put your load on one side and push down on the other, and you've got a force amplifier, if you push farther from the fulcrum than the load sits, you win. The game computes this as leverMA = effortArm / loadArm. A 2-meter effort arm and a 1-meter load arm give you 2×. A 3-meter and a 1-meter give you 3×. Simple, elegant, and exactly what Archimedes figured out over two thousand years ago.3
Next, the gear. Gears trade torque for speed in a precise ratio. If a 10-tooth driver gear turns a 20-tooth driven gear, the driven gear rotates at half the speed but with twice the torque. The game calls this gearRatio = drivenTeeth / driverTeeth, and it's the torque advantage that matters for chaining. Note that speed and torque are inverses here: more torque means less speed, which is a manifestation of the deeper conservation law that governs all simple machines.2
Then the pulley. A single fixed pulley just redirects force; it doesn't multiply it. But add a movable pulley, and you get advantage from the number of rope segments supporting the load. The formula is straightforward: pulleyMA = number of rope segments supporting the load. Two segments give you 2×, four segments give you 4×. The trade-off is that you have to pull more rope to lift the load the same distance.1
Finally, the inclined plane. Want to raise a heavy crate without lifting it straight up? Push it up a ramp. The gentler the slope, the less force you need, but the farther you have to push. The mechanical advantage is the ratio of the slope's length to its height: inclineMA = length / height. A ramp 4 meters long that rises 1 meter gives you 4× advantage. Again, the force is multiplied, but the distance you push is proportionally longer.1
These four machines are the complete toolkit. The game doesn't give you wedges, screws, or wheel-and-axle systems, even though classical physics identifies six simple machines.1 It focuses on the ones that chain cleanly, each contributing a clear multiplicative factor to your total.
Here's the key insight that separates Gearworks from a mere parts catalog: machines in series multiply. If you connect a lever with 2× advantage to a gear train with 3× advantage, the chain's total mechanical advantage is 2 × 3 = 6, not 2 + 3 = 5. Each stage takes the output force from the previous stage and amplifies it again.1
This is why the puzzle is about composition. You're not just picking machines; you're building a product. A chain of three modest machines, 2×, 2×, and 3×, yields 12× total. A chain of four, 2×, 2×, 3×, and 3×, yields 36×. Every part the game hands you is worth 2×, 3×, or 4× on its own, so the same target can often be reached in more than one way, and part of the pleasure is exploring those factorizations.
There's also the edge case of the empty chain. If you don't connect anything, the chain's mechanical advantage is 1. Force passes through unchanged. This makes sense mathematically (the empty product is 1) and physically (no amplification means no change).1
The chaining rule is deterministic. There's no randomness in how machines combine. Every time you build a chain from the same machines, you get the same total. This determinism is part of what makes the daily puzzle fair: the game derives a seed from the date, and everyone gets the same target and the same bank of parts on the same day, with the same answer.
Why does the game insist on an exact match? Why not accept "close enough"? The answer lies in the idealized physics that Gearworks models. In the real world, friction and imperfections mean that mechanical advantage is never quite as clean as the formulas suggest. A real lever loses some force to friction at the fulcrum; a real gear train loses some torque to tooth friction; a real pulley loses some force to rope friction; a real ramp loses some force to sliding friction.1
But Gearworks doesn't model those losses. It models ideal, frictionless machines, where the mechanical advantage is exactly what the geometry dictates. In that ideal world, there's no ambiguity. Your chain either produces exactly the target mechanical advantage, or it doesn't. The game's evaluation function compares your chain's MA to the target with floating-point-safe tolerance, and the result is binary: exact hit wins, over or under fails.1
This exactness is what makes the puzzle rigorous. You can't fudge it. You can't say "it's close enough." You have to reason precisely about the factors you're multiplying and ensure their product matches the target. It's a test of multiplicative thinking, not just mechanical intuition.
