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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

Doing Some Gardening
There is a garden is the shape of a rhombus whose side is 577.5 feet. Within the garden is an inscribed square flower bed whose side is 396 feet. What is the area of the garden?
Bridge Over Troubled Waters
A bridge is built across a river in 6 months by 45 men. It is washed away by the current. Find the number of workmen sufficient to build another of twice as much worth in 4 months.
Divide the Stakes
Two persons sit down to play for a certain sum of money, and agree that the first who gets three games shall be the winner. After a few games they resolve to divide the stakes. How much should each person receive?
The Cog-Wheel Revolution
Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?
Horse of Course
One person possesses 7 asava horses, another 9 haya horses, and another 9 camels. Each gives two animals away, one to each of the others.
The Amount of Time a Man Can Do Work
How long does it take a single man to do work when...
A Serious Series
Given the fraction ax/(a-x), convert it into an infinite series.
Four Integers
Given four integers which, if added together three at a time, their sums are: 20, 22, 24, and 27. What are the integers?
Golden Spheres
A California miner has a spherical ball of gold, 2 inches in diameter, which he wants to exchange for spherical balls 1 inch in diameter. How many of the smaller spheres should he receive?
Money Makes the World Go Around
You have two sums of money, the difference of which is 2 dirhems; you divide the smaller sum by the larger and the quotient is equal to 1/2. What are the two sums of money?

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