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Problems from Another Time

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

Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
What is the sum of the reciprocals of the triangular numbers?
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 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?
Suppose the area of an equilateral triangle be 600. The sides are required.
A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.
What is the sum of the following series, carried to infinity: 11, 11/7, 11/49, etc.?
Suppose that the propability of success in an experiment is 1/10. How many trials of the experiment are necessary to insure even odds on it happening at least once?
Given a pendulum as shown. The height of the pendulum is two units and its horizontal width is 2 units. What is the area of the pendulum?
I wish to find three numbers of such nature that the first and the second with 1/2 of the third makes 20...

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