Message #748

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Chronicles of a Rubik junkie’s experience with the {5}x{5}
Date: Fri, 30 Oct 2009 16:30:37 -0700

And yes, I loved your description of your experience. Thanks so much for
writing it up. I’m sure that everyone else appreciates it as much as I
do. :D

-Melinda

Roice Nelson wrote:
> Hi fellow hypercubists,
>
> I was sharing my experience on the "{5}x{5} 3" (Uniform Pentagonal Duoprism)
> puzzle with Melinda, and she encouraged me to post an expanded version of it
> here, and to describe how it felt while going through it :)
>
> I hadn’t thought I’d get to work on it Wednesday night since I had other
> plans, but when those ended earlier than expected I gave it a start - the
> impromptu beginning ended up a marathon session that still hadn’t ended by
> 5am the next morning! I used to do all night solves like this when I first
> joined the group, and it was fun to fully regress into circa 2000 obsessive
> mode.
>
> There were a number of interesting new scenarios in this puzzle. The
> duoprisms are neat because they are approximately two dual interlocking tori
> in 4-space (this is more obvious on the uniform duoprisms, where both "tori"
> are based on the same polygon). From my start on the {5}x{4} and the
> problems I had been encountering there, I knew it would be best to first
> solve the rings of 2C pieces along the two main circles of revolution of the
> tori. This did turn out to be the right decision because I could correct
> "parity problems" (which I did encounter) earlier without having to worry
> about the other 2C pieces. With the two rings done, the remaining 2C pieces
> went smoothly afterward. For those, I worked my way around one torus, then
> around the other.
>
> 3C pieces went smoothly as well, and this was the most enjoyable part for
> me. I got in the groove (even had a beer :)), and just picked them off one
> by one. I was saving my log file every 6 pieces (not sure why), which was
> about 15 minutes intervals, and finished these around midnight. I ran into
> another parity problem at the end of the 3C pieces, but luckily was able to
> find a sequence for it pretty quickly. So I was excitedly off to the
> corners feeling like I was making rapid progress…
>
> I had trouble finding a sequence which cycled only 3 corners (and in fact
> didn’t do so till the next morning), but I did find a sequence that swapped
> two sets of two corners. It was pretty easy to get into a rhythm with it,
> and I was feeling confident to finish the whole puzzle by 2am. But the
> sequence became more awkward as more pieces were solved, especially towards
> the end. And with 4 pieces left, those troubles escalated. I couldn’t get
> these rebels to swap with correct positions or orientations. I was able to
> reduce to 3 unsolved pieces, but still couldn’t find a sequence for that.
> Also, I could see the parity problems in these 3 (two swapped and one
> disoriented, instead of a 3-cycle). The tiredness was growing, but I was on
> a mission and didn’t want to stop!
>
> By 3:30am, there were just 2 pieces remaining (right positions, wrong
> orientations), but by this point and during that last hour and a half,
> instead of thinking about how to solve these two pieces, I was tired enough
> that I was literally just guessing sequences on my practice puzzle. I got a
> rush of adrenaline a couple times when I thought I was there, but each time
> it didn’t go quite right. Rush, disappointment, rush, despondence…
>
> At 5am, the final pieces had given me enough strain that I knew I needed to
> get some sleep first to have any hope with it, and as difficult as it was I
> pulled myself away from the computer. Besides exhaustion, I think what I
> was feeling at this point was a sense of urgency to have all this work and
> loss of sleep count as a first! (as silly as that is) Sarah legitimately
> called me a coocoo for staying up so ridiculously late, and my mind had
> enough inertia going that I couldn’t immediately turn it off - good thing is
> while trying to fall asleep I had the idea that ended up working.
>
> The sleep did the trick, and I was able to find the right sequence in about
> 15 minutes around 10am with a set of fresher eyes. Finishing felt like
> solving the 4^3 for the first time! My performance at work definitely
> suffered a bit on Thursday, but I think in this case it was worth it :)
>
> As an aside, it seemed I hit every possible parity problem along the way,
> and it made me wonder if the statistical chances of this were higher than on
> the 4^4. I also wonder if parity problems are more prevalent on odd uniform
> duoprisms. The "{4}x{4} 3", aka the 4^3, certainly doesn’t do these kinds
> of things. Would a {6}x{6}?
>
> Well, I hope you enjoyed the story, and that it wasn’t too long.
>
> Take Care,
> Roice
>
> P.S. If anyone is interested in the particular sequences, just let me know.
> Maybe we need a "sequence library" for each puzzle in the wiki?
>
>