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Problems from Another Time

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

Two men rent a pasture for 100 liras on the understanding that two cows are to be counted as being equivalent to three sheep. The first puts in 60 cows and 85 sheep; the second 80 cows and 100 sheep. How much should each pay?
A vessel is anchored in 3 fathoms of water and the cable passes over a sheave in the bowspirt which is 6 ft above the water.
On a certain ground stands two poles 12 feet apart, the lesser pole is 35 ft. in height and the greater 40 ft. It is sought, if the greater pole will lean on the lesser, then in what part will it touch?
Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?
A castle has n rooms each of which has 7 samurai in it.
A lady has two silver cups, and only one cover for both. The first cup weighs 16 oz, and when it is covered it weighs 3 times as much as the second cup; but when the second cup is covered, it weighs 4 times as much as the first.
Find two number with sum 20 and when squared their sum is 208.
Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?

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