Question 106
Let $n$ be a positive integer. Two people $P$, $Q$ play a game in which they call an integer $m$ ($1 \le m \le n$) alternately. $P$ calls the first number. They cannot call the numbers which are already called by themselves or by their opponent. The game is over when neither can call numbers. If the sum of the numbers that $P$ has called is divisible by $3$, $P$ wins, otherwise $Q$ wins. Find all $n$ which satisfy the condition below.
Condition: $P$ can win the game whatever $Q$ does.
Condition: $P$ can win the game whatever $Q$ does.