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The Tournament (Posted on 2004-06-15) Difficulty: 2 of 5
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?

See The Solution Submitted by Gamer    
Rating: 2.4000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Simple | Comment 2 of 12 |
For #2 to be 2nd, he must get to the finals -- so if #1 plays in the same "half" of the tournament, #2 will be defeated before getting to the final.

In this case, after #1 has been seeded, #2 has 3/7 odds of ending in "the same half".

  Posted by e.g. on 2004-06-15 07:59:06
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