Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between them-selves exceeds the number of games that the men played with the women by 66 , then the number of men who participated in the tournament lies in the interval

Step-by-step solution

Let the number of men participating in tournament = m . Number of women participating in tournament = 2 . Each player will play   2 games with every other player and two women will play 2 games with each man. Total numbers of games played by women = 2 × 2 m = 4 m Total number of games played by men = 2 · m C 2 From given data 2 ·   m C 2 - 4 m = 66 ⇒ 2 m m - 1 2 - 4 m = 66 ⇒ m 2 - 5 m - 66 = 0 ⇒ m - 11 m + 6 = 0 ⇒ m = 11 or - 6 but m ∈ N ,   m ≠ - 6