Question

A cuboid is divided into 192 identical cubelets. This is done by making minimum number of cuts possible. All cuts are parallel to some of the faces. But before doing so, the cube is painted with green colour on one set of opposite faces. Blue on the other set of opposite faces and red on remaining their pair of opposite faces.
What is the minimum no of cuts I have made?

• A. 15
• B. 18
• C. 21
• D. 12

Answer 1

The correct option is A 15

The no of cuts will be minimum when 192 will be factorized into 3 closest factors, 192=4$\times$6$\times$8, so we have two opposite faces of 4$\times$6 and two opposite faces of 6$\times$8 and two opposite faces of 4$\times$8. Hence the minimum number of cuts will be = ( 4 - 1) + ( 6 - 1 ) + ( 8 - 1 ) = 3 + 5 + 7 = 15.
Hence option (a)