men will win at least the matches among themselves 2n x(2n-1)/2 which should be less than what men won in the end which is 5/12 of the total wins 3n(3n-1)/2. if you solve 2n(2n-1)/2 <= 3n(3n-1)/2 x 5/12, you will get 0 <= n <= 3. eliminate 1 and 2 since for n= 1 or 2, 3n(n-1)/2 is not divisible by 12, you get n = 3.