Rubik S Cube Mathematics

Each of the six sides is painted a distinct color and the goal of the puzzle is to return the cube to a state in which each side has a single color after it has been randomized by.

Rubik s cube mathematics. Just a couple of years later toy company ideal negotiated an agreement to sell the cube worldwide. Twelve edge cubies each with two stickers on them. Eight corner cubies each with three stickers on them. The immediate math to be done with those numbers is the total number of ways you can scramble a rubik s cube.

Every element in g has an inverse g 1relative to the operation such that g g 1 g 1 g e. 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. 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. Rubik s cube takes its name from its creator hungarian sculptor designer and architect ernő rubik born on july 13 1944.

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. Rubik s cube is a 3 3 3 cube in which the 26 subcubes on the outside are internally hinged in such a way that rotation by a quarter turn in either direction or a half turn is possible in any plane of cubes. There is an identity element e g such that e g g e g. Written in a more mathematical way that number is 3 8 8.

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. In 1974 rubik patented his creation in hungary and in 1977 sales in the country began.