《孫子算經卷上》 "Sun Tzŭ's Computational Classic: Volume I"
§24. Results of multiplication & division: multiples of powers of 3

This section gives the results of multiplications and divisions of the form

\begin{aligned} (4 \cdot 3^n) \times (3^{n + 1}) &= 4 \cdot 3^{2 n + 1} \\ (4 \cdot 3^{2 n + 1}) \div (2 \cdot 3^n) &= 2 \cdot 3^{n + 1}, \end{aligned}

where n = 1, 2, \dots, 11.

Since this gets rather repetitive and boring, you may wish to skip to Volume II.

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text Target text Notes
以九乘一十二、得一百八。六人分之、人得一十八。 Multiplying twelve by nine, resulteth in one hundred [and] eight. [With] six people sharing it, [each] person getteth eighteen.
以二十七乘三十六、得九百七十二。一十八人分之、人得五十四。 Multiplying thirty-six by twenty-seven, resulteth in nine hundred [and] seventy-two. [With] eighteen people sharing it, [each] person getteth fifty-four.
以八十一乘一百八、得八千七百四十八。五十四人分之、人得一百六十二。 Multiplying one hundred [and] eight by eighty-one, resulteth in eight thousand seven hundred [and] forty-eight. [With] fifty-four people sharing it, [each] person getteth one hundred [and] sixty-two.
  • Version B erroneously has 六十二 for 一百六十二.
以二百四十三乘三百二十四、得七萬八千七百三十二。一百六十二人分之、人得四百八十六。 Multiplying three hundred [and] twenty-four by two hundred [and] forty-three, resulteth in seven myriad eight thousand seven hundred [and] thirty-two. [With] one hundred [and] sixty-two people sharing it, [each] person getteth four hundred [and] eighty-six.
以七百二十九乘九百七十二、得七十萬八千五百八十八。四百八十六人分之、人得一千四百五十八。 Multiplying nine hundred [and] seventy-two by seven hundred [and] twenty-nine, resulteth in seventy myriad eight thousand five hundred [and] eighty-eight. [With] four hundred [and] eighty-six people sharing it, [each] person getteth one thousand four hundred [and] fifty-eight.
以二千一百八十七乘二千九百一十六、得六百三十七萬七千二百九十二。一千四百五十八人分之、人得四千三百七十四。 Multiplying two thousand nine hundred [and] sixteen by two thousand one hundred [and] eighty-seven, resulteth in six hundred [and] thirty-seven myriad seven thousand two hundred [and] ninety-two. [With] one thousand four hundred [and] fifty-eight people sharing it, [each] person getteth four thousand three hundred [and] seventy-four.
  • Version C erroneously has 七千百九十二 for 七千二百九十二.
以六千五百六十一乘八千七百四十八、得五千七百三十九萬五千六百二十八。四千三百七十四人分之、人得一萬三千一百二十二。 Multiplying eight thousand seven hundred [and] forty-eight by six thousand five hundred [and] sixty-one, resulteth in five thousand seven hundred [and] thirty-nine myriad five thousand six hundred [and] twenty-eight. [With] four thousand three hundred [and] seventy-four people sharing it, [each] person getteth one myriad three thousand one hundred [and] twenty-two.
以一萬九千六百八十三乘二萬六千二百四十四、得五億一千六百五十六萬六百五十二。一萬三千一百二十二人分之、人得三萬九千三百六十六。 Multiplying two myriad six thousand two hundred [and] forty-four by one myriad nine thousand six hundred [and] eighty-three, resulteth in five square-myriad one thousand six hundred [and] fifty-six myriad six hundred [and] fifty-two. [With] one myriad three thousand one hundred [and] twenty-two people sharing it, [each] person getteth three myriad nine thousand three hundred [and] sixty-six.
以五萬九千四十九乘七萬八千七百三十二、得四十六億四千九百四萬五千八百六十八。三萬九千三百六十六人分之、人得一十一萬八千九十八。 Multiplying seven myriad eight thousand seven hundred [and] thirty-two by five myriad nine thousand [and] forty-nine, resulteth in forty-six square-myriad four thousand nine hundred [and] four myriad five thousand eight hundred [and] sixty-eight. [With] three myriad nine thousand three hundred [and] sixty-six people sharing it, [each] person getteth eleven myriad eight thousand [and] ninety-eight.
以一十七萬七千一百四十七乘二十三萬六千一百九十六、得四百一十八億四千一百四十一萬二千八百一十二。一十一萬八千九十八人分之、人得三十五萬四千二百九十四。 Multiplying twenty-three myriad six thousand one hundred [and] ninety-six by seventeen myriad seven thousand one hundred [and] forty-seven, resulteth in four hundred [and] eighteen square-myriad four thousand one hundred [and] forty-one myriad two thousand eight hundred [and] twelve. [With] eleven myriad eight thousand [and] ninety-eight people sharing it, [each] person getteth thirty-five myriad four thousand two hundred [and] ninety-four.
以五十三萬一千四百四十一乘七十萬八千五百八十八、得三千七百六十五億七千二百七十一萬五千三百八。三十五萬四千二百九十四人分之、人得一百六萬二千八百八十二。 Multiplying seventy myriad eight thousand five hundred [and] eighty-eight by fifty-three myriad one thousand four hundred [and] forty-one, resulteth in three thousand seven hundred [and] sixty-five square-myriad seven thousand two hundred [and] seventy-one myriad five thousand three hundred [and] eight. [With] thirty-five myriad four thousand two hundred [and] ninety-four people sharing it, [each] person getteth one hundred [and] six myriad two thousand eight hundred [and] eighty-two.
END of Volume I

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume I §24". <https://yawnoc.github.io/sun-tzu/i/24> Accessed yyyy-mm-dd.