Question

Three adjacent faces of a cube are coloured blue. The cube is cut (once horizontally and once vertically) to form four cuboids of equal size. Each of these cuboids is coloured pink on all the un-coloured faces and then cut into four cuboids of equal size. How many cuboids have two faces coloured pink?

Answer 1

Given:

A cube with adjacent faces = Blue colour

A cuboid with each side = Pink Colour

To Find:

How many cuboids have two faces coloured pink?

Solution:

The four cuboids that will be obtained from cube are -  

1 - Blue top and Blue front

2 - Blue top, Blue front and Blue Side

3 - Only Blue front

4 - Blue front and Blue side.

Now, all the uncoloured faces of each of the cuboid is coloured with pink and is  again cut into 4 cuboids.

Therefore,  

Set 1 and 4 - 2 cuboids will have 2 faces blue, 2 pink and 2 uncoloures

2 cuboids have 1 face blue, 3 pink and 2 uncoloured

Set 2 - 2 blue, 2 pink and 2 uncoloured.

1 cuboid will have 3 blue, 1 pink, and 2  uncoloured

1 cuboid will have 1 blue 3 pink and 2 uncoloured

Set 3 - all four cuboids have 1 blue 3 pink and 2 uncoloured

total pink faces - as there are 2 cuboids in set 1 and 2

and 2 in set 4, thus set 2 has 2 pink faces.

Therefore - 2 + 2 + 2 = 6

Answer: Total pink faces are 6