Let the number of men participating in the tournament be n. Since every participant played two games with every other participant. Therefore the total number of games played among men is 2×nC2=n(n−1) And the number of games played with each woman = 2n. but since there are two women, hence the total number of games men played with 2 women = 2 × 2n = 4n ∴ {n(n − 1)} − 4n = 66 ⇒n2−5n−66=0 ⇒n = 11 ( ∵ < 0, is not possible) ∴ Number of participants = 11 men + 2 women = 13.