There are 8 rectangular prisms as shown in the figure below.
All of them are used and those are piled up in the same direction so that a big rectangular prism is made. How many kinds of rectangular prism can be made?
Answer
8 kinds
Solution
8 = 1 × 1 × 8 = 1 × 2 × 4 = 2 × 2 × 2.
(1) In case of 1 × 1 × 8.
The length of each side of the rectangular prism which can be made is 3 kinds, (4 cm, 6 cm, 24 cm), (3 cm, 6 cm, 32 cm) and (3 cm, 4 cm, 48cm).
(2) In case of 1 × 2 × 4.
There are 6 kinds of (3, 8, 24), (3, 12, 16), (4, 6, 24), (4, 12, 12), (6, 6, 16) and (6, 8, 12).
(3) In case of 2 × 2 × 2.
There are 1 kind of (6, 8, 12).
Among these, (4, 6, 24) and (6, 8, 12) are double respectively.
Kinds of rectangular prism can be made is 3 + 6 + 1 - 2 = 8 kinds.
