《孫子算經卷中》 "Sun Tzŭ's Computational Classic: Volume II"
§25. Solving a linear equation (1)

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
今有五等諸侯、共分橘子六十顆、人別加三顆。問五人各得幾何。 Suppose there be [the] five ranks of all [the] marquesses, together sharing tangerines sixty, [and for each] person's distinction [there be] added three [unto his share]. [We] ask, how many getteth each of [the] five people?
答曰、公一十八顆、侯一十五顆、伯一十二顆、子九顆、男六顆。 Answer saith: [the] lord eighteen [tangerines], [the] marquess fifteen [tangerines], [the] elder twelve [tangerines], [the] master nine [tangerines], [and the] male six [tangerines].
術曰、先置人數別加三顆於下、次六顆、次九顆、次一十二顆、上十五顆。 Method saith: first put [the] number of people [and the] distinctional addition of three [tangerines] below; next, six [tangerines]; next, nine [tangerines]; next, twelve [tangerines]; above, fifteen [tangerines].
  • In modern notation, with n denoting the baseline number of tangerines, we have (n+3, n+6, n+9, n+12, n+15) tangerines for the five people; therefore
    5n + (3 + 6 + 9 + 12 + 15) = 60.
副并之、得四十五。 Subsidiarily combining them, resulteth in forty-five.
  • In modern notation,
    5n + 45 = 60.
以減六十顆、餘、人數除之、人得三顆。 Subtract of [the] sixty [tangerines] by [this]: [the] remainder, dividing it [by the] number of people, [each] person getteth three [tangerines].
  • In modern notation,
    \begin{aligned} 5n &= 60 - 45 = 15 \\ n &= 15 \div 5 = 3. \end{aligned}
各加不并者、上得一十八為公分、次得一十五為侯分、次得十二為伯分、次得九為子分、下得六為男分。 Adding unto each of those not combined: above [there] resulteth eighteen as [the] lord's share; next [there] resulteth fifteen as [the] marquess's share; next [there] resulteth twelve as [the] elder's share; next [there] resulteth nine as [the] master's share; below [there] resulteth six as [the] male's share.
  • In modern notation, the five people get (n+15, n+12, n+9, n+6, n+3) = (18, 15, 12, 9, 6) tangerines.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume II §25". <https://yawnoc.github.io/sun-tzu/ii/25> Accessed yyyy-mm-dd.