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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.
A California miner has a spherical ball of gold, 2 inches in diamter, which he wants to exchange for spherical balls 1 inch in diameter. How many of the smaller spheres should he receive?
A castle has n rooms each of which has 7 samurai in it.
The sum of two numbers is 10 and their product is 40. What are the numbers?
Find two number with sum 20 and when squared their sum is 208.
In baking a hemispherical loaf of bread of 10" radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
Given a triangular piece of land having two sides 10 yards in length and its base 12 yards, what is the largest square that can be constructed within this piece of land so that one of its sides lies along the base of the triangle?
Three hundred pigs are to be prepared for a feast.
What is the sum of the following series, carried to infinity: 11, 11/7, 11/49, etc.?

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