MathDB
'Covering' the integer 1998

Source: Baltic Way 1998

January 11, 2011
combinatorics proposedcombinatorics

Problem Statement

We say that some positive integer mm covers the number 19981998, if 1,9,9,81,9,9,8 appear in this order as digits of mm. (For instance 19981998 is covered by 2<spanclass=′latex−bold′>1</span>59<spanclass=′latex−bold′>9</span>36<spanclass=′latex−bold′>98</span>2<span class='latex-bold'>1</span>59<span class='latex-bold'>9</span>36<span class='latex-bold'>98</span> but not by 213326798213326798.) Let k(n)k(n) be the number of positive integers that cover 19981998 and have exactly nn digits (n≥5n\ge 5), all different from 00. What is the remainder of k(n)k(n) on division by 88?
Back to ProblemsView on AoPS