Message #1316

From: Melinda Green <>
Subject: Re: [MC4D] 8Colors solved
Date: Thu, 30 Dec 2010 16:11:19 -0800

You make a great point, Roice. I’ve gone over and over this in my mind
for a while now, and many times I thought I had some simple answers but
in the end I guess that I feel the same way that you do. It’s not the
hyperbolic space that throws me but the fact that this tiling involves
cells which each have an infinite number of faces. I bet it would be fun
to see a similar puzzle from tiling that contains both finite and
infinite cells. This is really fascinating stuff!


On 12/30/2010 10:14 AM, Roice Nelson wrote:
> […]
> For choosing the targets, I just tried to look at all the cells close
> by. Since there can be non-orientable topologies where some nearby
> copies are mirrored and others are not (an example in the 2D case is a
> hexagonal periodic painting that is topologically a Klein bottle), I
> was aware that looking at only a few nearby cells wouldn’t prove
> things are orientable. So in truth, I didn’t have 100% confidence in
> my claim that the 8Colors puzzle was orientable. Perhaps there is
> some rule by which you could guarantee you’ve looked at enough copies,
> though I don’t know what that might be. In any case, I agree with
> your guess :)[…]
> On Tue, Dec 28, 2010 at 3:53 PM, Melinda Green
> < <>> wrote:
> Hey, that is a really clever idea, Roice! I don’t know if I would
> have thought of that method but now that you point it out I see
> that it is definitely the most natural way to answer that
> question. One thing you didn’t mention was your method of choosing
> your target copy. I think that you would need to choose a face
> that appears to twist in the opposite direction to the starting
> face of the 4C piece that you then send on its journey to the copy
> face. I’m going to guess that puzzles are always orientable when
> twists of face copies are all in the same direction as the clicked
> face. I’m a little surprised that the inverse is not always true.
> -Melinda
> On 12/28/2010 9:02 AM, Roice Nelson wrote:
>> […]For any interested, to check to see if the puzzle was
>> non-orientable, I traced paths from a cell to its copies, then
>> looked to see if any of the 4C pieces in the copy appeared
>> mirrored relative to the parent cell.