1997 AHSME Problems/Problem 24
Problem
A rising number, such as , is a positive integer each digit of which is larger than each of the digits to its left. There are five-digit rising numbers. When these numbers are arranged from smallest to largest, the number in the list does not contain the digit
Solution
The list starts with . There are four-digit rising numbers that do not begin with , and thus also five digit rising numbers that do begin with that are formed by simply putting a before the four digit number.
Thus, the number is . There are three-digit rising numbers that do not begin with a or , and thus five digit rising numbers that begin with a .
Thus, the number is . Counting up, is the number, which does not contain the digit .
See also
1997 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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