Message #754

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Chronicles of a Rubik junkie’s experience with the {5}x{5}
Date: Mon, 02 Nov 2009 00:55:35 -0600

And yeah, it seems that 4^3 is unique in this regard. What about naming
conventions though? How do you decide what to use to notate the standard
hypercube, {4}x{4} or {4,3,3}? I’m not sure if there are other degeneracies
in naming conventions, so it’s possible this is the only case like this.

Yeah, the multiple names for a single object seems it may be confusing at
times. My personal thought on this was that I’d use {4}x{4} or {4,3,3} or
3^4 as needed depending on the context. I was favoring the first in my last
email since the discussion was all centered around duoprisms. I also see I
mistyped the 3^4 as 4^3 at one point. Oops, hopefully the mistake was
obvious and my intended meaning clear to those reading.

I have a question too: how do we decide which puzzles will be recorded on
the wiki record page? Since it’s a wiki, are we going to allow any puzzle?
I only ask because I realized that there are an infinity of duoprisms
possible to solve by using the "invent my own" feature, limited only by the
solver’s patience (and possibly computer specs :P). Couple this with the
fact that as you go higher, I don’t think the puzzles get fundamentally more
difficult, just much longer. I suspect that the algorithms can be
generalized for the duoprisms of higher order, much like how if you can
solve 3^4, 4^4, and 5^4, you should be able to adapt the algorithms to solve
any n^4 hypercube with enough time. Nevertheless, it is still quite a feat
to be able to solve these higher order puzzles, and I would not be opposed
to allowing such higher order records to stand.

My vote is to go ahead and add these to the wiki, and after seeing your
{6}x{6}, I did wonder if we should perhaps try to officially support uniform
duoprism up to {10}x{10}, and by that I mean show them in the UI (entered
now as issue 80
<http://code.google.com/p/magiccube4d/issues/detail?id=80>if anyone
wants to weigh in). In any case, I think it is safe to say the
puzzle engine can safely handle any {n}x{m} with n and m between 4 and 10
right now, which is a lot of firsts for people to grab.

Also, will the next release allow all possible twists for length 2 puzzles?
What will happen to the records of these puzzles set with the more limited
twists? And yes, I realize both of these questions put 3 of my 4 firsts on
thin ice, which was actual part of my motivation for going for the
dodecahedral prism this weekend, since that should be a permanent one :D.

This is trickier, and I doubt we’ll do it for 4.0. We did enter the thought
to perhaps mark the current puzzles in a special way to note their
limitation in the mean time (see issue
72<http://code.google.com/p/magiccube4d/issues/detail?id=72>).
That way, if the puzzles are ever enhanced in the future, we could at least
be clear on what solutions were done with what puzzle behaviors. If anyone
has opinions on this issue, we’d love your feedback as well. The
fundamental problem here stems from the fact that length-2 puzzles don’t
have enough stickers to represent all the grips of the parent polytope. On
the 2^4, this was handled by making where you click on the sticker do
different things (each sticker maps to multiple grips instead of just one).
This has caused a number of complications in the coding though, and for
these reasons Melinda and I are not inclined to further propagate this
design to the other puzzles, at least for now (we have even been considering
removing the special 2^4 behavior, though it will likely be good to keep
around for legacy reasons).

I will say that the unsupported triangle puzzles are more dangerous to
consider stable at this point. While your {6}x{6} is fully safe as a first,
I’m not confident that there won’t be meaningful changes in triangle puzzles
like the {3}x{3}, so people might take that in consideration in regards to
what you tackle with "invent my own". However, I encourage you to play with
triangle puzzles and give us feedback on the behavior! (If we are pointed
to specific problems, it will be easier to look at).

Anyway, those are some of the thoughts that have been floating around…

Take Care,
Roice