MathDB

Alice and Bob play a game on a numbered row of

n \ge 5

squares. At the beginning a pebble is put on the first square and then the players make consecutive moves; Alice starts. During a move a player is allowed to choose one of the following:
[*] move the pebble one square forward; [*] move the pebble four squares forward; [*] move the pebble two squares backwards.
All of the possible moves are only allowed if the pebble stays within the borders of the square row. The player who moves the pebble to the last square (a.k.a

n\text{-th}

) wins. Determine for which values of

n

each of the players has a winning strategy.

Problem Statement