Define an to be a positive integer of or more digits where the digits are strictly increasing moving left to right. Similarly, define a to be a positive integer of or more digits where the digits are strictly decreasing moving left to right. For instance, the number is an upno and is a downno. Let equal the total number of and let equal the total number of . What is ?
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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.