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Omni-MATH / A student at Harvard named Kevin was counting his stones by 11. He messed up n times and instead counted 9s and wound up at 2007. How many values of n could make this limerick true…

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problem

A student at Harvard named Kevin was counting his stones by 11. He messed up nn times and instead counted 9s and wound up at 2007. How many values of nn could make this limerick true?
Plain-text mathematical notation (without MathML)
A student at Harvard named Kevin was counting his stones by 11. He messed up n times and instead counted 9s and wound up at 2007. How many values of n could make this limerick true?
Original LaTeX notation
A student at Harvard named Kevin was counting his stones by 11. He messed up $n$ times and instead counted 9s and wound up at 2007. How many values of $n$ could make this limerick true?

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