MathDB

Let

\Gamma

be a circle in the plane and

S

be a point on

\Gamma

. Mario and Luigi drive around the circle

\Gamma

with their go-karts. They both start at

S

at the same time. They both drive for exactly

6

minutes at constant speed counterclockwise around the circle. During these

6

minutes, Luigi makes exactly one lap around

\Gamma

while Mario, who is three times as fast, makes three laps.
While Mario and Luigi drive their go-karts, Princess Daisy positions herself such that she is always exactly in the middle of the chord between them. When she reaches a point she has already visited, she marks it with a banana.
How many points in the plane, apart from

S

, are marked with a banana by the end of the

6

minutes.

Problem Statement