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A monotone positive integer

Source: Balkan MO 1993, Problem 2

April 25, 2006
calculusintegrationceiling functionfloor functioninequalitiescombinatorics proposedcombinatorics

Problem Statement

A positive integer given in decimal representation anan−1…a1a0‾\overline{ a_na_{n-1} \ldots a_1a_0 } is called monotone if an≤an−1≤⋯≤a0a_n\leq a_{n-1} \leq \cdots \leq a_0. Determine the number of monotone positive integers with at most 1993 digits.
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