# Message #745

From: Roice Nelson <roice3@gmail.com>

Subject: Chronicles of a Rubik junkie’s experience with the {5}x{5}

Date: Fri, 30 Oct 2009 09:58:23 -0500

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?