This page is under construction!
This page provides materials to accompany the paper
"Solving the Snake Cube Puzzle in Haskell"
(revised version finalized on August 22, 2012).
This paper has been submitted to be considered for publication in the
Journal of Functional Programming. Please consider it a draft document,
not intended for distribution at this time.
The following additional items are currently available:
A solution for the standard 3x3x3 snake cube puzzle in
pdf format.
A solution for the 4x4x4 "king" snake cube puzzle in
pdf format. In this particular solution,
the two ends of the snake end up in corners of the 4x4x4 cube,
so we refer to it as a cornertocorner solution. There is
also a reversed version of the same
solution.
An additional three solutions for the 4x4x4 king,
all of which start and end one position away from the corner of the 4x4x4.
The first two are very similar, differing in only 4 steps (35, 36, 38,
and 39). The third agrees with the first two for the first 13 steps and
then does its own thing (although, interestingly, all three solutions end
up putting the same pieces in place in Step 37). (For completeness, there
are also diagrams showing these three solutions in
reverse. It is easier to see the subtle difference between the first
two of these three solutions here: compare Steps 69 on Pages 1 and 5 and note
that all of the other steps are the same in those two solutions.)
A diagram of the search tree for the
standard snake cube, constructed using a modified version of the
solver and the GraphViz
toolset.
The Haskell source for solving snake cube puzzles
and for constructing a sequence of diagrams to
illustrate a solution to a snake cube puzzle.
Some additional solutions:
Another version of the the standard snake
cube solution that includes headers.
An alternative presentation of the
solution for the standard snake that assembles the pieces in the
reverse order. This solution is actually a little harder to use
in practice: it gets a little tricky around Steps 12 and 13. In
terms of the paper, this is the solution for
(advance (advance (reversePuzzle standard))).
An experiment showing the standard snake cube solution
with three distinct views at each step.
A similar threeviews version of the
cornertocorner solution for the king cube.
Solutions to the Ornery Orange version
(also available in reverse order),
and the Mean Green version (again
also available in reverse order).
Solutions to the designs shown
in Figure 2
and Figure 3 of Allen F. Dreyer's
US Patent 3,222,072. I'm not expecting to be able to test
these. You'll notice also that there are 18 variations
listed for the Figure 3 example, producing a monster
document of solutions. I've done some pruning using symmetry
to eliminate some essentially equivalent solutions, but there
might be scope for further reduction. On the other hand, it's
also possible that there are additional solutions that do not
start/end in a corner of the full cube; I haven't tried looking
for those yet.
Solutions for folding the standard snake,
the mean green snake, and the
ornery orange snake into their most compact
flat forms. Useful if you are transporting a snake and need to fit it into
a thin bag or briefcase, for example. (Really!)
I'll continue to update this page with additional related items of interest; if there
is something in particular that you are looking for, please let me know.
Acknowledgments: The diagrams on this page were generated with the
help of the Haskell programming language;
Gene Ressler's Sketch
tool;
Till Tantau's PGF and TikZ
graphic systems for TeX;
the LaTeX typesetting system;
some real snake cube puzzles from
Creative Crafthouse; and,
most importantly, the indulgence of my family.
