Find the number of members of chess club The members of a chess club took part in Round Robin competition in which each plays everyone else once. All members scored the same number of points, except 4 juniors whose total score were 17.5. How many members  were there in the club? Assume that for each win a player scores 1 point,  for draw 1/2 point and zero for losing.
Attempt:-
The total no. of games= C(n,2) . n being no. of members.
Every game leads to the business of 1 point, Hence sum of points of every member = C(n,2).
Total points must remain conserved => C(n,2) = 17.5 + points scored by seniors in terms of n .
I m not able to think upon "points scored by seniors in terms of n".
Also i m unable to use the fact that the points of seniors are equal.
Answer=27

Suppose there are $s$ seniors with $m/2$ points each.
What is $n$ in terms of $s$?
You should get an equation in integers that involves $s$ and $m$.
