The European zoos with exactly $100$ types of species each are separated into two groups $\hat{A}$ and $\hat{B}$ in such a way that every pair of zoos $(A, B)$ $(A\in\hat{A}, B\in\hat{B})$ have some animal in common. Prove that we can colour the cages in $3$ colours (all animals of the same type live in the same cage) such that no zoo has cages of only one colour