Question 72
There are 2013 cards bearing the digit $1$ and 2013 bearing the digit $2$. Vasya arranges all the cards into a 4026-digit number. In one move Petya may interchange any two cards and pay Vasya 1 rouble. The process ends when Petya obtains a number divisible by $11$. What is the greatest amount Vasya can earn if Petya seeks to pay as little as possible? (P. Kozhevnikov)