There's also a pedagogical reason for the exact-hit rule. It forces you to think about the factors themselves. If the target is 12, you might factor it as 3 × 4 or 2 × 2 × 3. Each factorization suggests different machine choices. A 3× lever (3:1 arm ratio) chained to a 4× pulley (four supporting ropes) is one solution. A 2× lever, a 2× gear pair, and a 3× ramp is another. Which one is open to you depends on the parts in the day's bank. The game doesn't tell you which is "better"; it just tells you whether you've hit the number.2
What makes Gearworks compelling isn't just the puzzle; it's the feeling of composing small advantages into a precise total. You start with a target that seems arbitrary. You experiment with levers, gears, pulleys, and ramps. You discover that a 3× lever pairs nicely with a 4× ramp. You try a gear pair with a 3:1 reduction and see what that unlocks. Slowly, you build an intuition for how the factors compound.2
There's a particular pleasure in reverse-engineering a target from its factors. If the target is 24, you might recognize that as 2 × 3 × 4, or 2 × 2 × 2 × 3. Each factorization suggests a different configuration. A 2× lever (2:1 arm ratio), a 3× gear pair (a 10-tooth driver turning a 30-tooth driven gear), and a 4× inclined plane (4:1 length-to-height) is one solution. Four stages of 2×, 2×, 2×, and 3× is another, if the puzzle offers four slots.1
This multiplicative thinking is deeply rooted in the physics of simple machines. When machines are chained, their advantages compound. Three modest stages of 2×, 3×, and 2× combine to 12×. Four stages of 2×, 2×, 2×, and 3× combine to 24×. The same total can be reached through different paths, and part of the game's depth is exploring those paths.
At the same time, the game is humble about its scope. It doesn't claim to model the real world perfectly. Real machines lose advantage to friction, which the game deliberately ignores. It models ideal machines, where the mechanical advantage is exactly what the formulas say. This idealization is what makes the exact-hit rule possible, and it's what makes the puzzle clean and rigorous.1
Every time you chain a lever in Gearworks, you're invoking a principle that dates back to the third century BC. Archimedes, the Greek mathematician, is credited with the earliest rigorous proof of the law of the lever: the mechanical advantage is the ratio of the effort arm to the load arm.3 That's exactly the game's leverMA = effortArm / loadArm formula.
Archimedes is also famous for the line "give me a lever long enough and a fulcrum on which to place it, and I shall move the world." It's a loosely-worded version of the original Greek, but it captures the spirit of leverage: small forces, properly multiplied, can accomplish extraordinary things. Gearworks is a digital embodiment of that idea. You're not moving the world, but you are learning how small advantages compound into large ones.3
The other machines in the game have similar histories. The inclined plane was added to the canonical list of simple machines by Renaissance scientists, completing the classical six. The pulley and gear have been used for millennia in everything from water wheels to clockwork mechanisms. Gearworks strips all of that context away and leaves you with the pure math: four formulas, one product, one target.1
But the math is where the beauty is. Mechanical advantage is a measure of force amplification: output force divided by input force. When it exceeds 1, the machine acts as a force amplifier. When it's less than 1, it's a speed amplifier (the gear case is a good example: a 0.5× gear ratio means half the torque but twice the speed). The game focuses on the force-amplifying cases, but the underlying principle is the same: force and distance are traded, not created.1
Simple machines are useful on their own. A lever can lift a heavy rock. An inclined plane can raise a crate. A pulley can hoist a sail. But chaining them multiplies their power. A lever that gives you 2× advantage can feed into a gear train that gives you 3×, which feeds into a pulley that gives you 4×. The total is 2 × 3 × 4 = 24×. That's the compounding of small advantages.1
This is why Gearworks is about composition. You're not just solving a puzzle; you're learning how mechanical systems build on each other. Every machine you add changes the force that the next machine sees. Every gear ratio, every arm ratio, every rope count matters because it's a factor in the product.1
The exact-hit rule enforces precision. You can't approximate. You can't guess. You have to think about the factors and ensure their product matches the target. This is multiplicative reasoning in its purest form, and it's a skill that extends far beyond the game. Understanding how factors compound is essential in everything from engineering to finance to everyday problem-solving. At the same time, the game is forgiving. A miss costs you some points on that puzzle's score, not the puzzle itself: you can rebuild and try again as often as you like. The daily seed ensures that everyone gets the same target, which means you can discuss strategies without worrying about different puzzles. It's a shared experience built on deterministic math.