MathDB

Ava and Tiffany participate in a knockout tournament consisting of a total of

32

players. In each of

5

rounds, the remaining players are paired uniformly at random. In each pair, both players are equally likely to win, and the loser is knocked out of the tournament. The probability that Ava and Tiffany play each other during the tournament is

\tfrac{a}{b},

where

a

and

b

are relatively prime positive integers. Compute

100a + b.

Problem Statement