Seven white cubes and 20 black cubes of the same volume are to be put together to form a large cube. If the white cubes are arranged so that the amount of white showing on the surface of the large cube is a minimum, what part of the large cube will be white?
In order to minimize the amount of white showing on the surface of the large cube, we need to arrange the white cubes in a way that they are mostly hidden inside the large cube.
One way to do this is to place all the white cubes in the center of the large cube, forming a smaller white cube inside the larger black cube. In this arrangement, only the corners of the white cube will be visible on the surface of the larger cube.
Since the ratio of white cubes to black cubes is 1:2, the volume of the white cube will be 1/3 of the volume of the large cube. Therefore, the white cubes will take up 1/3 of the volume of the large cube, while the black cubes will take up the remaining 2/3 of the volume.
So, the part of the large cube that will be white is 1/3, or approximately 33.33%.