Thursday, January 6, 2011

Ahmes's Papyrus

About 1650 B. C., Egyptian scribe Ahmes, made a transcript of even more ancient mathematical scriptures dating to the reign of the Pharaoh Amenemhat III. In 1858 Scottish antiquarian, Henry Rhind came into possession of Ahmes's papyrus. The papyrus is a scroll 33 cm wide and about 5.25 m long filled with funny math riddles. One of the problems is as follows:

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, as the fourth gets more than the third, and as the fifth gets 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?
(You can have fractional measures of corn.)

1 comment:

  1. Answer here:

    Ahmes's Papyrus solution
    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 (1.67) measures of corn
    2nd worker = 65/6 (10.83) measures of corn
    3rd worker = 120/6 (20) measures of corn
    4th worker = 175/6 (29.16) measures of corn
    5th worker = 230/6 (38.3) measures of corn