Rubiks Cube Math

Mathematically the rubik s cube is a permutation group.

Rubiks cube math. The immediate math to be done with those numbers is the total number of ways you can scramble a rubik s cube. The rubik s cube can be used to conceptualize surface area and volume as well as exhibit a net of a familiar three dimensional solid. If x and y are two moves on rubik s cube theircommutatoris the move xyx1y1. Mathematics of the rubik s cube factorals and exponents.

Because xyx1y1 xy yx 1 which equals the identity when yx 1is the inverse of xy i e. Written in a more mathematical way that number is 3 8 8. 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. Every element in g has an inverse g 1relative to the operation such that g g 1 g 1 g e.

Factorals and exponents download. Students will explore the possible number ways the pieces of a 3x3 rubik s cube can be arranged and still fit the criteria for a rubik s cube. Xyx1y1 1 exactly when x and y commute. 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.

There are several connections one can make between the rubik s cube and math. When yx xy thus the commutator of x and y measures the failure of x and y to commute. Play rubiks cube puzzle. There is an identity element e g such that e g g e g.

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. Click and drag to move. It s also a mathematical curiosity which can be used to explore concepts in the field of set and group theory. The rubik s cube can be connected to fractions ratios and proportional reasoning.