Matches in a tournament — Aptitude Question
Matches in a tournament: In a tournament where every team plays every other team once, 45 matches are played. Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 60 seconds
Question
In a tournament where every team plays every other team once, 45 matches are played. How many teams took part?
Options
- 9
- 10
- 11
- 12
Show the answer and the worked solution
Correct answer: B. 10
Worked solution
- n(n − 1)/2 = 45 → n(n − 1) = 90.
- 10 × 9 = 90, so n = 10.
Answer: 10.
The idea
Round-robin matches, handshakes and lines between points all count pairs, so all are C(n,2).
Shortcut. Double the matches: n(n − 1) = 90, a product of two consecutive integers, 10 × 9. The larger factor, 10, is the number of teams.
Common trap. "9" — taking the smaller of the two consecutive factors of 90; 9 teams play only 36 matches.