Nine L-ements
Designed, made and presented by Rick Eason
for International Puzzle Party 23
Chicago, Illinois, August 2003

Nine L-shaped 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 L-ements.

Click here for the related Eight L-ements 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

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