《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§17. Solving a linear equation (2)

This section gives a worked example of solving a linear equation.

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
今有婦人河上蕩桮、津吏問曰、桮何以多。婦人曰、家有客。 Suppose there be [a] woman washing cups upon [the] river, [and the] officer of [the] ford asketh, saying, Why [so] many cups? [And the] woman saith, [Mine] house hath guests.
津吏曰、客幾何。婦人曰、二人共飯、三人共羹、四人共肉、凡用桮六十五。不知客幾何。 [And the] officer of [the] ford saith, How many [be the] guests? [And the] woman saith, Two people together [for] rice, three people together [for] soup, [and] four people together [for] flesh, [in] total use cups sixty-five. Know [we] not how many [be the] guests?
  • Version C erroneously has 用聣 for 用桮.
  • 不知客幾何： know [we] not how many [be the] guests

    The quotation marks in Version C mark this as spoken by the woman. Personally I disagree, and think that 不知客幾何 is spoken by the narrator. The original Chinese is ambiguous as it carries no punctuation; I have preserved the ambiguity by not editing in any quotation marks.

答曰、六十人。 Answer saith: sixty people.
術曰、置六十五桮、以一十二乘之、得七百八十。以十三除之、即得。 Method saith: put [down the] sixty-five cups; multiplying it by twelve, resulteth in seven hundred [and] eighty. Dividing it by thirteen, [we] are done.
  • Version B has 十二 for 一十二.
  • In modern notation, supposing that the guests be n people, we have
    65 = \frac{n}{2} + \frac{n}{3} + \frac{n}{4} = \frac{13n}{12},
    and hence
    n = \frac{65 \times 12}{13} = 60.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §17". <https://yawnoc.github.io/sun-tzu/iii/17> Accessed yyyy-mm-dd.