In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:

Question: In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:

Solution:
Let there were x teams participating in the games, then total number of matches,
nC2 = 153
⇒ {n × (n - 1)}/2 = 153
⇒ n(n - 1) = 306
⇒ n² - n - 306 = 0

Since n typically represents a count or a positive quantity in such contexts, we discard the negative solution.
Therefore, n = 18.