“You see people around here with Rubik’s cubes; well multiply that by ten and that’s what it was like in the 80s,” Hoffman said. “Everyone was crazy about (them).”

The craze for the Rubik’s cube is starting once again as Hoffman introduces his students to group theory, a college level of math that relates to the rotations involved in solving a Rubik’s cube. A group consists of a set of elements which follow certain rules when an operation is performed on them. Hoffman explained that moves on Rubik’s cubes are considered elements of a group and by using rules of groups students can learn the theory behind the formulas which solve the cube. The Rubik’s cube has 43 quintillion arrangements, which can be thought of as a group, and any twist of the cube will render another element of the group, according to Hoffman. Rules of group theory help students develop moves to solve the cube without disturbing previous moves. Students learn to make a move and then do the inverse of it to bring the previous configuration back into place.

Students are learning the application of group theory through modular arithmetic, a fixed math where there is a finite number of elements in a set. Rather than arranging numbers on a number line, modular math arranges numbers in a circle. One phenomenal aspect of modular addition includes learning why 2+2=1, not 4. For example, mod 3 arranges the three elements 0, 1, 2 in a circle. Starting at 2 and moving two spots clockwise around the circle would result in 1. “Certain rules that apply to modular addition apply to elements on a Rubik’s cube,” Hoffman said.

First Hoffman wanted to incorporate the Rubik’s cube in his course to expose his students to higher level math. “The second reason is to just learn for the sake of learning,” he said. “It’s fun to do things like learn about the geometric symmetry of cubes.”

Many students express excitement over the Rubik’s cube, despite the difficult abstract theories they have to learn. “I see it as a pretty cool talent to have,” senior Rebecca Hu said. “I want to learn so I can have Rubik’s cube competitions with my family.” Senior Madina Tugizova said she also enjoyed learning about the cube. “It’s pretty fun and it’s a good way to spend the last two weeks of school,” Tugizova said. “For four years, you spend all the time learning math formulas and you finally see that you can apply it to something fun.” She said that many students are already showing off their new skill outside of class. “You can see that (the Rubik’s cube) is really a big deal to some people and you can see them showing off how fast they can do it,” Tugizova said. “For the people who don’t know it yet, in a couple of weeks we’ll be able to show off too.”

Although the Rubik’s cube was hottest while Hoffman was in middle school, he did not get involved with it until later. “I could never do it,” he said. “I didn’t learn how until four years ago when I started teaching.” He bases his approach in teaching the Rubik’s cube on a solution guide from a puzzle solving Web site (www.puzzlesolver.com), which he thinks gives the best explanation.

“About ten percent of the students know how to do it before I teach it to them,” Hoffman said. “If you learn about 20 formulas you can do it in about 120 turns.” But it’s often more difficult than that. “Even with formulas it’s not easy,” he said. “There are multiple formulas in each situation and you have to decide which ones to use. The easier the formula is to learn, the longer it takes to (solve the puzzle).”

“Rubik’s cube masters know about 100 formulas or more,” Hoffman said. “They can see the whole solution in their head. They do it under 45 to 50 turns, so that’s about three turns per second.”

To test the students on the tough theories and formulas, Hoffman will give them a Rubik’s cube to solve as the final test of the year.