∞∞∞ Daniel Pass - Chess and Rubik's Cubes ∞∞∞

Rubik's Cubes and Chess

    Several years ago, the sources of my inspiration for both Chess and the Rubik's Cube had nothing at all to do with education.  However, it was clear that I was onto something when I brought several cubes to school while working as substitute in mid-city Los Angeles.  To my surprise, almost all students were excited to explore the puzzle!  Two was not enough for a class that did not have a lesson plan for the day.  Now I understand very well that even those students that hate math with a passion can become intrigued by the math of the most popular puzzle game ever sold.

So Much Mathematics!

     There are 43,252,003,274,489,856,000 "permutations", or possible positions, of a standard 3X3 cube.  This is more than 43 quintillion, and to put this into perspective, "if one had as many 57-millimeter Rubik's Cubes as there are permutations, one could cover the Earth's surface 275 times." (Wikipedia)  Chess is unimaginably more complex than the standard Rubik's Cube.  A mathematician named Claude Shannon estimated the number of possible chess games in 1950.  The "game-tree complexity (is) at least  10¹²³ ... As a comparison, the number of atoms in the observable universe, to which it is often compared, is estimated to be between 4×10⁷⁹ and 10⁸¹." (Wikipedia)

     I find it fascinating that it wasn't until July 2010 that the lowest number of turns to solve a Rubik's Cube from any position was proven.  Before two years ago, this was an open problem and we did not have the answer (the answer, by the way, is 20)!  There is more mathematics involved with the cube itself, and the solutions of the cube are interesting as well.  "Speedcubers" compete in many countries throughout the world in many categories including blindfolded, multiple blindfolded, fewest moves, one-handed, and feet solving as official categories.  These include from 2X2 up to 7X7 cubes.  The fastest speedcubers of the traditional cube all use the same method, which includes the memorization of exactly 78 patterns.  These are very mathematical in their structure, and for each "situation" of these 78 patterns, speedcubers often choose their own patterns that they prefer.  For each of the 78 "situations", there is between 5 and 20 choices of patterns that will all work.  Click here to see what I mean.

Mr. Pass's Beginner's Solution

    With words like "algorithm" commonplace in all solutions, I edited my own  version of one of the best sources online for learning how to speedcube.