Answer:
341 matches
Step-by-step explanation:
Given
[tex]Players = 342[/tex]
[tex]Match = 2\ players[/tex]
Required
Total number of matches.
The total number of matches is calculated by getting the number of matches in each round.
i.e.
[tex]Matches = \frac{Players}{2}[/tex]
So, we have:
Round 1
[tex]Matches = \frac{342}{2} = 171[/tex]
Round 2
[tex]Matches = \frac{171}{2} = 85\ R\ 1[/tex] [R 1 means remainder 1]
Round 3
[tex]Matches = \frac{85 + 1}{2} = \frac{86}{2} = 43[/tex]
[The remainder is added to each round]
Round 4
[tex]Matches = \frac{43}{2} = 21\ R\ 1[/tex]
Round 5
[tex]Matches = \frac{21+1}{2} = \frac{22}{2} = 11[/tex]
Round 6
[tex]Matches = \frac{11}{2} = 5\ R\ 1[/tex]
Round 7
[tex]Matches = \frac{5+1}{2} = \frac{6}{2} =3[/tex]
Round 8
[tex]Matches =\frac{3}{2} = 1 + 1[/tex]
Round 9
[tex]Matches = \frac{1+1}{2} =\frac{2}{2} = 1[/tex]
So, the total is:
[tex]Total = 171 + 85 + 43 +21 + 11 + 5 + 3 + 1+1[/tex]
[tex]Total = 341[/tex]
