SOLUTION: There are twenty chess teams in a tournament. How many games will be played if each team is eliminated with one loss?

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Question 270738: There are twenty chess teams in a tournament. How many games will be played if each team is eliminated with one loss?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
first round you have 20 teams playing.

10 games are played and 10 teams advance to the next round.

second round you have 10 teams playing.

5 games are played and 5 teams advance to the next round.

third round you have 4 teams playing and one team doesn't play this round.

2 games are played and 3 teams advance to the next round (2 winners and the team that sat out).

fourth round you have 2 teams playing and one team doesn't play this round.

1 game is played and 2 teams advance to the final round (1 winner and the team that sat out).

fifth round you have 2 teams playing.

1 game is played and winner of that game is winner of the tournament.

total number of games played is:

10 + 5 + 2 + 1 + 1 = 19