**Yupana**

The graphic below on the left is an Inca yupana counting device. On the right is my abacus-like design based on the yupana to its left. Each row of digits in the abacus adds up to 39. So I figure, as does Nicolino De Pasquale, an Italian engineer, that the yupana may be working on a base 40 (0-39) numbering system. The analysis I've done on the yupana has been without prior knowledge of Pasquale's work.

Numbers shown in the five rows of the abacus from bottom to top individually add up to 20, 10, 27, 12, 17.

Therefore, we can do the following calculations to derive at a complete total:

Rows |
Base 40 |
Totals |
---|

5 |
17*40^4 |
43520000 |

4 |
12*40^3 |
768000 |

3 |
27*40^2 |
43200 |

2 |
10*40^1 |
400 |

1 |
20*40^0 |
20 |

| |
**44331620** |

The last four digits from the total above: "1620," look like a year. Try figuring out the totals for the yupana abacus shown below. Hint, the total is very close to the same total for the yupana abacus shown above.

Click on image above to see solution.

The Incas normally used a base 10 numbering system for their record keeping as can be seen in the use of their quipus. The abacus, or Inca yupana may have been used for a sacred calendar, or possibly a calculator for the tax gatherer, or to keep track of portions of grain and other produce, or for engineering mathematics.

If you would like a copy of this page in Microsoft Word format, please download the following file:

YupanaAbacus.doc

You may make copies of the doc file for publication, distribution, or for posting on your websites as long as you credit my name.

www.BordersChess.org/Yupana.htm *modified 2006.12.14
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