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Problems from Another Time

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

What is the sum of the reciprocals of the triangular numbers?
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.
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.
Suppose the area of an equilateral triangle be 600. The sides are required.
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 answer to the following question is obtained using as optimum strategy-the farmer is getting the "best deal" possible. Can you figure out the solution strategy?...
I am a brazen lion; my spouts are my 2 eyes, my mouth, and the flat of my foot. My right eye fills a jar in 2 days, my left eye in 3, and my foot in 4.
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.

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