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The Amazing Rubik's Cube

The main mathematical news

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.

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Additional Theorems / conjectures / Open questions

*  How many scrambled states require at least 16-20 moves?

*  What is “God’s Number” for larger Rubik’s Cubes?

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The main mathematical concepts / Principles

Plane 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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