Jack made a cube of 27 small white and black cubes. No two cubes of the same color have a common edge.

Jack made a cube of 27 small white and black cubes. No two cubes of the same color have a common edge. How many white dice did the jack use?

27 cubes – the volume of the resulting cube. Let’s find its side, for this we extract the 3-rd root of 27 this is 3, which means the base is 3×3
Now let’s think: since cubes of the same color do not have a common face, then they alternate, and one of the colors will be 1 more cube. Therefore, 2 options are either 14 white and 13 black, or 13 white and 14 black.