MathDB

Bugs Bunny plays a game in the Euclidean plane. At the

n

-th minute

(n \geq 1)

, Bugs Bunny hops a distance of

F_n

in the North, South, East, or West direction, where

F_n

is the

n

-th Fibonacci number (defined by

F_1 = F_2 =1

and

F_n = F_{n-1} + F_{n-2}

for

n \geq 3

). If the first two hops were perpendicular, prove that Bugs Bunny can never return to where he started.
Proposed by Dylan Toh

Problem Statement