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Problems from Another Time

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

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 square of a certain number multiplied by itself and by 200 is 446,976. What is the number?
Suppose that for every 4 cows a farmer has, he should plow 1 acre of land, and allow 1 acre of pasture for every 3 cows; how many cows could he keep on 140 acres?
A castle has n rooms each of which has 7 samurai in it.
Find two number with sum 20 and when squared their sum is 208.
The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".
Given a number, take 1/3 of the number away from itself and add 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
Three hundred pigs are to be prepared for a feast.
If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?

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