Problem 22 (1993 AJHSME)

Pat Peano has plenty of $0$'s, $1$'s, $3$'s, $4$'s, $5$'s, $6$'s, $7$'s, $8$'s and $9$'s, but he has only twenty-two $2$'s. How far can he number the pages of his scrapbook with these digits?