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 Post subject: Pantazis' Z8
PostPosted: Thu Jul 16, 2009 1:16 pm 
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Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
You all know I love maths.

In one of the older posts, I said I will test the properties of the "Frame" magic,
which was first invented by Juozas Granskas.

Here is the result:

Attachment:
Pantazis_Z8.jpg
Pantazis_Z8.jpg [ 128.81 KiB | Viewed 675 times ]



Note that this puzzle has *exactly* eight flat states, and I made it such each state
is one of the numbers 0, 1, 2, 3, 4, 5, 6, and 7, which correspond to the cyclic group
of eight elements Z8.

Everything in this puzzle is cruciallly important, even the way it is firstly strung.
And each solved state will use three tiles to represent one number on the left
with a background of the same color.

But the most amazing thing, is that, to go to the next or previous number, the EXACT
(slightly complex) sequence is needed.

Aaaah... I always loved cyclic groups, especially the Z8 (aka C8).

:)


Pantazis


PS. To see an interesting difference, the four square-tile magic is not related to a cyclic group,
but to the Dihedral group D8 (or D4).
PS2. Will try to make a video of the "countdown" from 7 to 0.

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 Post subject: Re: Pantazis' Z8
PostPosted: Thu Jul 16, 2009 1:20 pm 
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Joined: Mon Mar 30, 2009 5:13 pm
Very nice! Could the same algorithm be applied to cycle between successive pairs of numbers? Or do you need a unique algorithm for each transition?

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 Post subject: Re: Pantazis' Z8
PostPosted: Thu Jul 16, 2009 1:39 pm 
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Joined: Tue May 26, 2009 7:36 pm
Location: Kokomo, Indiana USA
Awesome puzzle OVERLOAD!!!
AGH!
So many wicked awesome puzzles at one time!

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 Post subject: Re: Pantazis' Z8
PostPosted: Thu Jul 16, 2009 1:47 pm 
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There are eight different positions to start the move, and there is no other way to move it around.
Half of those go forward (i.e. +1), and half go backward (i.e. -1).

For example, to go from 0 to 3, you need to go first to 1 and 2. You cannot go directly to 3.
(or you can go from 0 then to 7, 6, 5, 4, and then arrive to 3).
Sounds to me like a puzzle which can give bad times for speedsolvers! 8-)

A video will be presented shortly.

:)


Pantazis

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 Post subject: Re: Pantazis' Z8
PostPosted: Thu Jul 16, 2009 1:53 pm 
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kastellorizo wrote:
There are eight different positions to start the move, and there is no other way to move it around.
Half of those go forward (i.e. +1), and half go backward (i.e. -1).

For example, to go from 0 to 3, you need to go first to 1 and 2. You cannot go directly to 3.
(or you can go from 0 then to 7, 6, 5, 4, and then arrive to 3).
Sounds to me like a puzzle which can give bad times for speedsolvers! 8-)

A video will be presented shortly.

:)


Pantazis

Understood, but is it the same algorithm to go from 0 to 1 as 1 to 2, and so on?

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 Post subject: Re: Pantazis' Z8
PostPosted: Thu Jul 16, 2009 1:57 pm 
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Kelvin Stott wrote:
Understood, but is it the same algorithm to go from 0 to 1 as 1 to 2, and so on?



Yes, I made it exactly the same, and this is shown in the video.
And it was a real challenge because there were many other ways that it could have been made.
But I wanted to make it right!

Video here:
http://www.youtube.com/watch?v=-eq3bVp5lWE

;)


Pantazis

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