Grain and Camels

A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant. One camel was to carry the grain in 3 journeys, carrying 30 measures on each journey. The camel eats one measure for each leuca when carrying a load of grain How can the grain be transported? How much grain will get to the second house?

Propositiones ad acuendos juvenes (Problems to Sharpen the Young), Alcuin of York, c. 800 CE

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The answer is: On the first journey, the camel carries 30 measures a distance of 20 leucas (eating 20 measures along the way), leaves 10 measures and returns. On the second journey, the camel does the same. On the third journey, the camel carries the remaining 30 measures 20 leucas, but this time picks up the 20 measures left behind on the last two trips (bringing its load back up to 30 measures) and completes the 10 leuca journey to the new house (eating 10 measures along the way). So 20 measures will remain.

"Grain and Camels," Convergence (July 2006)

Convergence