The Chess Tournament Bracket

The Story: The all-India inter-school chess championship is held every year in Chennai. This year, 64 students have registered to compete. The tournament director, Mrs. Radha, is explaining the format to the school principals gathered in the auditorium. 'We use a single-elimination format,' she says. 'Every round, players are paired up. The winner advances. The loser is eliminated. No draws, no byes, no second chances.' One of the principals, a retired mathematics professor, raises his hand. 'So how many total games will be played across the entire tournament?' he asks. 'And,' adds another principal, 'how many rounds will it take before we have a champion?' Mrs. Radha smiles at the retired professor. 'You tell me,' she says. The Challenge: In a single-elimination tournament with 64 players, how many total games are played? How many rounds does it take? Now generalise for any number of players n that is a power of 2.