This image shows an ancient stone tablet containing rows of
numbers, dated from 1800BC. It is written in Babylonian cuneiform
script. The modern day versions of the last three columns of
numbers are written out to the right.
[image taken from
http://commons.wikimedia.org/wiki/Image:Plimpton_322.jpg]

119 
169 
1 
3367 
11521 
2 
4601 
6649 
3 
12709 
18541 
4 
65 
97 
5 
319 
541 
6 
2291 
3541 
7 
799 
1249 
8 
25921 
769 
9 
4961 
8161 
10 
45 
75 
11 
1679 
2929 
12 
161 
289 
13 
1771 
3229 
14 
56 
53 
15 

What do these numbers mean? Are there any patterns? Why are they in
this order? Is there some underlying structure? The writer of the
numbers went to a great deal of trouble to make the heavy clay
tablet, so we can be fairly sure that they are important in some
way.
Investigate these numbers. Create a hypothesis for their meaning or
to explain any patterns. Test your hypotheses.Why is it not
possible to
prove that
your hypothesis is true?
Note that although there is a very likely answer to the meaning of
the numbers, four rows are thought to contain errors in one of the
numbers. Can you work out which these are, and can you correct
them?
If you find the rule which explains all but four of the rows, you
might like to consider whether the author had other plans for those
numbers or whether, in actual fact, he made mistakes in his
calculations or writing.
NOTES AND BACKGROUND
Historians believe that the Babylonians were the first
mathematically sophisticated culture. They were active around 3000
 1000 BC. Whilst their knowledge was basic compared to today's
standards, they had discovered many of the properties of numbers
and geometry which are still studied in schools today.
Attaching meaning to an archeological discovery can be a difficult
process. Whilst we will probably never be
certain as to the meanings of the
numbers in the tablet, mathematicians have found plenty of
numerical evidence that they were generated according to a specific
rule. This supports the underlying hypothesis to a sufficient
degree that many mathematicians are confident that the mismatched
numbers in the table are, in fact, errors which can be corrected.
It is these corrected numbers which are often displayed in articles
concerning Plimpton 322.
If you enjoyed this challenge, you might like to investigate the
Ishango
Bone or
Stone
Age Counting