The members of a chess club took part in a round robin competition in which each player plays with other once. All members scored the same number of points, except four juniors whose total score ere 17.5. How many members were there in the club? Assume that for each win a player scores 1 point, 1/2 for a draw, and zero for losing.

Explanation

To solve the problem, let's break it down step by step:

### Step 1: Understand the Problem
We have a chess club with a certain number of members who participate in a round-robin competition. Each player plays against every other player once. All members scored the same number of points except for four juniors whose total score is 17.5 points. We need to find the total number of members in the club.

### Step 2: Define Variables
Let \( n \) be the total number of members in the chess club. Since each player plays against every other player, the total number of matches played is given by the combination formula \( \binom{n}{2} \), which is equal to \( \frac{n(n-1)}{2} \).

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