# Message #2409

From: Melinda Green <melinda@superliminal.com>

Subject: Re: [MC4D] Re: Which is the most difficult for it’s size?

Date: Fri, 05 Oct 2012 20:45:08 -0700

I checked with Roice and he is all for adding names to any of the MT

puzzles. I asked because I would like to see these difficult puzzles

stand out in the tree. Now the problem is deciding what to name these

bad boys. Anybody have suggestions? Feel free to propose names for other

puzzles as well.

-Melinda

On 10/5/2012 11:09 AM, Andrey wrote:

> {8,3} FT is more difficult - it has two types of moving pieces (2C and 3C, like 3^3). You can use some algorithms from 3^3, but be very careful with them. In ET you can work just with orbits of 2C, and only thing there is to remember that some commutators are forbidden (they work on two orbits in the same time).

>

> I’ve updated HOF. Now my count is 44.

>

> Andrey

>

> — In 4D_Cubing@yahoogroups.com, Melinda Green <melinda@…> wrote:

>> I don’t see Andrey’s {8,3} 10-color FT entry in the wiki HOF. How do you

>> guys feel about it’s difficulty compared to the. {8,4} 9-color ET? Which

>> is the baddest boy of the bunch?

>>

>> On 10/4/2012 9:38 PM, Melinda Green wrote:

>>>

>>> Definitely interesting. 2 questions come to mind.

>>>

>>> 1. Can you construct a puzzle in which all the octagonal edges

>>> contain digons, and

>>> 2. Can you flip some or all edges in order to create non-orientable

>>> versions?

>>>

>>> -Melinda

>>>

>>> On 10/4/2012 8:15 PM, Roice Nelson wrote:

>>>> Cool stuff! Taking a look, the underlying abstract shape has 10

>>>> faces, 24 edges, and 16 vertices. So its Euler Characteristic is 2,

>>>> and it has the topology of the sphere. This means the graph of it

>>>> can be drawn on the plane:

>>>>

>>>> http://www.gravitation3d.com/magictile/pics/83/83-10_graph.png

>>>>

>>>> Here is the unrolled version for reference:

>>>>

>>>> http://www.gravitation3d.com/magictile/pics/83/83-10_unrolled.png

>>>>

>>>> The first pic nicely shows how by starting your solution with the

>>>> digons (the "order 2" faces), it will be similar to solving a 3^3

>>>> starting with the middle layer.

>>>>

>>>> The "irregular" octagonal faces are interesting. I initially thought

>>>> these faces were hexagons in the abstract, until I realized they

>>>> shared multiple disjoint edges with the same neighbor. I hadn’t seen

>>>> anything like that before.

>>>>

>>>> Cheers,

>>>> Roice

>>>>

>>>>

>>>> On Fri, Sep 28, 2012 at 4:02 AM, Andrey <andreyastrelin@…

>>>> <mailto:andreyastrelin@…>> wrote:

>>>>

>>>> {8,3} 10 colors puzzle is an another strange beast. It has four

>>>> faces of order 2 (i.e. each of them has only 2 neighbors), two

>>>> faces of order 4 and 4 "irregular" faces. And if you start to

>>>> solve it from order 2 faces (that is good idea because puzzle is

>>>> the most dense there), you find yourself in situation where you

>>>> have two disjoint unsolved "layers" - around order 4 faces - and

>>>> have to sort pieces and exchange parity/orientation between them

>>>> (like when you solve 3^3 starting with the middle layer).

>>>> And there is a chance to meet parity problem: some 2C pieces

>>>> are identical and if odd number of pairs are swapped, you’ll need

>>>> to solve it (by swapping some pair once more). And repeat sorting

>>>> of order 4 layers again :)

>>>> Nice thing :)

>>>>

>>>> Andrey

>>>>

>>>

>>>

>>>

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