Problem of the day 15 sept 2011

Rachel and Brian are playing a game in a grid with 1 row of 2011 squares. Initially, there is one
white checker in each of the first two squares from the left, and one black checker in the third square
from the left. At each stage, Rachel can choose to either run or ght. If Rachel runs, she moves the
black checker 1 unit to the right, and Brian moves each of the white checkers one unit to the right. If
Rachel chooses to fight, she pushes the checker immediately to the left of the black checker 1 unit to
the left, the black checker is moved 1 unit to the right, and Brian places a new white checker in the
cell immediately to the left of the black one. The game ends when the black checker reaches the last
cell. How many different final configurations are possible?

a) 2011   b) 2010  c) 2009 d) None