Download presentation

Presentation is loading. Please wait.

Published byMorgan Stetson Modified over 3 years ago

1
THE MATHEMATICS OF RUBIK’S CUBES Sean Rogers

2
Possibilities 43,252,003,274,489,856,000 possible states Depends on properties of each face That’s a lot!! Model each as a set Define R_0 as the solved state {r_1, r_2, r_4 …, r_9, b_1, b_2, b_3 … b_9, w_1 …} So every set has 54 elements

3
Functions Define f: R_x R_y as this: We have a special name for this: L Similarly, we have R, U, B, D, R^2, L’, R’, etc. These functions are bijections from one set to another Obvious- one-to-one correspondence, |R_x|=|R_y|

4
How to get from A to B R_7 R_6 R_5 R_4 R_3 R_2 R_1 R_0

5
Algorithms We collect these bijections into algorithms (macros) to get from one set to another (when you know the properties of the 2 sets required)

6
Groups

7
Examples

8
To Rubik’s Cubes Our group will be R, all possible permutations of the solved state (remember there are ~43 quintillion) * will be a rotation of a face (associative so long as order is preserved) Inverse is going the opposite direction

9
Cycles and Notation Cycle- permutation of the elements of some set X which maps the elements of some subset S set to each other in a cyclic manner, while fixing all other elements (mapping them to themselves) (1)(2 3 4) 1 stays put, 2, 3, and 4 are cycled in some manner Ex. {1,2,3,4} {3,4,1,2} is a cycle You can’t just switch 2 blocks- permutations are products of 2-cycles Ex. (1 2 3)=(1 2)(1 3) Analogue- Prime factorizations

10
Importance of Cycles

11
Conjugacy

12
The Cube Several methods to solve They make even bigger, harder cubes You don’t need this math though- its just a rigorous way of defining a puzzle Invented in 1974 by Ernő Rubik

Similar presentations

OK

Mathematics for IT Lecture 4 trigonometric. TRIG REVIEW Trig Function Evaluation : How to use the unit circle to find the value of trig functions at some.

Mathematics for IT Lecture 4 trigonometric. TRIG REVIEW Trig Function Evaluation : How to use the unit circle to find the value of trig functions at some.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on object-oriented programming examples Ppt on pin diode application Ppt on applied operations research analyst Ppt on indian culture and tradition free download Ppt on case study of mcdonald's Ppt on yamuna action plan Ppt on home automation using rf Make a ppt on how to control noise pollution Ppt on indian sea ports Ppt on social networking addiction