Game Plugs

How many games must be played to determine the tournament winner?

In a basketball tournament, each team plays until it loses a game, then it is out of the tournament. If 64 teams are in the tournament at the start, how many games must be played to determine the tournament winner?

Public Comments

1. 63
2. You pair up the teams: 64 teams → 32 games That eliminates 32 teams. So you have 32 left. Pair them up: 32 teams → 16 games That eliminates half again. Keep it up: 16 teams → 8 games 8 teams → 4 games 4 teams → 2 games 2 teams → 1 game After that, you are of course done (one team left). The total is: 32 + 16 + 8 + 4 + 2 + 1 = 63. This is actually related to a rule in mathematics: 2^(n-1) + 2^(n-2) + .... + 4 + 2 + 1 = 2^n - 1 But it's more obvious than that! Just think. How many teams need to be eliminated to have one left? All but one. That requires one game per team to be eliminated. So to eliminate 63 teams, you need 63 games.