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.

yupana.jpg     YupanaAbacus2.gif

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

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.

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www.BordersChess.org/Yupana.htm   modified 2006.12.14