Question 73
Pete and Bazil have a deck of $4026$ cards, $2013$ of which contain a digit $1$, while $2013$ others contain a digit $2$. Initially, Bazil uses all these cards to make a $4026$-digit number. After that, Pete makes several moves, each consisting in switching two cards and paying $1$ rouble to Bazil. The process stops when the resulting $4026$-digit number is divisible by $11$. Find the maximal amount of roubles Bazil may guarantee to receive by a suitable choice of the initial number. (P. Kozhevnikov)