Posted by **avinash kumar** on Thursday, August 25, 2011 at 6:35am.

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

- math -
**drwls**, Thursday, August 25, 2011 at 6:59am
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.

- maths -
**Damon**, Thursday, August 25, 2011 at 7:01am
(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

- maths -
**Damon**, Thursday, August 25, 2011 at 7:03am
Whew, we agree :)

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