Sports tournament probability: 3 tournaments held over 3 different days....

Rout

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Hi there. I am hoping someone out there can help me come up with a solution to help me settle an argument about a sports event

There were 3 tournaments held over 3 different days. Fri, Sat and Sun. The fri tournament had 84 players entered in it. There was a prelim round, to whittle 84 down to 72. Then 72 played in the first round.

In both the sat and sun tournaments there were exactly 128 players.

The same two players drew each other in the first round proper on Fri (the last 72 stage). And then on both Saturday and Sunday in the first round (Last 128 stage)

To complicate matters, there were seedings. There were 18 seeds on the Friday. and 16 seeds on the Sat and Sun. They are kept apart in the draw until the last 32 stage (last 36 stage on Fri).

The two players involved were not seeds on any of the days. (So could draw anyone)

Youve probably guessed by now, I am looking for the odds (ie 1 in. . . ) of this happening

Any help would be massively appreciated!
 
Hi there. I am hoping someone out there can help me come up with a solution to help me settle an argument about a sports event

There were 3 tournaments held over 3 different days. Fri, Sat and Sun. The fri tournament had 84 players entered in it. There was a prelim round, to whittle 84 down to 72. Then 72 played in the first round.

In both the sat and sun tournaments there were exactly 128 players.
Where did the extra players come from?

The same two players drew each other in the first round proper on Fri (the last 72 stage). And then on both Saturday and Sunday in the first round (Last 128 stage)
I'm sorry, but I don't understand what this means...?

To complicate matters, there were seedings. There were 18 seeds on the Friday. and 16 seeds on the Sat and Sun. They are kept apart in the draw until the last 32 stage (last 36 stage on Fri).

The two players involved were not seeds on any of the days. (So could draw anyone)

Youve probably guessed by now, I am looking for the odds (ie 1 in. . . ) of this happening
Please reply with the full and exact text of the exercise, the complete instructions, and a clear statement of your thoughts and efforts so far. Thank you! ;)
 
For the Friday tournament, do you mean there was a prelim round to whittle 84 down to 64​?
 
Where did the extra players come from?


I'm sorry, but I don't understand what this means...?


Please reply with the full and exact text of the exercise, the complete instructions, and a clear statement of your thoughts and efforts so far. Thank you! ;)

Thanks for your reply!

Sorry, this isn't homework. Ive only realised on revisiting the forum that its aimed at help with peoples homework. I just googled it and saw freemathhelp and thought it was open to all!

So its about 3 darts competitions that took place over a Friday, saturday and sunday.

The sat and sun comps are pretty straight forward. There are 128 players that entered each. There are 32 seeds, who are spaced out in the draw so they are kept apart until the last 32 stage at the earliest. The two players in question drew each other in round 1 (the last 128 stage) on both days.

On the friday, though it was a different event which acted as a qualifier for a bigger tournament. 84 started the tournament. There was a prelim round to get from 84 down to 72. The two players in question drew each other in the last 72 stage. So it was their first game as they avoided having to play one of the few preliminary round games.

So basically I am trying to find out the odds of two people being drawn together in round 1 in all three of these comps.

My thoughts are Sat and Sun is 1/127x1/127 and then times that by the friday odds - but to be totally honest i really don't know about the Friday, other than 1/71 or 1/83.

Someone else says the friday odds shouldn't be included as both players had to play someone so you only start adding the odds together from the second onwards, but that doesn't sound right to me!

Anyone who thinks they can crack this id appreciate it!
 
For the Friday tournament, do you mean there was a prelim round to whittle 84 down to 64​?

Hi Jonathan.

No, because the friday was a qualifier for a bigger event. So there were quite a few "winners" of this comp, not just playing down to a 1v1 final. There were 9 qualifiers so the tournament bracket went 9/18/36/72 instead of the normal 2/4/6/8/16/32 etc
 
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