Answer: We can start by noticing that the total number of small cubes used is 64, which is the same as the total number of unit squares on the surface of the large cube. To maximize the white surface area, we want to arrange the cubes in a way that maximizes the number of white faces on the surface.
Each small cube has 6 faces, so there are a total of 6 x 64 = 384 faces. Half of these faces are white and half are black, since we have an equal number of white and black cubes. Therefore, there are 192 white faces and 192 black faces.
Now, let's consider how the small cubes can be arranged to maximize the white surface area. If we arrange all the white cubes together in a 4 x 4 x 4 block, then all the faces of this block that are adjacent to a black cube will be black, and all the faces that are adjacent to another white cube will not contribute to the surface area. This leaves only 16 white faces that contribute to the surface area.
On the other hand, if we alternate white and black cubes in each layer of the cube, then all the faces that are adjacent to a black cube will be white, and all the faces that are adjacent to another white cube will be black. This maximizes the white surface area. Specifically, there are 6 layers of the cube, and each layer has 16 white faces (4 along the top and bottom and 4 along each side). Therefore, there are a total of 6 x 16 = 96 white faces that contribute to the surface area.
So the fraction of the surface that is white is:
96 white faces / 384 total faces = 1/4
Therefore, one quarter of the surface area of the cube is white.
Explanation: