Arjun and Beth play a game in which they take turns removing one brick or two adjacent bricks from one “wall” among a set of several walls of bricks, with gaps possibly creating new walls. The walls are one brick tall. For example, a set of walls of sizes 4 and 2 can be changed into any of the following by one move: (3,2),(2,1,2),(4),(4,1),(2,2), or (1,1,2).
Arjun plays first, and the player who removes the last
brick wins. For which starting configuration is there a strategy that guarantees a win for Beth?
Answer Choices
A. (6,1,1)
B. (6,2,1)
C. (6,2,2)
D. (6,3,1)
E. (6,3,2)