1. Solving Rubik's Cube
By: Etai Nativ

2. History Invented by Erno Rubik an Hungarian architect
Created as an engineering challenge
Patent in 1975
Mass production 1977
Sold half a billion cubes up untill today

3. The Cube 6 Sides – Center Faces - pivots
Colors – Red, Orange, Blue, Green, Yellow, White (Black)
8 corners
12 edges
Number of legal permutation:
8!𝑋 3 7 𝑋12 ! 2 𝑋 2 11 ≈4.33𝑋 10 19

4. Solutions Optimal solution – God Solution – does not exist yet
1981 – Morwen Thistlethwaite – 100 face moves
1995 – Michael Reid - 29 face moves
1997 – Korf's Algorithm
2009 – Tomas Rokicki proved it takes 29 quarter moves
2010 – Tomas Rokicki, Herbert Kociemba and John Dethrigde set the maximum to 20 face moves

5. Algebra – Group Theory
The space of the group consists of all allowed positions
The group has 6 generators – the rotation of one face 90 degrees clockwise
The states will be represented by a vector of size 48 for each location, the colors will be represented by numbers 1-6
To represent the group operators we will use 48X48 matrix

6. Exmple – ClockWise Turn
Left
Upper
Right
Lower
... 1 :

7. Implementation
Recursive – Brute force
MPI – Manager + Slaves
C/C++

8. Some Optimizations
Can reduce the number of rotations from 18 to 15 by not including steps that repeat the last step
Building a tree data base with 5-6 move 1M-10M
Solution complexity assuming 10M DB:
18𝑋 ≈3.5𝑋 ≈ 2 55