God's Number and the Robotic Turn Metric Public Deposited
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Since the invention of the Rubik’s cube in the 1970s, mathematicians have been captivated with finding out the maximum number of moves needed to solve the Rubik’s cube optimally from any of the cube’s approximately 43 trillion possible positions. This value, known as God’s number, depends on the metric, which is the set of allowed moves. This thesis proposes a new “robotic turn metric” based on allowing antipodal faces of the cube to be turned simultaneously. Although human solvers cannot easily accomplish such moves, they are used by various robotic cube solvers, thus the name. We explore lower and upper bounds for God’s number in this metric and how it compares to God’s number in the Face Turn Metric and Quarter Turn Metric.
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