1993 AJHSME Problems/Problem 22
Problem
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?
Solution
There is two in the one-digit numbers.
The number of two-digit numbers with a two in the tens place is and the number with a two in the ones place is . Thus the digit two is used times for the two digit numbers.
Now, Pat Peano only has remaining twos. You must subtract 1 because 22 is counted twice. The last numbers with a two that he can write are and . He can continue numbering the last couple pages without a two until , with the last number he writes being .
See Also
1993 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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