Question 156
In a chess tournament, there were $n$ contestants and any two of them played at most one game against each other. Each contestant has played exactly $100$ games. For any two contestants $A$ and $B$ who had played against each other, there were exactly $50$ other participants who have played against both $A$ and $B$. On the other hand, for any two contestants $C$ and $D$ who had not played against each other, there were exactly $4$ other participants who have played against both $C$ and $D$. Find the value of $n$.