If 10 teams participated, then the first team plays matches against the other 9 teams. The second team has already played against the first team, and so has to play matches against only the other 8 teams. In this manner, the second-last team has to play against only one team, and the last team has already played against all the teams. Thus, the total number of matches is
9 + 8 + ........ + 2 + 1 = 45 .
If 45 matches are totally played, then 10 teams participated.
Food for thought:
Is there a formula to conveniently add
9 + 8 + ........ + 2 + 1 ?
Indeed, there is! It simply equals 9 × 10 / 2. Can you show why such a formula holds? Click here to find out more.
is the number of teams and m
is the total number of matches, then the above formula provides the following relationship: n
− 1) / 2 = m
. Given m
, the quadratic equation needs to be solved for n
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