Discussion
In a certain cricket tournament 45 matches were played. Each team played once against each of the other teams. The number of teams participated in the tournament is
Answer: B
The number of teams was 10.
If each of n teams plays every other team once, the number of matches is the number of ways of choosing 2 teams from n.
\[ \frac{n(n-1)}{2} = 45 \]
\[ n(n-1) = 90 = 10 \times 9 \]
So n = 10. Check with the others: 8 teams give 28 matches, 12 teams give 66 and 14 teams give 91.
Another way to see it: every team plays 9 others, 10 teams times 9 matches is 90 team-appearances, and each match involves two teams, so 45 matches in all.
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