Question

A tennis tournament has 342 players. A single match involves 2 players. The winner of a match will play the winner of a match in the next round, whereas losers are eliminated from the tournament. The 2 players who have won all previous rounds play in the final game, and the winner wins the tournament. What is the total number of matches

Answer 1

341 matches

Explanation:

Given

`Players = 342`

`Match = 2\ players`

Required

Total number of matches.

The total number of matches is calculated by getting the number of matches in each round.

i.e.

`Matches = (Players)/(2)`

So, we have:

Round 1

`Matches = (342)/(2) = 171`

Round 2

`Matches = (171)/(2) = 85\ R\ 1` [R 1 means remainder 1]

Round 3

`Matches = (85 + 1)/(2) = (86)/(2) = 43`

[The remainder is added to each round]

Round 4

`Matches = (43)/(2) = 21\ R\ 1`

Round 5

`Matches = (21+1)/(2) = (22)/(2) = 11`

Round 6

`Matches = (11)/(2) = 5\ R\ 1`

Round 7

`Matches = (5+1)/(2) = (6)/(2) =3`

Round 8

`Matches =(3)/(2) = 1 + 1`

Round 9

`Matches = (1+1)/(2) =(2)/(2) = 1`

So, the total is:

`Total = 171 + 85 + 43 +21 + 11 + 5 + 3 + 1+1`

`Total = 341`