Question 83
Initially $100$ numbers $1$ are arranged on a circle. Petya and Vasya play the following game, taking turns; each boy performs $10^{10}$ moves; Petya starts. By his move, Petya chooses $9$ consecutive numbers and decreases each of them by $2$. By his move, Vasya chooses $10$ consecutive numbers and increases each of them by $1$. Prove that Vasya can play so that after each his move among the numbers on the circle there will be at least $5$ positive numbers (regardless of Petya's moves).