I'm Confused!

[saintpeter48]

512 men enter a singles darts knock-out tournament how many matches have to be played in total to get a winner?

[JimF]

Surely it will depend how it's structured. E.g. think of the football World Cup finals - all teams don't play all other teams, because they're initially divided into groups, etc.

[sandyRoe]

309, I think

[Tilly2]

256
148
74
37
?????

[saintpeter48]

Tilly
256
128
64
32
16
8
4
2
1
I think.

[Tilly2]

Try again
256
128
64
32
16
8
4
2
1

[Tilly2]

511 games

[sandyRoe]

510?
Do you count the last 1?

[Calibax]

In a straight knock-out between n teams (where n is a power of 2) there will be n-1 matches, so 511

[Tilly2]

Perhaps not, Sandy. :-)

[Tilly2]

Then again...a mathematician has got it sorted. :-)

[Tilly2]

Thanks, Calibax.

[Calibax]

If there were only 8 participants, there would be 4 quarter finals, 2 semi-finals and a final = 7

[fiction-factory]

512 enter. So 511 people have to lose a match. Each loser loses once. Hence answer is there are 511 matches

The answer to all these knockout competitions with n entrants is n-1 matches

[fiction-factory]

Sorry, got distracted before submitting- didn't see Calibax's

[Tilly2]

Hee hee! I was right.

I had to use a pencil and a piece of paper though. I could not have done that in my head.

[fiction-factory]

If there were 7 entrants one would get a bye and6 would play quarter finals. So that's 3 matches so far.
Then 2 in the semi
Then 1 in the final
So I think it works even if n isn't a power of 2.

3 entrants- 1 bye, 1 semi, 1 final. So 2 matches

[Mozz71]

I worked it out the same way as Sandy, so curse FF and his flawless logic.

[Tilly2]

I just read the question to Mr T and, half a minute later, he said, 8 rounds plus the final.

Pfft!

[Tilly2]

How did Sandy work it out, Mozz? He hasn't said.

[Cloverjo]

Fiction-factory has it.
Only one winner; 511 men have to be knocked out. No byes. So 511 matches.