A solid cube is painted yellow blue and black

Asked by admin @ in Math viewed by 412 People

A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?

its an UPSC question of prelims GS2 in 2019​

Answered by admin @


Given : A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are big.

None of the faces of the bigger cubes is painted blue.

To Find : How many cubes have only one face painted

Solution:

4 x 4 x 4 = 64

32 ( 1 x 1 x 1) + 4 ( 2 *2*2) = 64

None of the faces of the bigger cubes is painted blue.

Hence bigger cube of size 2 * 2 * 2 are cut from middle

Each bigger  cube have two face painted

Yellow & Black  

Cube having only one face painted will be blue painted

4 + 4 = 8

8 cubes have only one face painted

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