A Tennis Tournament

At the end of the match, there is only one winner, meaning that there are $99$ losers. Since each match determines exactly one loser, there must be exactly $\boxed{99}$ matches.

You sort of have to read this twice to understand it.

So every time you have a number of competitors, you must divide it in half in order to see how many players will be left over. You can think of this by using simple numbers like $4$ or $6$ . What you'll find by doing that is that the number of competitors remaining after all of those 1 v 1 matches is the also the number of matches that took place. So if there were $4$ competitors, there would be $2$ matches before the second round started. So this is how I did it...

$\frac{100}{2} = 50$

$\frac{50}{2} = 25$

Now here's the tricky part. We have an odd number of players, so how do we go about dividing it? This is where reading the problem again helps. If there are only 1 v 1 matches, and anybody who loses is out of the tournament , then you can just take out one of the contestants and sit them off to the side. Think of that contestant being in a sort of waiting line.

Now we can continue...

$25 - 1 = 24$

$\frac{24}{2} = 12$

$\frac{12}{2} = 6$

$\frac{6}{2} = 3$

Now here's the last tricky part. We have three players left. That's an odd number, so we can just take that player that we put in the waiting line, and throw him in there. Now if we do the simple math, we will find that there will be $3$ matches between those $4$ players before the winner is determined. So now we can just simply add up the number of matches!

$50 + 25 + 12 + 6 + 3 + 3 = \boxed{99 }$

So there will be $99$ matches before the winner is determined from those $100$ competitors.

THERE ARE 100 PLAYERS. WE HAVE TO CALCULATE THE NUMBER OF MATCHES BEFORE THE WINNER IS DETERMINED. IF FIRST MATCH IS PLAYED BETWEEN ANY TWO PLAYERS, THEN ONE WOULD BE WINNER AND ANOTHER WOULD BE LOSER. THE LOSER WILL BE ELIMINATED. THEREFORE FROM THE TOTAL NUMBER OF PLAYERS, 1 WOULD BE ELIMINATED OR SUBTRACTED. FOR ANY MATCH TO BE PLAYED BETWEEN TWO PLAYERS, ONE WOULD BE ALWAYS ELIMINATED. THEREFORE FOR N PLAYERS, N-1 MATCHES WOULD BE REQUIRED BEFORE THE WINNER IS DETERMINED. THEREFORE FOR 100 PLAYERS, 100-1=99 MATCHES WOULD BE REQUIRED BEFORE THE WINNER IS DETERMINED. ANS:-\BOXED{99}

With technical meeting usually, an organization had processed that 100 ----- (50)----- 50 ------(25)------25 ---> 25 = 16 + 9. Then, 16------(8)-----8-----(4)-------4 --------(2)--------(1)------1 ; 9 = 8 + 1 ----> 8 ----- (5)-----4----(2)----2------(1)-----1 , (1). So, matches must be played before the winner is determined is (50)+(25)+(8)+(4)+(2)+(1)+(5)+(2)+(1)+(1) = 99. Answer : 99.

100-1=99

It's obvious

You have 100 players, and 1 is knocked out per match leaving one winner, ergo you must have 99 matches to knock out the 99 losers.

50+25+12+6+3+2+1=99

After 50 matches between 100 players, 50 will remain. After 25 more matches between 50 players, 25 will remain. After 12 more matches between 24 players, 12 will remain plus one player who haven't played a match yet. After 6 more matches between 12 players, 6 will remain. After 3 matches between 6 players, 3 will remain. The played without a match will come in to play. After 2 matches between 4 players, 2 will remain. and the Final one Match from which one will be a winner.

50+25+12+6+3+2+1 =99

the formula os single tournament is n-1. so 100-1 = 99.

100-1 = 99 If there is a third place, use 100-1+1

Here is 100 player and the tournament has single-elimination so we ensure that first round has 100/2=50 match.Second round has 50/2=25 match.Third round has 25/2=12+1 match.Fourth round has 12/2=6 match.Fifth round has 6/2=3 match. sixth round has 3/2=1+1 match, So total number of match is 50+25+(12+1)+6+3+(1+1)=99