### Brain Teasers

# Ahmes's Papyrus

About 2000 B.C. there lived Ahmes, a royal secretary and mathematician of the Pharaoh Amenemhat III. In 1853 an Englishman Rhind found one of Ahmes's papyruses near the temple of Ramses II in Thebes. The papyrus is a rectangle 33 cm wide and about 5 m long. There is the following math brain teaser on it (besides others).

100 measures of corn must be divided among 5 workers, so that the second worker gets as many measures more than the first worker, as the third gets more than the second, the fourth more than the third and the fifth more than the fourth. The first two workers shall get seven times less measures of corn than the three others.

How many measures of corn shall each worker get?

100 measures of corn must be divided among 5 workers, so that the second worker gets as many measures more than the first worker, as the third gets more than the second, the fourth more than the third and the fifth more than the fourth. The first two workers shall get seven times less measures of corn than the three others.

How many measures of corn shall each worker get?

### Answer

2 equations give a clear answer to the given question:5w + 10d = 100

7*(2w + d) = 3w + 9d

Where w is amount of corn for the first worker, d is the difference (amount of corn) between two consecutive workers. So this is the solution:

1st worker = 10/6 measures of corn

2nd worker = 65/6 measures of corn

3rd worker = 120/6 (20) measures of corn

4th worker = 175/6 measures of corn

5th worker = 230/6 measures of corn

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