MAT 101 Lecture Notes - Lecture 14: Pocket Cube, Rubik'S Cube

• School: University of Maine
• Department: Mathematics and Statistics
• Course: MAT 101
• Professor: Kevin Roberge

Document Summary

Rifi: how many pieces were affected by fr, example: fr, how many pieces were affected by fr, there are 13 pieces affected, six corners and 7 edges. Orientation is tricky: example: fr, cycle structure (ufl, ubr, dbr, dfr, dfl) : 5-cycle (uf, ur, br, dr, fr, df, fl) : 7- cycle (ufr) : 3-cycle order: example: fr, cycle structure (ufl, ubr, dbr, dfr, dfl) : 5-cycle (uf, ur, br, dr, fr, df, fl) : 7- cycle (ufr) The smallest number that 3, 5, and 7 go into is 105. It affects so much of the cube (13 pieces out of all 20 of them: an order of 105 (meaning that things are so messed up that it takes 105 repetitions to restore it, vs (f. 3 which affects four pieces with an order of 2: long cycles, 5 corners and 7 edges, so repetition does(cid:374)"t look pro(cid:373)isi(cid:374)g. (cid:894)fr(cid:895)5 leaves 7 edges messed up (fr)