Date: Thu 26 May 83 09:27:30-PDT
From: ISAACS@SRI-KL.ARPA
Subject: anybody there; 5x5x5; circular
To: cube-lovers@MIT-MC.ARPA

  There doesn't seem to be much happening with the cube, but the (at least)
3 newletters are still being published. Ideals "Rubik's Cube Newsletter" no.
3 came, marked winter, 1983.  Mostly about contests, also an article on 
computer cubing and the calendar cube.  Rubik's magazine from Hungary is 
also on issue 3, with article on contests, other games and toys, and a little
bit of mathematics.  Singmasters "Cubic Circular" is on issue 5/6 (phisically,
the forth issur), and is the best of the lot mathematically.  He describes
and talks some about rotating rings, about Tsukuda's square (and how to 
solve it), generalized Hungarian rings, the Incredi-ball (equivalent
to the corners of a Magic Dodecahedron without centers?? anyway, about
2*10**25 positions), rotating rings of cubes and tetrahedra (STarburst, 
Kaleido Puzzle, etc), some notes on the 4x4x4 (his suggested order:  2
opposite face centers, say L and R; Pair up and place the F,C,B edge
pairs on the L & R faces; D corners; Pair up FD & store them, then pair BD
edges, then put these edge pairs in place; check parity of U corners - if
odd, apply U; 3-cycle U edges to get UR & UL edge pairs;  EXAMINE, carefully,
the parity of the 4 edge pieces at UF&UB - if odd, r2D2l'D2r2, which 4 cycles
these edges; get all edges together and place; do U corners; do centers with
3-cycles like [[r,b],U].  phew.  If people are interested, he gives 
slightly more information on his method, also "Useful moves", and some other
strategies taken from the literature.  He talks about "Evisceration", 
that is, the principle of Duality, that if you replace capitals with small
letters and vice versa, in any move sequence, you turn the cube inside out -
corners become invisable centers, edges become face centers, etc.  Singmaster
uses this to transfer knowledge of 3x3x3 to 4x4x4.  He guesses the minimum
for God's Algorithm on the 4x4x4 to be about 44 "hand moves" or 66
quarter turns.  (question, from DS: how should we count moves?  "r" is
really 2 hand moves - Rr followed by R' - while Rr and even Rrl' could be
counted as a single move.)  The circular talkes about Pyraminx, and gives
God's Algorithm as between 8 and 17 moves; there was some work on that done
in the Journal of Recreational Mathematics (a minimum solution was
presented), but I can't find the issue right off hand.  Also a bunch of
Pyraminx patterns are given.  There is an article on the prehistory of
the cube,and a little on the legal problems.  Anyway, this parenthetical
paragraph is way out of hand - if anybody wants more, or more organized,
on the Circular, let me know.)
    The 5x5x5:  Yes, I saw one and played with it (a very little bit) at
Jerry Slocums' puzzle party.  I also got an add from Meffert for one, and
have sent him my money, but it hasn't come yet.  Neither has my Skewb, for
which I sent money half a year ago or so.
    What else is new?  Well, nothing much.  Sales in the stores are slow,
and the number of puzzles available has lessened.  Doug Engels rotating
circles are ready for production, and his manufacturer is mainly waiting
for the "right time" to release them.  (These are 2 overlapping rotating
circles, with 3 piece overlap and 21 pieces all together.)  He is trying
to decide between 2 colorings; if he choses the more difficult one, it 
is a fairly hard puzzle, very cube like, but harder to get the already
solved pieces "out of the way".  
   Sorry this turned out so long and rambling - I was just going to 
write a short note, and got carried away.  Happy puzzling.
   -- Stan
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