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, 2025

Number theory Difficulty 5.0 AIME, harder Prove it United Kingdom

Consider the number $M = 99\ldots99$ which consists of several digit nines. A single division sign is placed between two adjacent digits of $M$ and the resulting calculation is evaluated to produce a whole number $N$ . In the case when $M$ has nine digits, how many digits does the smallest possible value of $N$ have?

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