posted by avinash kumar on .
a cube painted on its six faces and then it is cut into 4913 smaller cubes of equal size
how many cubes are painted only on one face
hw many cubes are painted only 2faces
4913 is 17 cubed. There are 17^2 = 289 small squares visible on each face.
6x15^2 = 1350 are painted on one side only.
Fifteen cubes along each of the 12 edges are painted on two sides. That makes 180
The eight at corners are painted on three sides.
4913 - 1350 - 180 - 8 = 3375 are not painted at all. That happens to be 15 cubed.
(4913)^(1/3) = 17
so this big cube is 17 of the little ones on a edge. That means 6*17*17 = 1734 are on the outside and would be painted on one side except that the ones on the edges are painted on at least two sides so it is really 6*15 *15 = 1350
Only the ones along the 12 edges (excluding the 8 corner cubes which are painted on three face) are painted on two faces. Therefore 15*12
Whew, we agree :)