《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§27. A system of linear equations (3)

This section gives the solution to a specific system of linear equations.

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
今有獸六首四足、禽四首二足。上有七十六首、下有四十六足。 Suppose there be beasts [with] six heads [and] four feet, [and] fowls [with] four heads [and] two feet. Above be there seventy-six heads; below be there forty-six feet.
  • Version B erroneously has 禽二首 for 禽四首.
問禽獸各幾何。 [We] ask, how many each [be the] fowls [and the] beasts?
  • Version C erroneously has 篱 for 禽.
  • In modern notation, we have the system
    \begin{aligned} 6b + 4f &= 76 && \text{(heads)} \\ 4b + 2f &= 46 && \text{(feet)} \end{aligned}
    in b the number of beasts and f the number of fowls.
答曰、八獸七禽。 Answer saith: eight beasts [and] seven fowls.
術曰、倍足以減首、餘、半之、即獸。 Method saith: double [the] feet with [which] subtract of [the] heads; [the] remainder, halving it, is [the] beasts.
  • Version C erroneously has 之即禽 before 即獸.
  • In modern notation,
    \begin{aligned} \frac{2 (4b + 2f) - (6b + 4f)}{2} &= \frac{2 \times 46 - 76}{2} \\[\tallspace] b &= 8. \end{aligned}
以四乘獸減足、餘、半之、即禽。 Subtract of [the] feet by four times [the] beasts; [the] remainder, halving it, is [the] fowls.
  • Version C is erroneously missing 之即禽.
  • In modern notation, the feet equation rearranges to give
    f = \frac{46 - 4b}{2} = \frac{46 - 4 \times 8}{2} = 7.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §27". <https://yawnoc.github.io/sun-tzu/iii/27> Accessed yyyy-mm-dd.