MathDB

Let

n

be a positive integer. Two players

A

and

B

play a game in which they take turns choosing positive integers

k \le n

. The rules of the game are:
(i) A player cannot choose a number that has been chosen by either player on any previous turn. (ii) A player cannot choose a number consecutive to any of those the player has already chosen on any previous turn. (iii) The game is a draw if all numbers have been chosen; otherwise the player who cannot choose a number anymore loses the game.
The player

A

takes the first turn. Determine the outcome of the game, assuming that both players use optimal strategies.
Proposed by Finland

Problem Statement