Song of Eight Sons Dividing Cotton

Nine hundred and ninety-six jin A jin is a traditional unit of weight often translated as a "catty," roughly equivalent to 600 grams. of cotton

Divided among eight sons for their travel expenses.

In sequence, each receives seventeen more than the next;

We must calculate the amount for the eighth son.

It must be clearly divided according to their order,

In filial harmony, let no rumors spread abroad.

Answer:
The eldest son receives 184 jin; the second receives 167 jin;
The third receives 150 jin; the fourth receives 133 jin;
The fifth receives 116 jin; the sixth receives 99 jin;
The seventh receives 82 jin; the eighth receives 65 jin.

The Method says: Set down the seven factors 1, 2, 3, 4, 5, 6, 7 and add them together to get 28, which serves as the dividend original: 實 (shí); here referring to an intermediate product used in the calculation. Multiply this by the "excess" of 17 to obtain 476. Subtract this from the total amount of cotton [996] to get a remainder of 520. Divide this by the number of sons 8 to obtain 65 jin, which is the amount for the eighth son. To find the shares of the other sons, one simply adds the difference of 17 incrementally to this base amount: 65 + 17 = 82, and so on.