perplexus.info :: Games : The Tournament

The Tournament (Posted on 2004-06-15)

In a basketball tournament, there are teams named 1 through 8, such that a lower number team is better than a higher numbered team. (1 is best, 2 is second best... 8 is worst) Also, a better team will always win over a worse team. (There are no upsets)


?-\__
?-/  |
     |--\
?-\__|  |
?-/     |
        |-WINNER
?-\__   |
?-/  |  |
     |--/
?-\__|
?-/

Here is the grid for the tournament

If the better team always wins (there are no upsets) and if the pairing is completely random, what is the easiest way to figure the probability that team 2 doesn't win second place?

Submitted by Gamer

Rating: 2.4000 (5 votes)

Solution: (Hide)

Since the pairing is symmetric, put 1 in any spot. There are 3 spots where 1 will play 2 before the last branch, and 4 places where 2 will not. Because the only way 2 won't win second place is if it plays 1 before the last branch, the probability is 3/7.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	Arthur Swanson	2022-12-12 04:09:37
Amazing	Nick Williams	2004-07-21 20:09:07
May be like this...	Strahinja	2004-07-10 05:18:16
No Subject	David	2004-07-07 01:29:55
easy...	Strahinja	2004-07-02 09:28:23
The Answer is Easy...	seant	2004-06-18 20:40:56
just a guess	kristi	2004-06-18 00:56:10
re: this is easy	Charlie	2004-06-15 13:02:49
this is easy	nate	2004-06-15 12:58:01
re: So why not do it the hard way? WHY NOT EVEN HARDER	Ady TZIDON	2004-06-15 12:05:18
So why not do it the hard way?	Jer	2004-06-15 09:09:21
Simple	e.g.	2004-06-15 07:59:06
ELEMENTARY, DEAR WATSON	Ady TZIDON	2004-06-15 06:11:39

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