AMC 10 Step by Step
2023 AMC 10BProblem 16P16-20~4 minPrint

Define an upnoupno to be a positive integer of 22 or more digits where the digits are strictly increasing moving left to right. Similarly, define a downnodownno to be a positive integer of 22 or more digits where the digits are strictly decreasing moving left to right. For instance, the number 258258 is an upno and 86208620 is a downno. Let UU equal the total number of upnosupnos and let DD equal the total number of downnosdownnos . What is UD|U-D| ?

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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.