Sun Zi's Mathematical Classic

Page Two Hundred Fifty-Five

Eight times nine is seventy-two; this number multiplied by itself|original: 自相乘; zì xiāng chéng yields five thousand, one hundred eighty-four. Calculation: $(8 \times 9) = 72$, and $72 \times 72 = 5,184$.

Divided among eight people, the result is six hundred forty-eight. Calculation: $5,184 \div 8 = 648$. Note that $81 \times 8 = 648$.

Seven times nine is sixty-three; this number multiplied by itself yields three thousand, nine hundred sixty-nine. Calculation: $(7 \times 9) = 63$, and $63 \times 63 = 3,969$.

Divided among seven people, the result is five hundred sixty-seven. Calculation: $3,969 \div 7 = 567$, which is $81 \times 7$.

Six times nine is fifty-four; this number multiplied by itself yields two thousand, nine hundred sixteen.

Divided among six people, each person receives four hundred eighty-six. Calculation: $2,916 \div 6 = 486$.

Five times nine is forty-five; this number multiplied by itself yields two thousand, twenty-five.

Divided among five people, each person receives four hundred five. Calculation: $2,025 \div 5 = 405$.

Four times nine is thirty-six; this number multiplied by itself yields one thousand, two hundred ninety-six. The page ends before the final division for this set is recorded.