Question 9
Alice and Bob play a game on a $1 \times m$ board using $2012$ cards numbered from $1$ through $2012$. At each step, Alice chooses a card and Bob places it on an empty square of the board. Bob wins the game when numbers on the cards on the board are in an increasing order after $k$ steps where $1 \leq k \leq 2012$, otherwise Alice wins. Find all pairs $(k, m)$ for which Bob can guarantee to win the game.