maths……………………………………….?

ambrin f: maths……………………………………….?
There are 20 unit cubes all of whose faces are white, and 44 unit
cubes all of whose faces are red. They are put together to form a
bigger cube (444). What is the minimum number of white faces
visible on this larger cube?

Answers and Views:

Answer by ignoramus
There is a hidden “core” within the block of 2 x 2 x 2 = 8 cubes which cannot be seen. If all these are white cubes, there must be 12 white cubes somewhere in the outer “skin” of which at least one face must be visible.

In the centre of each face, there is a group of 4 cubes of which only one face is visible. If the remaining white cubes are positioned in one of these positions, then only one face of each will be visible.

So the minimum number of white faces which are visible is 12.

Answer by kavin
12 cubes will be visible on the larger cube.
When you make a 4 x 4 x 4 cube and if you want the white ones to be minimum, then place the white cubes in the middle of the larger cube. you’ll place 8 white cubes in the middle to make 2x2x2. Since you got 20 white cubes, you’ll fill with the outer surface of 4x4x4 with 12 white cubes.