Question 21
Positive integers are written on $2012$ cards, one number on each side. On the first card, numbers $1$ and $2$ are written, on the second, $3$ and $4$, ..., on the $2012$th, $4023$ and $4024$. All cards are arranged in line along a table. Two players play the following game. During each move a player chooses $5$ cards and swaps them. If after his move the set of numbers face up is the same as after one of previous turns, he loses. Which of the players has a winning strategy?