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Using the currently provided best algorithm for solving the cube for example would take the computer you re reading this on.
Rubicks cube math. The math of the rubik s cube by larry hardesty massachusetts institute of technology erik demaine s collection of rubik s cube type puzzles includes cubes with five six and seven squares to a. The simple rubik s cube is a harder problem than most people realize. Because xyx1y1 xy yx 1 which equals the identity when yx 1is the inverse of xy i e. The immediate math to be done with those numbers is the total number of ways you can scramble a rubik s cube.
Xyx1y1 1 exactly when x and y commute. Rubik s cube lends itself to the application of mathematical group theory which has been helpful for deducing certain algorithms in particular those which have a commutator structure namely xyx 1 y 1 where x and y are specific moves or move sequences and x 1 and y 1 are their respective inverses or a conjugate structure namely xyx 1 often referred to by speedcubers colloquially as a setup move. When yx xy thus the commutator of x and y measures the failure of x and y to commute. If x and y are two moves on rubik s cube theircommutatoris the move xyx1y1.
See if you can solve this famous puzzle in this great version by eric lin. Written in a more mathematical way that number is 3 8 8. Mathematically the rubik s cube is a permutation group. 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.
Play rubiks cube puzzle. Every element in g has an inverse g 1relative to the operation such that g g 1 g 1 g e.
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