MathNet 2014 Question 53

Let $n$ be a positive integer. Daniël and Merlijn play a game. Daniël has $k$ sheets of paper lying side by side on a table, where $k$ is positive integral. On each sheet he writes some of the numbers from $1$ to $n$ (possibly none or all). On its reverse he writes exactly the remaining numbers from $1$ to $n$. When Daniël finishes, Merlijn may turn some sheets reverse-side up (possibly none or all). If he can make every number from $1$ to $n$ simultaneously visible, with repetitions allowed, he wins.

Determine the smallest $k$ for which Merlijn can always win, whatever Daniël does.