Problem Solving

7 teams compete in a track competition. If there are 20 events in the competition no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?

a. 3
b. 4
c. 5
d. 6
e. 7

Annswer is 7

More teams winning the maximum number of games leaves less games for other teams to win. Label the teams 1-7. Now suppose each team wins the max number of games(3) and distribute all the wins.

1 2 3 4 5 6 7 (team number)
3 3 3 3 3 3 2 (number of wins)

Each team must have one at least one event. The answer is E.

Thank you