Message #2220

From: Melinda Green <>
Subject: "Three strange {8,4} colorings"
Date: Fri, 01 Jun 2012 03:23:43 -0700

That was about all that Roice said about these three puzzles and nobody
seems to have noticed them. That’s understandable because he was
dropping hundreds of new puzzles on us at the same time and the {8,4}s
were at the very end. Well I stumbled into them a couple of days ago and
can say "Mighty strange indeed!" As you know, I’ve been focusing on
edge-turning puzzles that I can solve intuitively and found the 5-color
and 10-color versions to be a lot of fun. They start out easy enough and
finish with enough of a brain stretch to be quite rewarding to solve. I
had tried and failed with with the 9-color version after a couple of
half-hearted attempts, but since I had solved the other two I figured it
was time to make a serious attempt to collect all three, and all I can
say is "OH………………………….., MY GOD!" Roice mentioned
that they have some interesting topological properties that would be fun
to study and I completely agree. The best single word I can find to
describe tthe 9-color version is "perverse". Rather than try to
describe what I found, I want to invite Ed and Nan and any other serious
puzzlers to give these a shot. Then please let us know what you think.
Do they yield easily to your standard methods? Do the face and vertex
turning version behave as oddly as the edge-turning? I definitely want
to learn more about these bad boys!