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Bedouin Breakfast

Two bedouins were traveling across the desert to a distant village. They had begun walking long before daybreak to avoid the midday heat. An hour after sunup, they sat down to eat the loaves of bread that they had brought with them. One of them had three loaves and the other had two.

Just as they were ready to eat, a stranger came along and asked if he might share their meal. He said he had plenty of money, which he showed to them, but no food. The two agreed to divide their loaves equally among the three of them.

After the meal was finished, the stranger laid down five coins of equal value for what he had eaten, and he went away. The first traveler took three of the coins since he had contributed 3 loaves. This left two coins for the second traveler. Was this a fair split? Explain why or why not.

Note: This venerable problem was collected from the Near East by Fibonacci (c. 1200), but it may be hundreds of years older than that.

See: Gies, Leonard of Pisa.

Solution

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