THE Y PUZZLE
Take 25 identical pieces, the solid Y-pentomino. This is one of the twelve solid pentominoes and consists of 5 unit cubes glued together as given below.
Using all of the pieces, build a 5 x 5 x 5 cube.
The puzzle was discovered by David Klarner and published by him and C.J. Bouwkamp in an article in 1970 in the Journal of Recreational Mathematics.
In addition, see if you can build the following boxes using these pieces:
|
Dimensions of Box |
Number of Y's Needed |
|
1 x 5 x 10 |
10 |
|
2 x 5 x 6 |
12 |
|
3 x 4 x 5 |
12 |
|
2 x 4 x 10 |
16 |
|
2 x 5 x 8 |
16 |
|
4 x 4 x 5 |
16 |
|
4 x 5 x 5 |
20 |
|
2 x 5 x 11 |
22 |
|
2 x 4 x 15 |
24 |
|
5 x 5 x 5 |
25 |
All ten boxes above are called prime boxes. It means that there does not exist a solution that can be split into smaller boxes.
Torsten Sillke compiled
a ‘complete’ set of 40 two-dimensional and 22 three-dimensional Y-pentomino prime box packings and are summarized below.
|
Two Dimensional Rectangles |
Three Dimensional Boxes |
|
9 x {20, 30, 45, 55} |
2 x {4, 7} x {10, 15} |
|
10 x {5, 14, 16, 23, 27} |
2 x 5 x {6, 8, 11, 13, 15} |
|
{11, 13} x {20, 30, 35, 45} |
{3, 4, 5} x 4 x 5 |
|
12 x {50, 55, 60, 65, 70, 75, 80, 85, 90, 95} |
3 x 5 x {9, 11} |
|
15 x {14, 15, 16, 17, 19, 21, 22, 23} |
3 x {6, 7} x {10, 15} |
|
17 x {20, 25} |
5 x 5 x {5, 6, 7} |
|
18 x {25, 35} |
5 x 7 x 7 |
|
22 x 25 |
|
I