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 Post subject: Rubik's UFO alternative solution...!
PostPosted: Fri Nov 25, 2005 11:13 am 
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Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Well, I was playing with the UFO and please allow me to share a solution that is good for those who don't want to remember too many routines or generators! :wink:


Rubik's UFO numbering:

Top side:

*** 6 *** 1 ***
5 ********* 2
*** 4 *** 3 ***

Bottom side (imaginary view from the top side):

***12 *** 7 ***
11 ********* 8
*** 10 *** 9 ***


There are four generators in total

a = vertical right flip
b = lower (diagonal) right flip
c = upper (diagonal) right flip
d = clockwise rotation of front side


I used the GAP program to find those sequences (don't get me wrong, there may be simpler ones, but those I already found are easy enough to remember).
The code shows more clearly how the generators a,b,c and d act on the puzzle.

Code for generating the group:

a:=(1,9)(2,8)(3,7);
b:=(2,10)(3,9)(4,8);
c:=(1,7)(6,8)(2,12);
d:=(1,2,3,4,5,6);
G:=Group(a,b,c,d);
Order(G);


The required algorithms (which are the only things required to remember in order to solve the puzzle) are two:

ddda da dbc (must be applied SEVEN times) which swaps 1 and 8 and keeps all the rest invariant.
ad bdddd cd (mus be applied THREE times) which swaps 1 and 7 and keeps all the rest invariant.


corresponding GAP code:

(d^3*a*d*a*d*b*c*)^7; equals (1,8)
(a*d*b*d^4*c*d)^3; equals (1, 7)


It can be mathematically proved, that the above two algorithms are enough to bring the Rubik's UFO into a state where only flips (and no rotations) are required to completely solve it. It all depends on targeting the correct pieces you need to swap. And since there are only 96 combinations of them in that state, there shouldn't be any trouble... right? RIGHT??? :lol:

I realise that there may be simpler formulas, but in a memory point of view (where, the less defined, the better) and if you don't mind applying a simple algorithm seven times (until your fingers get blisters), I think this is not a bad method!



I hope you like it! :-)




Peter


PS In most of times I mixed it and solved it, I only used the first algorithm!!! (that swaps 1 and 8).

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Educational R&D, Gravity, 4D Symmetry, Puzzle Ninja, Matrix Mech, Alien Technology.


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 Post subject: UFO
PostPosted: Thu Oct 26, 2006 1:39 pm 
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Joined: Sat Apr 01, 2006 8:55 pm
Location: Dallas, TX
WHOA!!! I think you are probably an alien from the Planet Uranus!!!

So, I can solve the Rubik's UFO, BUT.... I am having much much trouble with my Kite cube!!

Can you help me out? I always end up with 2 pieces transposed. the one on the top goes to the bottom and the one on the bottom goes on the top. Or maybe its actually 3 or even 4 pieces that are really transposed.

I can take a few photos to send to you. Just bill me your consulting fee as usual and I will wire it into your swiss banc account.

Cheers.


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 Post subject:
PostPosted: Thu Oct 26, 2006 2:35 pm 
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Joined: Thu Nov 20, 2003 7:29 am
Location: San Diego, California
here is my solution for the UFO. most of these i found myself. have fun


Attachments:
Advanced Solution to the Rubik.doc [188.5 KiB]
Downloaded 381 times
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 Post subject:
PostPosted: Fri Oct 27, 2006 8:05 am 
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Joined: Fri Apr 28, 2006 10:29 am
Am I the only one who solves the UFO layer by layer? I discovered a simple solution (2 algs) in about 90 minutes. I won't be breaking any records with it, but the UFO is awkward enough that I don't particularly like playing with it anyway.

But it does fit into a coat pocket nicely, which is not the case with my megaminx or 5x5x5. :-)


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 Post subject:
PostPosted: Fri Oct 27, 2006 10:49 am 
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Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Actually, my solution in this post dates a year ago, I had posted a simpler solution (requiring just one or two simple key moves) around 9 months ago! ;)

And I like Adam's dive into the more complex stuff of the ufo! :)




Pantazis

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 Post subject:
PostPosted: Sat Oct 28, 2006 11:20 am 
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Joined: Fri May 06, 2005 10:13 am
Location: Norway
Hi :)

Adam Zamora wrote:
here is my solution for the UFO. most of these i found myself. have fun


I beat you on the H-perm and the parity 3 8-)

Have fun!

-Per

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"Life is what happens to you while you are busy making other plans" -John Lennon, Beautiful Boy


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