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In a chess tournament, all participants were to play one game with the other. Two players fell ill after having played 3 games each. If total number of games played in tournament is equal to 84. Then total number of participants in the beginning was equal to

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answer is 15.

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Detailed Solution

$^{(n - 2)} C_{2} + 6 = 84 \Rightarrow \frac{(n - 2) (n - 3)}{2} = 78 \Rightarrow n^{2} - 5 n + 6 - 156 = 0 \Rightarrow n^{2} - 5 n - 150 = 0 \Rightarrow (n - 15) (n + 10) = 0 \Rightarrow n = 15$

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