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A Game of Cat and Mouse

A mouse is at the top of a poplar tree 60 braccia high, and a cat is on the ground at its foot.  The mouse descends \(\frac{1}{2}\) a braccia a day and at night it turns back \(\frac{1}{6}\) of a braccia.  The cat climbs one braccia a day and goes back \(\frac{1}{4}\) of a braccia each night.  The tree grows \(\frac{1}{4}\) of a braccia between the cat and the mouse each day and it shrinks \(\frac{1}{8}\) of a braccia every night.  In how many days will the cat reach the mouse?

Summa de arithmetica, Luca Pacioli, 1494

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"A Game of Cat and Mouse," Convergence (July 2006)