From:

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I last week picked up one of the same octagonal cubes (Wonderful Puzzler

brand) as Alan R. Katz in his message. I might point out that it shares the same

workmanship and twistability (lack thereof) which Katz attributes to their brand

of standard cube.

After some experimenting, I found that the "parity error" involved is always a

pair of edges in reverse locations on the bottom. My solution algorithm is top,

equator, bottom [corner locations, edge locations, edge orientations, corner

orientations]. On an ordinary cube, one pair of edges reversed never happens

when you go to position edges. I suspect that if your algorithm does edge

locations before corners, then two corners in wrong locations would be the parity

error. Incidentally, the parity of Katz's cube is the reverse of mine, though the

center cubie colors are in the same relation to each other.

Edge orientation (I assume that is what Katz meant by "edges must be fliped")

parity errors are irrelevant to getting the cut-edge-colors rightly paritied. Edge

orientation parity errors happen because one of the cut-edges may have been

oriented wrongly. Or more precisely, an odd number of them reversed from the

way they were virginally (but they look right either direction). This is easily

cured by any of the "flip a pair of edges" macros.

The change in cube shape is actually helpful in solving, except for being

difficult to grab sometimes. Corners that need orientation really stand out. The

Greenwich meridian edges (assuming you solve it from the top down with the

octagonal faces left and right), being different shape, are instantly located.

The best part of the Wonderful Puzzler is the instructions, which I quote here:

THE CHALLENGE:

"ORIGINAL PUZZLER" presents not only a unique challenge but offers the

possibility of countless hours of relaxation. Your mental ingenuity may be tested

for a few hours -- many days -- several weeks -- or even a period of much

longer duration. If you can determine the key to unlock the knack for solving

the PUZZLER, the final trimph can be the psychological turning point in your

life. Mathematicians may be tested to the limit and cry over this one -- and you

may, too! You will gain a measure of satisfaction when you align one plane.

You will be delighted with the completion of two. You will be elated with the

completion of three or four! The completion of the fifth plane will quicken your

pulse!! -- and you will have scaled the peak once the last unit of the sixth plane

falls into place!!!!

PREPARATION & CAUTION:

*Spin the PUZZLER several times, as indicated on the cover, until all color units

are randomly distributed on each of six planes.

*Do NOT remove any color unit in the process of play.

*Initially, activate the random distribution GENTLY. With little use, this can be

accomplished easily and smoothly.

Patience and persistence will beat the Puzzler! Good Luck!

Challenge

Can you contend with more than 18'000'000'000 combination to reach a solution?

*end of quote*

I think the errors remaining above are all theirs. It is full of little gems: turning

point in your life, solving five planes (on the standard cube, which I believe

has the same instructions), 18 billion (better than Ideal's guess). The GENTLY

caution is valid; a neighbor kid blew mine apart, including a center cubie, by

ignoring this.