## Professor tetraminx puzzle
[Tetraminx](https://alpha.twizzle.net/explore/?puzzle=professor+tetraminx) is a tetrahedron-shaped puzzle similar to [Rubic's cube](https://en.wikipedia.org/wiki/Rubik%27s_Cube). Tetraminx comes in different sizes, usually denoted as "regular" (often referred as just "tetraminx"), "master", "professor", "royal" and "emperor". 

![](https://www.googleapis.com/download/storage/v1/b/kaggle-user-content/o/inbox%2F2262596%2F0d6ec8f2c24142390f062df50f121c9f%2Fdiagram-20250829%20(4).png?generation=1756485108536781&alt=media)


In contrast to mechanical puzzles,  we consider each tile to have its own "color" (number from 0 to 87 - shown as "a,b,c..." on the pictures).  So states are vectors which are permutations of numbers 0…87. In that setup [Professor tetraminx](https://alpha.twizzle.net/explore/?puzzle=professor+tetraminx) puzzle contains 1.846 · 10^33 states, which is small enough to get meaningful results relatively easily, but large enough to provide a challenge for the participants. For comparison Rubik's cube 333 has 4.3 · 10^19 states, while  444:  7.4 · 10^45 states. So it is between these two.