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Puzzles & Brain Teasers
Football Matches
If 28 matches are totally played, how many teams participated?
8
Solution:
If 8 teams participated, then the first team plays matches against the other 7 teams. The second team has already played against the first team, and so has to play matches against only the other 6 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
7 + 6 + ........ + 2 + 1 = 28 .
If 28 matches are totally played, then 8 teams participated.
Food for thought:
Is there a formula to conveniently add
7 + 6 + ........ + 2 + 1 ?
Indeed, there is! It simply equals 7 × 8 / 2. Can you show why such a formula holds? Click here to find out more.
If n is the number of teams and m is the total number of matches, then the above formula provides the following relationship: n (n − 1) / 2 = m. Given m, the quadratic equation needs to be solved for n.
Wish to try another puzzle similar in concept to this one? Then click here.
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