• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 35,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

Cube probability and coin flips

Joined
Dec 26, 2015
Messages
35
Likes
29
Location
Brazil, MG
WCA
2015CAMP17
YouTube
user/afonsocampos20
Thread starter #1
Have you ever considered the probability of getting a random state cube solvable optimally with n moves? Well, I have. Since normal probability are not that readable when talking about cube, one can picture the scene with exciting coin flips.

The chance you get a cube that can be solved with 10 moves is approximately the same as getting 28 Heads in a row in a coin flip (or 5.37e-07%. See, coin flips are better).

Here's a table:

Moves

Flips



Now, how was that calculated? Well, first we can go to http://cube20.org/. The number of cubes solvable with 10 moves is c10 = 232,248,063,316 and but the total number is ctotal = 43,252,003,274,489,856,000. So, ctotal is approximately 186,231,922.2686 times c10. Taking log2 (to calculate coin flips) we have 27.4725. Its ceiling is 28. Repeating this process, we can build this table.
 
Last edited:
Top