Knock-out Cricket Tournament

A single elimination (knock out – one loss & out) cricket tournament has 16 teams competing. How many games must be played to get one champion?

Typically, the majority problem solvers will do something like this –

i) Taking 2 groups of 8 teams, playing 1st round. In each group there are 4 matches, eliminating 4 teams. Total 8 matches & 8 teams remaining in the tournament.

ii) Now 4 Quarter-final matches to get the top 4 teams of the tournament. (8 + 4 = 12 matches so far)

iii) 2 Semi-finals & a final to get the champion. (12 + 2 + 1 = 15 matches total)

A much simpler way to solve this problem is to focus only the losers, not the winners.

“How many losers must be there in a tournament of 16 teams to get one winner?” The answer is simply 15.

“How many games must be played to get 15 losers?” Naturally 15.

That’s the answer.