Seven vertices of a cube are labelled with the number \(0\), and the remaining vertex is labelled with \(1\). You are allowed to repeat the following move: choose an edge of the cube and increase by \(1\) the numbers at both ends of that edge.
Is it possible to reach eight numbers that are all divisible by three?
Each number on the number line (not only whole numbers!) is painted black \((B)\) or white \((W)\). Is it always possible, regardless of how the number line is painted, to find a line segment such that both its endpoints and its middle point are painted with the same colour?