Message #2888

From: qqwref@yahoo.com
Subject: RE: MagicTile Solving
Date: Mon, 13 Jan 2014 18:24:43 -0800

I have solved more puzzles and should be up to 198 or so now.

However, I have noticed something weird while trying to go for movecount records. To put it simply, some puzzles require a large number of moves to be properly scrambled, and previous solvers have not always used enough moves. The best example is very shallow-cut edge turning puzzles on tilings with many faces. This type of puzzle is quite simple and pretty much just involves orienting each edge while placing small center pieces (which can be moved around with algorithms of the form PQPQ, with P and Q single moves). The phenomenon is not only limited to edge-turning puzzles; another one is the Klein Quartic {7,3} 24-Color F0:1:0 V1:0:0.

As a test case, here’s the Klein Quartic {7,3} 24-Color, E1:0:0, done with a 100-move scramble:
http://mzrg.com/rubik/magictile/%7B7,3%7D%20E1_0_0%20%28382t%29%20%28500scramble%29.xml
And here is a solve with a 500-move scramble:
http://mzrg.com/rubik/magictile/%7B7,3%7D%20E1_0_0%20%28112t%29%20%28100scramble%29.xml

In the two solves above I did not deliberately use more moves on the second one, or get a lot of extra experience before doing the first one. Actually, if you look at the scrambles and at my solution, it is clear that the second scramble is much more random. Why does this happen on these edge-turning puzzles? Well, in puzzles like this, the small center pieces are on circular "orbits" that limit the set of places where each piece can be. In this case the orbits are 8 pieces long (and there are 21 of them) but in other puzzles they can be even longer, like in the Infinite Regular Polyhedron {3,7} 56-Color E0:1:0, where they are 24 pieces long (with only 7 orbits). Each move only affects two orbits, and all it does is swap two adjacent pieces in each orbit. So each orbit must be affected by a large number of moves to be really scrambled, and in some puzzles it may take many moves just to move one piece as far as possible across the puzzle. After only 100 moves the majority of pieces are very close to where they are supposed to be.

So what should we do? One option is to look at what puzzles behave this way and get rid of all results with less than, say, 500 moves (meaning the people with those solves would have to redo the puzzle). Another option is to allow people going for solutions or records to scramble with as many moves as the previous record holder, which is what I have tried to do. What do you guys think?

–Michael Gottlieb