October 10, 1988
This second printing of "HOLEY 6-PIECE BURR !" was
prepared for duplication by Rex Shudde using PC TEX and
PICTEX. The text, drawings, and computer output have been
redone but have essentially the same content as the first
printing.
The following are recent developments in the analysis
of 6-piece burrs:
"Level" usage
The second version of the program BURR6 uses a
definition of level which does not allow pieces to move
different amounts in the same direction in one move or
"level". (See comment 2. on page 6). The program allows
for use of the older definition as an option.
Challenge Questions
The "Challenge Questions" section consists of questions
which I do not know the answer to (though I may have strong
thoughts on the subject). In particular, I do not know of a
6-piece burr with normal, cubic-cut pieces which requires a
twist move. I would be quite surprised if there were one,
but have not attempted to prove this.
Peter Marineau and Bruce Love sent designs which are
solvable using length 10 pieces, but are not solvable using
length 12 pieces. Peter Marineau sent a proof that this is
the longest length for which there is a difference, but I
am not completely convinced of this answer. For notchable
burrs, no solution exists with length 10 pieces which is not
a solution for length 12 or longer pieces.
Peter Marineau's record of a unique level-9 solution
still holds at this date.
Bruce Love has a design, "Love's Dozen", which is
level-12, but not unique. This is now the record for
non-unique solutions.
Notchable Analysis
A complete analysis of 13,354,991 essentially different
notchable assemblies was completed by computer runs from
March to June of 1987. The highest levels found were:
Level-10 (non-unique) - 2 solutions, one with 9 holes,
and the other with 11 holes.
Level-5 (unique) - many such solutions.
The results will be published in a sequel to this
booklet entitled: "Holey 6-Piece Burr - The Notchable Case".
Copyright 2000-2016 Bill Cutler Puzzles, Inc.
