MathDB

Six ants are placed on the vertices of a regular hexagon with an area of

12

. At each point in time, each ant looks at the next ant in the hexagon (in counterclockwise order), and measures the distance,

s

, to the next ant. Each ant then proceeds towards the next ant at a speed of

\frac{s}{100}

units per year. After T years, the ants’ new positions are the vertices of a new hexagon with an area of

4

. T is of the form

a \ln b

, where

b

is square-free. Find

a + b

Problem Statement