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Distribution of the Mangoes

Of a collection of mango fruits, the king took \(\frac{1}{6}\); the queen \(\frac{1}{5}\) the remainder, and the three princes took \(\frac{1}{4}, \frac{1}{3}\) and \(\frac{1}{2}\) (of the same remainder); and the youngest child took the remaining 3 mangoes.  O you who are clever in miscellaneous problems on fractions, give out the measure of that collection of mangoes.

Ganita Sara Samgraha, Mahavira, 850

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"Distribution of the Mangoes," Convergence (March 2006)