MathDB
A Rising Number

Source:

January 18, 2009

Problem Statement

A rising number, such as 34689 34689, is a positive integer each digit of which is larger than each of the digits to its left. There are \dbinom{9}{5} \equal{} 126 five-digit rising numbers. When these numbers are arranged from smallest to largest, the 97 97th number in the list does not contain the digit <spanclass=latexbold>(A)</span> 4<spanclass=latexbold>(B)</span> 5<spanclass=latexbold>(C)</span> 6<spanclass=latexbold>(D)</span> 7<spanclass=latexbold>(E)</span> 8 <span class='latex-bold'>(A)</span>\ 4\qquad <span class='latex-bold'>(B)</span>\ 5\qquad <span class='latex-bold'>(C)</span>\ 6\qquad <span class='latex-bold'>(D)</span>\ 7\qquad <span class='latex-bold'>(E)</span>\ 8