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Systematic Treatise on Arithmetic, Volume 14

Looking from Afar at a Towering Seven-Story Pagoda

Answer: Three lamps on the top floor.

Method: Set the total of 381 lamps as the dividend original: 實 (shí). Arrange the proportional factors original: 衰 (shuāi) as 1, 2, 4, 8, (16), (32), (64) and sum them. This gives 127 as the divisor original: 法 (fǎ). Divide the dividend by the divisor to get 3, which is the number of lamps on the top floor. Double this value for each subsequent floor to find the lamp counts for every level and satisfy the question.

Compensation Among Three Classes, Fame Spreading to the Heavens

Eight horses, nine oxen, and fourteen sheep,
Were driven to the pasture south of the village.
They ate a patch of a man's grain,
And it was agreed to compensate him with six shi of rations.
A shi (also pronounced dan) is a traditional unit of volume for grain, roughly 60 to 100 liters depending on the era.
One ox is valued at two sheep,
And four oxen are equal to two horses in compensation value.
If you can calculate this without error,
Your name and fame will spread everywhere above the crowd.