6. Pete and Vasya are playing a game. On the board, there is a number: 11223334445555666677777. In one move, it is allowed to erase any number of identical digits. The player who erases the last digit wins. Pete goes first. Can he play in such a way as to guarantee a win?
Answer: Yes, he can.

Solution: On his first move, Petya can, for example, erase all the digits 7. The remaining digits can be written as:

113335555 | 666644422.

After this, Petya symmetrically (relative to the middle line) repeats Vasya's moves.