An Old Babylonian Problem Text

The tablet pictured below is an example of an Old Babylonian problem text.  Although only part of the tablet remains, originally it had 22 related problems arranged in ascending order of difficulty. For each one, the problem is stated and the answer is given, but there are no indications of the method used to find the solution.  The tablet is YBC 4652 in the Yale Babylonian Collection.  It was first published by Neugebauer and Sachs in Mathematical Cuneiform Texts, as Text R.

Picture of tablet

A translation of the first complete problem is:
    I found a stone.  I did not weigh it.  A seventh I added.  An eleventh I added.
    I weighed it.  1 mana.  What was the original weight of the stone?  The weight of the stone was 2/3 mana 8 gin 22 1/2 še.

The other problems are all similar, but more complicated.

A discussion of the problems on this tablet and a suggested procedure for finding the solutions is in my paper:
'Weighing stones in ancient Mesopotamia'. Historia Mathematica 29, 1-12.

I thank Professor W.W. Hallo for permission to use the images of the tablet.

Go to Mesopotamian Mathematics.

Last modified: 19 September 2002

Duncan J. Melville