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Problems from Another Time

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

I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.
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.
Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.
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.
Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?
A castle has n rooms each of which has 7 samurai in it.
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

Find two number with sum 20 and when squared their sum is 208.
A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
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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