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MathNet 2007-part-03 — 185 problems (EN–VI) Question 71

Math Olympiad Vault · MathNet 2007-part-03 — 185 problems (EN–VI)

Question 71

A student at Harvard named Kevin
Was counting his stones by $11$
He messed up $n$ times
And instead counted $9$s
And wound up at $2007$.
How many values of $n$ could make this limerick true?