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A Wealth of Plantains

Twenty-three weary travelers entered a delightful forest. There they found 63 numerically equal piles of plantain fruit. Together they gathered 7 more plantains, then they divided all the plantains equally amongst themselves in a manner such that no plantains remained. For this to happen, what was the smallest number of plantains possible in each pile?

Ganita Sara Samgraha, Mahavira, 850

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"A Wealth of Plantains," Convergence (June 2008)