A right $100$-gon $P$ is given, which has $x$ vertices coloured in white and all other in black. If among some vertices of a right polygon, all the vertices of which are also vertices of $P$, there is exactly one white vertex, then you are allowed to colour this vertex in black. Find all positive integers $x \leq 100$ for which for all initial colourings it is not possible to make all vertices black. A. Vaidzelevich,M. Shutro