MathDB

Consider a cube and two of its vertices

A

and

B

, which are the endpoints of a face diagonal. A path is a sequence of cube angles, each step of one angle along a cube edge is walked to one of the three adjacent angles. Let

a

be the number of paths of length

2012

that starts at point

A

and ends at

A

and let b be the number of ways of length

2012

that starts in

A

and ends in

B

. Decide which of the two numbers

a

and

b

is the larger.

Problem Statement