Difference between revisions of "1997 AHSME Problems/Problem 24"
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==Problem== | ==Problem== | ||
− | A rising number, such as <math>34689</math>, is a positive integer each digit of which is larger than each of the digits to its left. There are <math>\binom{9}{5} = 126</math> five-digit rising numbers. When these numbers are arranged from smallest to largest, the <math>97^{th}</math> number in the list does not contain the digit | + | A rising number, such as <math>34689</math>, is a positive integer each digit of which is larger than each of the digits to its left. There are <math>\binom{9}{5} = 126</math> five-digit rising numbers. When these numbers are arranged from smallest to largest, the <math>97^{\text{th}}</math> number in the list does not contain the digit |
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8 </math> | <math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8 </math> |
Revision as of 18:51, 23 March 2020
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 . The answer is .
See also
1997 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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