Navy volleyball competes in the Patriot League. There are 7 teams in the
Patriot League (Navy and 6 others). Each team plays 2 volleyball matches
against each of the other teams; it is not possible for a volleyball match
to end in a tie. At the end of the season, the 4 teams with the best
league win-loss records are invited to the league tournament. (Ties in
win-loss records are possible; it's not important to this question how
they're broken.)

What is the largest number of Patriot League losses the Navy volleyball
team can have and still be certain it will go to the tournament?

What is the smallest number of Patriot League wins the Navy volleyball
team can have and still have a chance to go to the tournament?

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All midshipmen submitting correct solutions to problem #95 by 3:30 pm on
Tuesday, September 14, win a cookie. The best solution will be posted on
the problem bulletin board.
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A solution is "correct" if it answers the question correctly and explains
the answer; a solution is "best" if it includes the clearest correct
explanation.  Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil,
or via the mailbox in Chauvenet 301.