Question

Thirty-two players ranked $1$ to $32$ are playing in a knockout tournament, Assume that in every match between any two players the better ranked players wins, the probability that ranked $1$ and ranked $2$ players are winner and runner up respectively is $p$, then the value of $\left[2/p\right]$ is, where [.] represents the greatest integer function.

• A. $2$
• B. $3$
• C. $4$
• D. $1$

Answer 1

The correct option is B $3$

Yes, the player ranked number 11 will win all of his matches, and will eventually win the tournament.

probability is that the players ranked 11 and 22 will meet in the final (because only in this scenario, the ranked 11 player will win, and the ranked 22 player will be the runner-up),for the two players to meet in the final, we need to avoid that they meet before the final

In round 1, 1 can meet all 31 player except 2 p=31/32

In round 2, 1 can meet all 14 player except 2 p=14/15

In round 3, 1 can meet all 6 player except 2 p=6/7

In round 4, 1 can meet all 2 player except 2 p=2/3

Therefore required probability=(31/32)*(14/15)*(6/7)*(2/3)=16/31

2/p=62/16=3.7

[2/p]=3