1995: At least 20 moves are necessary for solving certain scrambled states of the Rubik’s cube. (A move is any rotation of any face).
2010: 20 moves are sufficient to solve any scrambled state.
2011: The optimal number of moves for an n×n×n Rubik’s Cube is proportional to n2/log(n)
2014: 26 is “God’s number” for moves limited to quarter-turn
2018: A robot can solve any Rubik’s Cube in 0.38 seconds.
To the MNS presentation* How many scrambled states require at least 16-20 moves?
* What is “God’s Number” for larger Rubik’s Cubes?
To the MNS presentationPlane and solid geometry (MSC2010#97G40)
* Cube (edge, face, vertex, rotation axis)
* Congruence
Combinatorics (MSC2010#97K20)
* Combinatorics
* The multiplication principle
Logic (MSC2010#97E30)
* Constructive proof
Groups, rings, fields (MSC2010#97H40)
* Lower/upper bound
* Sufficient/Necessary condition
* Group theory
*Algorithm
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