Q.A league-cum-knock-out tournament has 20 teams divided into 4 pools of 5 teams each. Each pool plays a round-robin league, and the top 2 teams from each pool enter a knock-out stage. Calculate the total number of matches played in the whole tournament.

The tournament unfolds in two stages: a league (round-robin) stage within each pool, followed by a knock-out stage among the qualifiers.

Stage 1: League matches within pools

Each of the 4 pools contains 5 teams playing a round-robin. For a league of N teams, the number of matches is

Matches per pool = (N(N-1))/2.

Substituting N = 5:

Matches per pool = (5 × 4)/2 = 10.

Since there are 4 pools,

Total league matches = 4 × 10 = 40.

Stage 2: Knock-out matches

The top 2 teams from each pool advance, giving 4 × 2 = 8 teams in the knock-out stage. For a knock-out tournament with N teams, the number of matches is …

This question tests your understanding of combination tournaments, where two formats are chained together. The league-cum-knock-out structure is common in major sporting events: it ensures every team gets multiple games (fairness and spectator value) while the knock-out stage delivers a clear, dramatic champion. You must calculate matches for each stage separately, then sum them.

Stage 1: League (Round-Robin) in Each Pool

Each of the 4 pools contains 5 teams. Within a pool, every team plays every other team exactly once — a round-robin league.

The prescribed formula for a league tournament with N teams is:

For one pool of 5 teams:

Matches per pool = (5 × (5 - 1))/2 = (5 × 4)/2 = 20/2 = 10

Since there are 4 pools, the total number of league matches is:

Total league matches = 4 × 10 = 40

Stage 2: Knock-Out Among Qualifiers

The top 2 teams from each pool advance to the knock-out stage. That gives us:

Qualifiers = 4 pools × 2 teams = 8 teams

These 8 teams now compete in a single-elimination knock-out tournament. The prescribed formula for a knock-out tournament with N teams is:

For 8 teams: …