Which Algorithm Is the Most Efficient in Solving Alexander's Star?

Overview

Objectives/Goals To identify the most efficient algorithm in terms of time and number of moves (rotations of 72 degrees upon the puzzle's twelve axes of rotation) required to solve the twisty puzzle Alexander's Star (the ultimate configuration). This could ultimately be applied to handle configurations of software and data on computers. Methods/Materials Alexander's Star is manually subjected to two algorithms Optimal solution and God's Algorithm, with one trial for each algorithm consisting of 15 tests each. The puzzle's configuration is randomized before each test (in order to avoid the repitision of results). Materials: written algoriths; stop watch; alexander's star puzzle; data log to record results. Results OPTIMAL (TRIAL 2) RAW DATA 1/18/2008 mental reasoning(control ) 3 48.18 67 time moves mean 4 08.89733333333333333 71.93333333 median 4 29.82 71 mode none 69 range 54.66 22 SUBJECTION OF ALEXANDER'S STAR TO GOD'S ALGORITHM RAW DATA mental reasoning(control ) 3 48.18 67 time moves MEAN 3 26.096 55 MEDIAN 3 34.91 54 MODE NONE 57 RANGE 1 05.28 29 Conclusions/Discussion Generally all of the ultimate configurations generated by God#s algorithm were the most efficient in terms of times to moves and the applicability. Then the traditional logical reasoning method (the control )and finally the optimal solution was the least efficient in terms of moves to time and was a bit more challenging or cumbersome to apply (hence generating ultimate configurations in a greater allotment of time) and generally the most frivolous. In short my hypothesis was supported through all examinations of

Competition history

• CSEF 2008 Mathematics & Software · Entry J1303

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