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+1 vote
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in Iteration and Recursion by (49.1k points)
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A knockout tournament is a series of games. Two players complete in each game; the loser is knocked out (i.e. does not play any more), the winner carries on. The winner of the tournament is the player that is left after all other players have been knocked out. Suppose there are 1234 players in a tournament. How many games are played before the tournament winner is decided?

1 Answer

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by (54.8k points)
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Best answer
No. of players 2 3 4 5 n 1234
Mo. of games 1 2 3 4 n-1 1234 - 1 = 1233

On the other hand let n be the number of games, played and r be the number of players remaining in the tournament.

After every game, r will be reduced by 1.

r → no. of players remaining

n → no. of games played

If r = 2 then n = 1

As n increases, r decreases

n, r : = n + 1, r – 1

n + r = (n + 1) + (r – 1)

= n + 1 + r – 1

= n + r

Therefore n + r is invariant. n + r = 1234 (No. of players initially)

The winner of the tournament is the player that is left after all other players have been knocked out. After all the games, only one player (winner) is left out.

i. e. n = 1

Put n = 1 in (1)

n + r = 1234 …. (1)

1 + r = 1234

r = 1234 – 1 = 1233

No. of games played = 1233

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