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Using the numbers 2 22 times in a sequence starting with 1

Source: 1993 AMC 8 Problem 22

June 28, 2011
AMC

Problem Statement

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?
(A) 22(B) 99(C) 112(D) 119(E) 199\text{(A)}\ 22 \qquad \text{(B)}\ 99 \qquad \text{(C)}\ 112 \qquad \text{(D)}\ 119 \qquad \text{(E)}\ 199
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