MathDB

C3

Part of 2019-IMOC

Problems(1)

walking around circle of two sexes

Source: IMOC 2019 C3

8/19/2021
There are a total of nn 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+k Then we say this point is good. What is the maximum of rr with the property that there is at least one good point whenever the number of girls is rr?
combinatorics