What is the God's Number of the Rubik's Cube?
----Leslie Leung (Y13)
While countless methods of solving the Rubik's Cube have been discovered, the optimal solution for any scrambled Rubik's Cube remains unresolved. The God's number of the Rubik's Cube is the maximum number of face turns required to solve any instance of the Rubik's Cube 23 . This problem has been investigated since the 1980s by creating upper and lower bounds of the God's Number, but the final answer 20 was not reached until 2010 with the help of Google donating 35 CPU years to perform the necessary calculations. In this essay, we will explore the mathematics behind the Rubik's Cube and how it is used to find the God's number.
Notation and Definitions
A 'move' is defined to be a rotation of 90 o (clockwise/anticlockwise) or 180 o of one of the six faces. Notation for face turns (see image below) 24 : (e.g. F = Front face clockwise 90 o , F'= Front face anti-clockwise 90 o , F2= Front face 180 o )
Notation used to represent cubies: Centres : One letter, e.g. F = centre cubie of the front Face Edges : Two letters, e.g. FU = edge on the boundary of the up and front faces
23 Optimal solutions for Rubik’s Cube (2014) in Wikipedia. Available at: http://en.wikipedia.org/wiki/Optimal_solutions_for_Rubik’s_Cube#Move_notation (Accessed: 19 August 2014) 24 MIT (2009) The Mathematics of the Rubik’s Cube. Available at: http://web.mit.edu/sp.268/www/rubik.pdf (Accessed: 19 August 2014
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