How many solutions does the Bedlam cube puzzle have?
competition/games/bedlam.cube New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
How many solutions does the Bedlam cube puzzle have?
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The Bedlam cube has 19,186 solutions excluding rotations and
reflections.
-- Bent Schmidt-Nielsen <bent@world.std.com>, December 1993
Years ago there was (is?) a game out of England called Boggle
that uses mostly 5 cube pieces to make a 4X4X4 cube. There are
19186 solutions but I have include only 3.
[ Editor: a 4x4x4 cube from 13 pieces with 19186 solutions is the
Bedlam cube described above; "Boggle" is presumably a slip of memory. ]
BOGGLE: all pieces but 7 have 5 blocks
_ _ _ _ _ _ _
_|_|_ |_|_ |_|_ |X| |X|_ |X|X|
|_|_|_| |_|_|_ |X|_| |_|_ |X|_| |_|
|_| |_|_| |_| |_|_| |_| |_|
1 2 3 4 5 6
_ _ _ _ _ _ _ _
|_|_ |_|_ |X|_ |_|_|_ |X|_ |_| _|_|
|_|X| |_|X| |_|_| |_|_| |_|_| |_|_ |X|_|
4 pieces |_| |_| |_| |_| |X|_| |_|
7 8 9 A B C D
X = block above;
Y=4 _______ ____________
__| | /__/__/__/__/|
__| | Z=4 | /__/__/__/__/ |
__| |3 | | /__/__/__/__/ |
| |2 | |_______| /__/__/__/__/ |
|1 | |________| z=4 |__|__|__|__| / y=4
| |________| z=3 |__|__|__|__| / y=3
|________| z=2 |__|__|__|__| / y=2
Y=1 z=1 |__|__|__|__|/ y=1
x=1 2 3 4
z=1 z=2 z=3 z=4
y=4 c225 ca55 cc31 8333
y=3 ba22 ba51 c851 8831
y=2 bb42 da77 6a91 8999
y=1 db47 dd47 6d44 6669
z=1 z=2 z=3 z=4
y=4 c4aa c444 cc16 8666
y=3 baa2 b514 c816 8813
y=2 bba2 d572 5513 8933
y=1 db77 dd72 5d92 9993
z=1 z=2 z=3 z=4
y=4 cc63 c233 7223 7722
y=3 c168 1113 71b9 44b9
y=2 c668 d688 55bb 4599
y=1 daa8 ddaa 4dab 4559
-- Paul Krause <pkrause@micro.ti.com>, December 1997