MathDB

There are

23

balls on a table, all of which are either red or blue, such that the probability that there are

n

red balls and

23-n

blue balls on the table (

1 \le n \le 22

) is proportional to

n

. (e.g. the probability that there are

2

red balls and

21

blue balls is twice the probability that there are

1

red ball and

22

blue balls.) Given that the probability that the red balls and blue balls can be arranged in a line such that there is a blue ball on each end, no two red balls are next to each other, and an equal number of blue balls can be placed between each pair of adjacent red balls is

\frac{a}{b}

, where

a

and

b

are relatively prime positive integers, find

a+b

. Note: There can be any nonzero number of consecutive blue balls at the ends of the line.
Proposed by Ada Tsui

Problem Statement