Gearo

This CAD model was designed by Oskar van Deventer, copyright (c), 24 December 2022

Gearo is based on an idea by Bram Cohen: "We want three gears where two of them can get rotated at once while the other is forced to stay in place. Since you want the LCM on any two gears to not be 1 and them to all be about the same the cleanest set is 12, 15, and 20 teeth on the gears. That's probably the nicest 'simple' puzzle. There are lots of ways of adding more gears to it which result in interesting nuances to the solve experience but that also makes it a lot more mathy and less simple, and even that set of three might be pushing it. An interesting mechanism for three gears would be a setup where all three gears were on a very short track where they can move in and out and there's something which rotates about the center and forces them slightly in and out as it rotates and is set up so that there are three places where it just barely pulls in two of the gears enough that they aren't locked by a notch which is on the outside holding them in place but meshes them in the process."

The resulting puzzle uses magnets to keep the three gears pulled together. One can pull a gear outward. Once pulled outward, pins prevent a gear from rotating, so that only the two inners ones can rotate. A plate prevents more than one gear from being pulled outward. The most intuitive way to play this puzzle is to rotate a gear. Depending on the direction of rotation, another gear rotates with it, and the third gear is pushed outward. This way, the third gear remains stationary, locked by a pin, while the other two rattle under it. One could rotate backward, but that requires one to pull the third gear outward manually. Intuitively, people only make those rattling moves. Even though there are only three gears, the puzzle is far from obvious to solve. Intuitively, people rattle one gear up and down till two gears get aligned. This still leaves a 1-in-12 chance, or lower, that the puzzle turns up solved. And even from two gears aligned, it is non-obvious how to get the third one right.