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1500 teams compete in a tournament. The organizers let the teams know that every game is played with exactly 2 teams and must have a winner and that the team that loses a game is immediately excluded from the tournament. How many games will be played until the champion is known? Show how to use the bijection rule to solve this problem and show a numeric answer.

Respuesta :

Answer:

1499

Step-by-step explanation:

Given there are 1500 team in a tournament .

Game is played between exactly 2 team

And looser immediately exclude from tournament.

We calculate the number of game :

We constant divide the number of teams by 2 and the quotient is divided for the next division until we get quotient as 1 and the remainder as 0.

And each time we divide, if the divident is even add quotient to the number of game in tournament if add then quotient + 1 to the number of game in the tournament.

2 | 500

2 | 750

2 | 375

2 | 187

2 | 93

2 | 46

2 | 23

2 | 11

2 | 5

2 | 2

     1

Therefore, 750 + 375 + 187 + 1 +93 + 1 + 46 + 1 +23 + 11 + 1 + 5 + 1 + 2 + 1

                   = 1499

Therefore, total number of games is 1499.

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