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Problems from Another Time

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

Lunchtime at the Fish Pond
A fish sees a heron looking at him from across a pool, so he quickly swims towards the south. When he reaches the south side of the pool, he has the unwelcome surprise of meeting the heron.
Dimensions of a Box
The dimensions of a rectangular box in inches are expressed by three consecutive numbers. The surface of the box is 292 square inches. Find the dimensions.
A Tower on a Cliff
A cliff with a tower on its edge is observed from a boat at sea; find the height of the cliff and the tower.
Dealing in Sheep
A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received $150 for them. How many did he buy?
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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