MathDB

A friction-less board has the shape of an equilateral triangle of side length

1

meter with bouncing walls along the sides. A tiny super bouncy ball is fired from vertex

A

towards the side

BC

. The ball bounces off the walls of the board nine times before it hits a vertex for the first time. The bounces are such that the angle of incidence equals the angle of reflection. The distance travelled by the ball in meters is of the form

\sqrt{N}

, where

N

is an integer. What is the value of

N

Problem Statement