Topic: Coloring of a surface of a cube
The daughter from the Olympic Games brought: There is a white cube with the side of 3 cells. Surface cells (54 pieces) can be painted over in black color but so that no two painted over cells adjoined on the side (including lying on different edges). What maximum number of cells can be painted over? The answer is quickly, and here to prove why it maximum - was necessary to break a head. Probably, someone from you finds more simple proof.