Some facts about Rubik's cube

posted by @ulaulaman about #RubikCube

Rubik's cube is a 3d puzzle game crated by Ernő Rubik.

In a classic Rubik's Cube, each of the six faces is covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. In currently sold models, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white and blue are arranged in that order in a clockwise arrangement.

On of the first optimal solution is dued to Richard Korf

As far as we have been able to determine, we have found the first optimal solutions to random instances of Rubik's Cube, one of the most famous combinatorial puzzles of its time. The median optimal solution length appears to be 18 moves. The key idea, due to (Culberson and Schaeffer 1996), is to take a subset of the goals of the original problem, and precompute and store the exact number of moves needed to solve these subgoals from all possible initial states. Then the exact solution to the subgoals is used as a lower bound heuristic for an IDA* search of the original problem.⁽¹⁾

Some years before this paper, Korf proposed a self-learning software in order to solve the cube:

This paper describes a program which learns efficient strategies for solving problems such as Rubik’s cube and the eight puzzle. It uses a new general problem solving method based on macro-operators. The strategies learned by the program are equal to or superior to strategies used by humans on these problems, in terms of number of moves required for solution.⁽²⁾

Searching about Rubik's cube, I found a couple of curious papers in which the puzzle is applied to study some deseases:

Like Rubik's Cube, the pancreatic islet is a dynamic puzzle comprised of many interrelated components requiring proper alignment and integration. Phospholipid turnover is one “panel” in the islet; however, an obligate role for phospholipase activation in glucose-induced insulin secretion is not yet rigorously established, despite tantalizing, inferential evidence. It may be that glucose serves principally to potentiate the phospholipase and secretory responses to other signals that act by initiating phospholipid hydrolysis.⁽³⁾

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God's Number is 20
David Joyner. Adventures in Group Theory: Rubik's Cube, Merlin’s Machine, and Other Mathematical Toys (pdf)

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(1) Richard E. Korf (1997). Finding optimal solutions to Rubik's Cube using pattern databases. Proceedings of the fourteenth national conference on artificial intelligence (pdf)
(2) Richard E. Korf (1982). A Program That Learns to Solve Rubik's Cube. Proceedings of the fourteenth national conference on artificial intelligence (pdf)
(3) Metz S.A. (1991). The Pancreatic Islet as Rubik's Cube: Is Phospholipid Hydrolysis a piece of the Puzzle?, Diabetes, 40 (12) 1565-1573. DOI: 10.2337/diab.40.12.1565