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5:12 AM
@Randal'Thor I added my vote to Maltese literature just now to break the tie. :) (I'd already upvoted the suggestion for Bibhutibhushan Bandyopadhyay.)
 
 
1 hour later…
6:28 AM
0
Q: Meaning of a Phrase In the The 'Third Level' Book by Jack Finney

HrishiI turned into Grand Central from Vanderbilt Avenue, and went down the steps to the first level, where you take trains like the Twentieth Century. Can somebody please elaborate on this phrase 'where you take trains like the Twentieth Century.' PS: I'm an Indian, so I'm unable to relate to the west...

 
@bobble Seen it, haven't voted or answered yet. My TL;DR is that it's potentially a useful question with useful answers for Rubik's cube people, and especially the top answer shows how this real problem is solved in practice.
@Namaskaram Thanks :-)
There's a whole bunch now scoring 4, so we might have another tie situation at the end of next month.
 
I'll try to help out next month, too :P But, how are ties usually resolved?
 
2
A: Rule for selecting a topic challenge among those with the same number of votes

Rand al'ThorI propose: pick the oldest suggestion. Using a criterion based on number of downvotes or upvotes will quite often result in a tie: if two answers are both sitting at (for example) +4 / -1, then we're right back in the same situation needing to find a tie-break criterion. The criteria based on age...

 
Ahh, okay
@Randal'Thor I think it's an interesting question about how one can rigorously define a "random" configuration of an n^k Rubik's cube. I recently came across the probabilistic method, and was taking a look at the Erdős–Rényi model for generating random graphs... Fascinating stuff! I don't know if there's any literature on the Rubik's cube from this angle, though.
 
7:10 AM
I think there is some published mathematical literature on the Rubik's cube.
Like proving the maximum number of twists needed from any position to solve it (apparently around 20 for a standard 3x3x3 cube).
 
Oh definitely. But specifically about how to randomize, I'm not sure.
I think that the minimum number was arrived at through brute force computation, though. I remember being a tad disappointed, which is why the factoid is stuck in my head :(
 
There's a good deal of literature (probably mostly combinatorial) on recreational maths like games and puzzles.
I keep meaning to self-answer this question based on some searching in academic papers.
 
7:36 AM
@Randal'Thor Upvoted and bookmarked :) I read Gareth's answer, but the rest will still take me time. The OEIS sequence is terribly short. :( A closed-form solution may be too much to expect, but one may try to get some asymptotic results perhaps...
I'm only just starting to dive into this sort of stuff. Entering combinatorics was completely unplanned when I joined the PhD program :)
 
Combinatorics was about the only pure-maths course I didn't take as an undergrad. I know it just to the level of some olympiad stuff, but no further.
 
That's still a lot more than what I knew when I went to talk to my professor about doing a PhD under him :P
I never looked at Olympiad material seriously when I was an undergrad. At that time I had the impression that there was not much depth in the "bag of tricks" that one needs to know to solve those kinds of problems.
 

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