Message #1951

From: schuma <>
Subject: Re: Another {7,3} puzzle
Date: Mon, 12 Dec 2011 04:10:00 -0000

Hi Melinda,

This puzzle ({7,3} FEV turning) is indeed huge. It has 612 pieces, certainly much larger than the {7,3} FT, its dual {3,7} VT, {7,3} ET and {7,3} VT. These simpler puzzles have 100~200 pieces. But {7,3} FEV is smaller than {3,7} ET and {3,7} FT, which have 800~900 pieces. Solving {7,3} FEV is easier than {3,7} ET and FT in several ways:
(1) Fewer pieces.
(2) Shorter algorithms to do pure 3-cycles. All 3-cycle algorithms here are 4-move [1,1] commutators. Easy to remember.
(3) Fewer colors: 24 colors vs 56 colors: easier to find a piece.

I’ve started solving it for a while. Although I’m still in the early stage of this solution, I’ll say it’s a bit tedious. Just too many pieces.

It’s an interesting observation that you can’t see the other copies of the moving circle. The default view is as same as the classic KQ. where you can see the other copies. I think the reason is simple the circles here are smaller than in the classic KQ.


— In, Melinda Green <melinda@…> wrote:
> Wow! That’s amazing, Roice!!
> Here’s the link to the puzzle, just to make it easier for everyone to get:
> Note that there isn’t even an install involved. Just unpack the zip file
> and run the executable. The new puzzle is found in the menus here:
> Puzzle > Hyperbolic > Klein’s Quartic > {7,3} FEV Turning.
> You know it’s funny but I don’t think I had even considered the idea of
> a hyperbolic puzzle with more than one type of twist. I have to say that
> I *really* like the way they work together. It’s funny that the edge
> pieces can’t be moved, they can only be flipped. Of course the face
> centers can’t move either but all the other types can freely roam the
> whole surface.
> Looking closely I now see that you already support a {6,3} with two
> types of twists. I didn’t recall discussing it on the list. Looking at
> it now, it seems like such a frightening crazy-quilt. Somehow this new
> {7,3} with many more colors and three types of twists seems much more
> tractable to me and much more elegant. Might there be other similarly
> {6,3} or perhaps even {5,3} puzzles that are as elegant as this new gem?
> Some minor suggestions:
> * Even with the maximum scramble of 5,000 twists it still doesn’t look
> quite fully scrambled. You might consider adding a "Full" scramble item
> for all of your puzzles and use David’s Goldilocks function at least as
> a starting point to select a good number. One nice thing about a "Full"
> option is that the solver is then assured that that it counts as fully
> solved it they manage to solve it.
> * It seems to need different twisting speeds for the different element
> types.
> * It seems to want a more fitting name. I can’t think what though so
> maybe someone else on the list can suggest one.
> This thing is really huge! I’m noticing that when I twist something it
> is hard to see other copies also twisting. So will this be much harder
> than the other KQ puzzles? What do you think, Nan?
> Tremendous job, Roice! I love it.
> -Melinda
> On 12/11/2011 3:43 PM, Roice Nelson wrote:
> >
> >
> > I added a fun version of the {7,3} which has all three types of
> > twisting. The cuts are shallow, so the puzzle is relatively easy.
> > The vertex-centered and face-centered circles are all tangent to each
> > other. If the puzzle only had these two types of twists, there would
> > only be trivial tips to solve, and face turning twists would scramble
> > nothing. Adding edge-centered twisting makes things much more
> > interesting.
> >
> > With all the tangencies and mutual intersections, the pattern of cuts
> > is quite nice. A picture is here
> > <>.