Question 92
Let $n$ be a positive integer, and write down $1, 2, \dots, n$ on the blackboard. Alpha and Lee take turn choosing a number from the board according to the following rules:
(i) You cannot choose any number that was previously selected by either player.
(ii) If you have chosen $k$, you cannot choose $k-1$ or $k+1$.
(iii) The game is a draw if all numbers are chosen. Otherwise, the player who cannot choose any number first loses the game.
Suppose Alpha chooses first. Determine all $n$ such that Lee has a winning strategy.
(i) You cannot choose any number that was previously selected by either player.
(ii) If you have chosen $k$, you cannot choose $k-1$ or $k+1$.
(iii) The game is a draw if all numbers are chosen. Otherwise, the player who cannot choose any number first loses the game.
Suppose Alpha chooses first. Determine all $n$ such that Lee has a winning strategy.