Question

Traditionally, the annual end-of-season badminton tournament at St. Sebastian's High School features 32 pupils. This year, the tournament has attracted 54 entrants. Members of the school team are always automatically admitted to the tournament.
It is decided to play one qualifying round during the week before the tournament for all of the other entrants.
How many matches take place in the qualifying round? How many members does the school team have?
How many matches in total (qualifying plus tournament) will have taken place by the time a champion is crowned?

Answer 1

Let the number of school team members be x, then
(54 - x)/2 + x = 32
54 + x = 32 x 2 = 64
x = 64 - 54 = 10

Therefore, the school has 10 team members.
(54 - 10) / 2 = 44/2 = 22 matches took place in the qualifing round.

22 + 16 + 8 + 4 + 2 + 1 = 53 matches took place by the time a champion is crowned.