Let no. of men =n No. of women =2 Total participants =n+2 No. of games that M1 plays with all other men =2(n−1) These games are played by all men M2,M3,......,Mn So, total no. of games among men =n⋅2(n−1). However, we must divide it by '2', since each game is counted twice (for both players). So, total no. of games among all men =n(n−1).......(i) Now, no. of games M1 plays with W1 and W2=4 (2 games with each) Total no. of games that M1,M2,.....,Mn play with W1 and W2=4n ......(ii) ...... (ii) Given :n(n−1)−4n=66⇒n=11,−6 As the number of men can't be negative. So, n=11