Question 174
There are $4950$ ants. Assume that, for any three ants $A$, $B$ and $C$, if the ant $A$ is the boss of the ant $B$, and the ant $B$ is the boss of the ant $C$, then the ant $A$ is also the boss of the ant $C$. We want to divide the ants into $n$ groups so that in any group, either any two ants have the boss relationship or no two ants have the boss relationship. Find the smallest $n$ for which we can always do this, in any case.