Question

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?

$22$

$99$

$112$

$119$

$199$

Solution:

Numbering $1$ through $99$ uses ten $2$ 's in the units place and ten in the tens place, a total of twenty $2$ 's. Pages $100$ and $101$ use none.

The remaining two $2$ 's are used on pages $102$ and $112.$ After that, pages $113$ through $119$ need no $2,$ but $120$ would require another $2,$ so he can number up to $119.$

Thus, the correct answer is D .

1993 AMC 8 Problem 22

Solution:

Problem 22 in Other Years