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2024 SSMO Relay Round 5 Problems/Problem 1

Revision as of 16:02, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let the super factorial <math>!(n)</math> be defined on positive integers as <math>\prod_{i=1}^n i!.</math> Find the largest positive integer <math>k</math> such...")
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Problem

Let the super factorial $!(n)$ be defined on positive integers as $\prod_{i=1}^n i!.$ Find the largest positive integer $k$ such that that there are exactly $k$ positive integers $n$ such that $!(n)$ has fewer than $k$ trailing zeroes.

Solution

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