[Peekay]

Here's an easy one and may have been posted earlier but I couldn't find it...

The other day our local club organized a knock-out tennis tournament. Unfortunately, there were only 29 players who signed up. If there were 3 more players, everything would have been so much easier! But now, the organizers had to figure out 1st round "bye"s and, if necessary, "bye"s for other rounds as well. Well they did take care of it ultimately. Considering all these "bye"s and what not, how many matches were played?

There is a regular way of figuring this out and an easy way. I'm more interested in the easy solution.

[preflop]

Not hard

For any single elimination tournament, the total number of games needed to determine a champion is (# of entrants) - 1.

So in this case 28

[Guest]

[spoiFirst 3 seeds get a bye initially, no byes after 1st round total games played 28

Round Games Byes

1 13 3

2 8

3 4

4 2

5 1

Total 28

[Guest]

as said preflop: "the number of game is equal to the number of player entrant minus 1".

The explanation is this: for each game one player is eliminated.

You have to keep on until one player (the torunament winner) is left.

I think that this is the more simple answer because it is indipendent from the torunament formula.

In other words you have not to think to the formula to know how many games you have to arrange.

And there's no way (i.e. no tournament formula) with a different number of games.

Not hard

For any single elimination tournament, the total number of games needed to determine a champion is (# of entrants) - 1.

So in this case 28

Edited April 26, 2011 by gramp

[Guest]

28

Edited April 27, 2011 by dwardodweebs067

[Peekay]

Absolutely correct preflop (#2)- gramps (#4) gives a nice explanation. So, I don't have to add anything!

[Guest]

14 matches first round, 1 person gets bye. 15 people after first round.

7 matches second round, 1 person gets bye. 8 people after second round.

4 matches third round. 4 people left

2 matches fourth round 2 people left

1 match last round.

15+8+4+2+1 = 30 matches, including byes.

to gramps and others, you generally want as few byes as possible every round. in this case byes are counted toward matches.

if you don't count byes then i agree the answer is #of entrants -1, but when you do, the answer is generally #of entrants +1. (there are obvious exceptions to this formula of course.)

[Guest]

14 matches first round, 1 person gets bye. 15 people after first round.

7 matches second round, 1 person gets bye. 8 people after second round.

4 matches third round. 4 people left

2 matches fourth round 2 people left

1 match last round.

15+8+4+2+1 = 30 matches, including byes.

to gramps and others, you generally want as few byes as possible every round. in this case byes are counted toward matches.

if you don't count byes then i agree the answer is #of entrants -1, but when you do, the answer is generally #of entrants +1. (there are obvious exceptions to this formula of course.)

yes Phillip,

... but for us getting a bye is not counted as playing the game!

Edited April 28, 2011 by gramp

[Guest]

14 matches first round, 1 person gets bye. 15 people after first round.

7 matches second round, 1 person gets bye. 8 people after second round.

4 matches third round. 4 people left

2 matches fourth round 2 people left

1 match last round.

15+8+4+2+1 = 30 matches, including byes.

to gramps and others, you generally want as few byes as possible every round. in this case byes are counted toward matches.

if you don't count byes then i agree the answer is #of entrants -1, but when you do, the answer is generally #of entrants +1. (there are obvious exceptions to this formula of course.)

Your formula 15+8+4+2+1 is counting people left, not matches. By your own description there are

14+7+4+2+1 matches, which equals 28!