Sun Zi's Mathematical Classic

Page Eight

Divided among four people, each person receives one hundred ninety-six. This line completes the calculation for $(4 \times 7)^2 \div 4$. Calculation: $4 \times 7 = 28$; $28 \times 28 = 784$; $784 \div 4 = 196$. Note that $49 \times 4 = 196$.

Three times seven is twenty-one; this number multiplied by itself|original: 自相乘; zì xiāng chéng yields four hundred forty-one. Calculation: $21 \times 21 = 441$.

　　Divided among three people, each person receives one hundred forty-seven. Calculation: $441 \div 3 = 147$. Note that $49 \times 3 = 147$.

Two times seven is fourteen; this number multiplied by itself yields one hundred ninety-six. Calculation: $14 \times 14 = 196$.

　　Divided among two people, each person receives ninety-eight. Calculation: $196 \div 2 = 98$. Note that $49 \times 2 = 98$.

One times seven is seven; this number multiplied by itself yields forty-nine.

　　One person receives forty-nine.

To the right, the seven-seven sequence|original: 七七一條; qī qī yī tiáo yields one hundred ninety-six; this number multiplied by itself yields thirty-eight thousand, four hundred sixteen. The "seven-seven sequence" refers to the set of calculations involving the seven-times table. The number 196 here refers to the result of the first calculation on this page; squaring it ($196 \times 196$) results in 38,416.