Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum
 It is currently Thu Jul 24, 2014 5:53 am

 All times are UTC - 5 hours

 Page 1 of 1 [ 3 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Megaminx SuperflipPosted: Mon Oct 15, 2012 11:35 am

Joined: Mon Oct 15, 2012 2:32 am
I'm interested in finding algorithms to do a superflip on a megaminx -- that is, to rotate all 30 edge pieces by 180 degrees around a central axis. In particular, I'm interested in approximating the smallest possible length of a superflip. This is a hard number to calculate and is related to God's number for the megaminx. (God's number for the rubicube is 20, and a rubik's superflip takes 20 moves.) Here's what I know so far:

1. A megaminx superflip takes at least 24 moves. Proof: Consider the "join" between a corner piece and a neighbouring edge piece. There are three of these for each corner piece. Each corner piece must leave an edge piece and then come back to it flipped. It can't do this in one move, so it must move twice with respect to that join. That makes a total of 20*3*2 = 120 join changes. Each face move changes 5 joins, so a superflip requires at least 120/5 = 24 moves. (Can a similar proof technique yield a better limit, like 36 or 48?)

2. A superflip can be done in 83 moves. Here are the moves:
[6]'[9]'[4][11] ([1][2]'[1][2]2[3]'2)*6 [11]'[4]'[9][6] ([12]'2[9][11]'[7]'[8]')*9
(Number a face [1], then number touching faces [2] to [6] in clockwise order, then number [7] opposite [2], [8] opposite [3] etc, and finally [12] opposite [1] -- sorry if there's already a standard notation for the whole megaminx but I couldn't find one.)
I found this one by doing a lot of computer searching.

So an optimal superflip takes N moves, and 24 <= N <= 83. I'd be interested to hear if either of these limits can be improved upon... More generally, it would be interesting if there was *any* pattern on the megaminx for which tighter limits than 24,83 could be found.

Top

 Post subject: Re: Megaminx SuperflipPosted: Mon Oct 15, 2012 11:49 am

Joined: Mon Mar 30, 2009 5:13 pm
The upper limit seems very high. All you need to do is find a shorter path than 83 moves. I'm sure someone on this forum (or perhaps the speedsolving forum) can provide an algorithm to beat this limit. Anyone?

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson

Top

 Post subject: Re: Megaminx SuperflipPosted: Mon Oct 15, 2012 11:53 am

Joined: Wed Dec 14, 2011 12:25 pm
Location: Finland
Maybe mention this in the patterns thread?

_________________
My pen-and-paper puzzles

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 3 posts ]

 All times are UTC - 5 hours

#### Who is online

Users browsing this forum: No registered users and 9 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ Announcements General Puzzle Topics New Puzzles Puzzle Building and Modding Puzzle Collecting Solving Puzzles Marketplace Non-Twisty Puzzles Site Comments, Suggestions & Questions Content Moderators Off Topic