Nine Lements
Designed, made and presented
by Rick Eason
for
International Puzzle Party 23
Chicago,
Illinois, August 2003
Nine
Lshaped pieces, no two alike, form a solid cube



The pieces 
An assembled puzzle 
Objective: Make a solid cube out of the nine pieces. There are 169 solutions. Most solutions are closely related to other solutions. Only six solutions cannot produce another solution by rearranging two pieces. Of these, one solution requires rearranging at least four pieces to produce another solution. One might argue that there are really only 14 substantially different solutions. For those interested, here are a list of solutions and an analysis showing related solutions.
Click here for a discussion on variations of Nine Lements.
Click here for the related Eight Lements puzzle that has only one solution.
Other simpler problems are given by trying to create a solid cuboid (a.k.a. rectangular parallelpiped) out of subsets of the pieces. Six pairs of pieces can form simple cuboids. (Can you find them?) The following table gives all remaining sets making cuboids, the number of solutions and the cuboid dimensions.
Other Cuboids 

Pieces 
Number of Solutions 
Dimensions 

ABDH 
1 
7x7x11 
BDEG 
4 
7x7x11 
BEGH 
2 
7x7x11 
CEFG 
1 
7x8x11 
CFHI 
7 
7x8x12 
DEFI 
1 
4x11x15 
DEGI 
4 
7x8x11 
DEGI 
8 
4x11x14 
DEGI 
8 
4x7x22 
DFGH 
8 
4x11x15 
DGHI 
8 
4x7x23 
EFHI 
9 
4x11x15 
EGHI 
6 
7x8x11 
EGHI 
8 
4x11x14 
EGHI 
16 
4x7x22 
ABCDEF 
1 
7x11x11 
ABCDGI 
6 
7x11x11 
ABCGHI 
3 
7x11x11 
ABDEHI 
22 
7x11x11 
DEFGHI 
38 
8x11x11 
DEFGHI 
113 
4x11x22 
ABCDEFGH 
102 
7x11x15 
I really hate to give out solutions, but if you really, really must have my solution sheet, then click here.
© R. Eason, 2003