Ruth is scheduling a soccer tournament in which 64 teams will participate. After each round of soccer games, half the teams advance to the next round of the tournament. After all the rounds are played, how many total games are in the tournament?
Is it 48?
The 1st round consist of 64 teams and
32 games. After each round, the number of teams and the number of games is re-
duced by a factor of 2:
Round Team Games.
1. 64 32.
2. 32 16.
3. 16 8.
4. 8 4.
5. 4 2.
6. 2 1.
Total = 61 Games.
32+16+8+4+2+1=63
- Cheat Code Maven
To determine the total number of games in the tournament, we need to consider that after each round, half of the teams advance to the next round. We start with 64 teams.
In the first round, half of the teams advance, which leaves us with 32 teams for the second round. In the second round, half of the teams advance again, leaving us with 16 teams for the third round. This process continues until only one team remains.
To calculate the total number of games, we can observe that in each round, the number of games is equal to half the number of teams from the previous round. So, for example, in the first round, with 64 teams, there are 32 games (64/2).
To find the total number of games, we can sum the number of games in each round.
Starting with 64 teams, we have:
Round 1: 32 games
Round 2: 16 games
Round 3: 8 games
Round 4: 4 games
Round 5: 2 games
Round 6 (final): 1 game
Adding up the number of games in each round, we have:
32 + 16 + 8 + 4 + 2 + 1 = 63
Therefore, the total number of games in the tournament is 63, not 48.