Direction: Four colours namely Blue, Green Red and White are used to paint a cube such that each face is painted in exactly one colour and each colour is painted on at least one face. The cube is now cut into 120 identical pieces by making least number of cuts.
-
If K is the number of cuboids which have more than one face painted in the same colour then find the maximum value of k.
-
- 24
- 36
- 13
- None of these
Correct Option: C
For least number of cuts 120 = 4 x 5 x 6 i.e number of cuts must be 3, 4 and 5 in three planes in this case number of cubes on a face is either 6 x 5 = 30 or 6 x 4 = 24 or 4 x 5 = 20 cubes . And number of cuboids on an edge is 4 or 5 or 6
In this case when k is maximum, one particular colour is used on there faces such that any two faces are adjacent to each other. Required number of cuboids will come from edges but not from vertex = 3 + 4 + 5 + 1 = 13
