MathDB

There are a total of

n

boys and girls sitting in a big circle. Now, Dave wants to walk around the circle. For a start point, if at any time, one of the following two conditions holds:
1. he doesn't see any girl 2. the number of boys he saw

\ge

the number of girls he saw

+k

Then we say this point is good. What is the maximum of

r

with the property that there is at least one good point whenever the number of girls is

r

Problem Statement