MathDB

Let

n

be a positive integer. A \emph{pseudo-Gangnam Style} is a dance competition between players

A

and

B

. At time

0

, both players face to the north. For every

k\ge 1

, at time

2k-1

, player

A

can either choose to stay stationary, or turn

90^{\circ}

clockwise, and player

B

is forced to follow him; at time

2k

, player

B

can either choose to stay stationary, or turn

90^{\circ}

clockwise, and player

A

is forced to follow him.
After time

n

, the music stops and the competition is over. If the final position of both players is north or east,

A

wins. If the final position of both players is south or west,

B

wins. Determine who has a winning strategy when:
(a)

n=2013^{2012}

(b)

n=2013^{2013}

Problem Statement