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2025 SSMO Speed Round Problems/Problem 5

Revision as of 11:10, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>N = 101112\cdots9899</math> be the number formed when all the two-digit positive integers are concatenated in increasing order. How many ordered triples...")
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Problem

Let $N = 101112\cdots9899$ be the number formed when all the two-digit positive integers are concatenated in increasing order. How many ordered triples of digits $(a,b,c)$ are there such that $a,$ $b,$ and $c$ appear as consecutive digits (in that order) in the decimal representation of $N$?

Solution

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