Difference between revisions of "1997 AHSME Problems/Problem 24"

(Created page with "== See also == {{AHSME box|year=1997|num-b=23|num-a=25}}")
 
Line 1: Line 1:
 +
==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
 +
 +
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8 </math>
 +
 +
 
== See also ==
 
== See also ==
 
{{AHSME box|year=1997|num-b=23|num-a=25}}
 
{{AHSME box|year=1997|num-b=23|num-a=25}}

Revision as of 18:22, 9 August 2011

Problem

A rising number, such as $34689$, is a positive integer each digit of which is larger than each of the digits to its left. There are $\binom{9}{5} = 126$ five-digit rising numbers. When these numbers are arranged from smallest to largest, the $97^{th}$ number in the list does not contain the digit

$\textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8$


See also

1997 AHSME (ProblemsAnswer KeyResources)
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
Invalid username
Login to AoPS