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Two opposite faces of a large cube are painted red, two adjacent faces are painted yellow and the rest of the faces are painted blue. On each axis of this big cube, 4 equal cuts have been made and some smaller cubes have been obtained. How many such small cubes will be there in which one face is painted blue and one is painted yellow?

Two opposite faces of a large cube are painted red, two adjacent faces are painted yellow and the rest of the faces are painted blue. On each axis of this big cube, 4 equal cuts have been made and some smaller cubes have been obtained. How many such small cubes will be there in which one face is painted blue and one is painted yellow? Correct Answer 10

A big solid cube is cut into small cubes.

If 4 cuts are made on each axis then the total cubes made from each edge is 5.

Now the total number of cubes = 53 = 125

The number of cubes will have one face painted with blue colour and one face painted with yellow colour are the cubes which are on the combined faces of blue and yellow coloured at the edges = 5 + 5 = 10

Hence, "10" is the correct answer.

Shortcut Trick

For a cube of side n*n*n painted on all sides which is uniformly cut into smaller cubes of dimension 1*1*1,

Number of cubes with 0 side painted = (n-2) ^3

Number of cubes with 1 side painted =6(n - 2) ^2

Number of cubes with 2 sides painted= 12(n-2)

Number of cubes with 3 sides painted= 8(always)

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