林德纸草问题79Problem 79 of the Rhind papyrus

13° Problem 79 of the Rhind papyrus. One of our chief primary sources concerning the mathematics of ancient Egypt is the Rhind, or Ahmes, papyrus, a mathematical text partaking of the nature of a practical handbook and consisting of eighty-five problems copied about 1650 B.C. in hieratic writing by the scribe Ahmes from an earlier work. The papyrus was purchased in Egypt by the English Egyptologist A. Henry Rhind and then later acquired by the British Museum.

Although little difficulty was encountered in deciphering and then interpreting most of the problems in the Rhind papyrus, there is one problem, Problem Number 79, for which the interpretation is not so certain. In this problem occurs the following curious set of data, here transcribed:

| Estate | | |--------|---| | Houses | 7 | | Cats | 49 | | Mice | 343 | | Heads of wheat | 2401 | | Hekat measures | 16807 | | | 19607 |

One easily recognizes the numbers as the first five powers of seven, along with their sum. Because of this it was at first thought that perhaps the writer was here introducing the symbolic terminology houses, cats, and so on, for first power, second power, and so on.

A more plausible and interesting explanation, however, was given by the historian Moritz Cantor in 1907. He saw in this problem an ancient forerunner of a problem that was popular in the Middle Ages, and which was given by Leonardo Fibonacci in 1202 in his Liber abaci. Among the many problems occurring in this work is the following: "There are seven old women on the road to Rome. Each woman has seven mules; each mule carries seven sacks; each sack contains seven loaves; with each loaf are seven knives; and each knife is in seven sheaths. Women, mules, sacks, loaves, knives, and sheaths, how many are there in all on the road to Rome?" As a later and more familiar version of the same problem we have the old English children's rhyme:

As I was going to St. Ives

I met a man with seven wives;

Every wife had seven sacks;

Every sack had seven cats;

Every cat had seven kits.

Kits, cats, sacks, and wives,

How many were going to St. Ives?

According to Cantor's interpretation, the original problem in the Rhind papyrus might then be formulated somewhat as follows: "An estate consisted of seven houses; each house had seven cats; each cat ate seven mice; each mouse ate seven heads of wheat; and each head of wheat was capable of yielding seven hekat measures of grain. Houses, cats, mice, heads of wheat, and hekat measures of grain, how many of these in all were in the estate?"

Here, then, may be a problem that has been preserved as part of the puzzle lore of the world. It was apparently already old when Ahmes copied it, and older by close to three thousand years when Fibonacci incorporated a version of it in his Liber abaci. More than seven hundred and fifty years later we are reading another variant of it to our children. One cannot help wondering if a surprise twist such as occurs in the old English rhyme may also have occurred in the ancient Egyptian problem, though, in all likelihood, this twist was an Anglo-Saxon contribution.

There are many puzzle problems popping up every now and then in our present-day magazines that have medieval counterparts. How much further back some of them go is now almost impossible to determine.