Rubik S Cube Math Problem

The simple rubik s cube is a harder problem than most people realize. Here s the solution to that problem. It has 6 different colors and each color is repeated exactly 9 times so the cube can be considered as an ordered list which has 54 elements with numbers between 1 and 6 each number meaning a color being repeated 9 times.

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There is an identity element e g such that e g g e g.

Rubik s cube math problem. Mathematically the rubik s cube is a permutation group. Every element in g has an inverse g 1relative to the operation such that g g 1 g 1 g e. Using the currently provided best algorithm for solving the cube for example would take the computer you re reading this on. Because xyx1y1 xy yx 1 which equals the identity when yx 1is the inverse of xy i e.

For example on one face of a scrambled rubik s cube there may be three red one blue two green two yellow and one orange tile. Xyx1y1 1 exactly when x and y commute. If x and y are two moves on rubik s cube theircommutatoris the move xyx1y1. Sp 268 the mathematics of the rubik s cube the operation is associative so for any elements f g and h f g h f g h.

The teacher can ask what fraction of the visible face do the red tiles represent. The rubik s cube can be connected to fractions ratios and proportional reasoning. When yx xy thus the commutator of x and y measures the failure of x and y to commute.

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