Question 35
Each of the lattice points $(x, y)$ ($x$ and $y$ integers) in the plane can be coloured black or white. A single strike by an L-shaped punch changes the colour of the four lattice points $(a, b)$, $(a+1, b)$, $(a, b+1)$ and $(a, b+2)$. All lattice points are initially coloured white. Prove that after any number of strikes, the number of black lattice points will be either zero or greater than or equal to four.