Message #1496

From: Andrey <andreyastrelin@yahoo.com>
Subject: [MC4D] Re: MagicTile Extension in Superliminal/Wiki
Date: Sat, 05 Mar 2011 12:27:54 -0000

I haven’t seen neither this puzzle nor M12 before.
At first I found that operation X1=SR9SL9 keeps all balls from 6 to 11 in place, and performs permutation of order 3. Then my idea was to find for any given ball operation that keep balls 6,7,8,9, and sets the given ball to place 5. I took operations X1, X2=X1*X1, Aij=R*Xi*L*Xj (i,j=1,2) and Bij=R2*Xi*L2*Xj. It was easy to draw tansformation graph for them and find a way from any point to "5".
By this operations I put five balls (say, 1,2,3,4,5) in raw. Unfortunately ather balls were un disorder (one of 47 wrong states), so I set 0 before 1 (and lost ball 5), then 23 before 0 and so on. After 10 or 15 such operations puzzle appeared in the solved state. I don’t know why.
What is interesting - to fing group that is generated by these permutations. It’s easy, that spots are numbers from Z/23Z with "infinity" number, so that rotation of circle works like +1 or -1. Swapping is some fraction like P(x)/x (or P(x)/Q(x), where Q(0)=0), and I’m trying to find it. Their hint says that it may be about some object in 5 dimensions, but I don’t see it now.

Andrey

— In 4D_Cubing@yahoogroups.com, Melinda Green <melinda@…> wrote:
>
> Wow.
> Just, wow.
> OK, please do tell us if you’ve seen these before and how you solved it?
>
> -Melinda
>
> On 3/4/2011 11:45 PM, Andrey wrote:
> > Solved :)
> > Took about two hours.
> >
> > Andrey
> >
> > — In 4D_Cubing@yahoogroups.com, Melinda Green<melinda@> wrote:
> >> I like Andrey’s and Roice’s opinions on missing log files. "B.L." is a
> >> very clever notation. It also seems like a term with applications that
> >> extend beyond our needs.
> >>
> >> Andrey talks about very hard puzzles, so I’m going to share a new one
> >> that I think is also very hard. You can find it here
> >> <http://www.scientificamerican.com/media/inline/2008-07/puzzles/m24.html>.
> >> Be sure to notice the "Help" button for instructions and hints. It
> >> doesn’t support log files but it *does* display history that you can
> >> copy. It does support macros however. I’ve never solved it but let’s see
> >> who here can validly claim to have solved it first. Ready.., set…,
> >> GO! :-)
> >>
> >> -Melinda
>