Non-Transitive Gears by OSKAR


Hi iMaterialise fans,

Non-Transitive Gears is a puzzling mechanism based on an idea by Alexander Poddiakov. In his article “Intransitive Machines”, Poddiakov writes about non-transitivity, wher A is larger than B, B is larger than C, and C is larger than A. There exist many examples, including non-transitive dice, and non-transitive election results. Poddiakov also showed an example of a set of three gears that are non-transitive. When two of these are put against each other, then A spins faster than B, B spins faster than C, and C spins faster than A. See also Poddiakov’s post at with lots of interesting responses.

A physical implementation would not allow Poddiakov’s gears to be put all three together, as then the mechanism would jam. A solution was the addition of three ratchets. Whichever of the three knobs you turn, one of its neighbours will turn 2x faster and the other 2x slower.

Watch the YouTube video.
Buy the puzzle at my iMaterialise Shop.
Read more at the Twisty Puzzles Forum.
Check out the photos below.




Alexander Poddiakov shows in a paper that Non-Transitive Gears can also be played as a three-player game, where the third player always wins.