Tips: Tournament Problems

Tournament Problems
There are 16 teams and they are divided into 2 pools of 8 each. Each team in a group plays against one another on a round-robin basis. Draws in the competition are not allowed. The top four teams from each group will qualify for the next round i.e round 2. In case of teams having the same number of wins, the team with better run-rate would be ranked ahead.

1. Minimum number of wins required to qualify for the next round _____?
2. Minimum number of wins required to guarantee qualification in the next round _____?

Now, i don't know how many of you are aware of the following method. But 1 thing I mention in advance that this should take only 30 seconds to solve
1.
1 group is consisting of 8 teams. So each team will play 7 match each. Suppose each of the 8 teams were seeded and we consider the case where a higher seeded team will always win.

So the number of wins for the 8 teams would be 7,6,5,4,3,2,1,0 with highest seeded team winning all and lowest seeded team losing all.

For minimum number of wins we allow 3 teams to win maximum number of matches. Of the remaining 5 teams just find out the mean of their number of wins.

In this case it would be (4+3+2+1+0)/5=2.

So 5 teams can end up with 2 wins each and a team with better run rate will qualify with 2 wins.

2.

In this case consider the mean of first 5 higher seeded teams (7+6+5+4+3)/5=5

So it may be the case that 5 teams can end up having 5 wins each. And hence 1 team will miss the second round birth. So minimum number of wins to guarantee a place would be 6.

The trick is to consider wording, qualify means best case scenario while guarantee qualify means worst case scenario.