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Problems from Another Time

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

A wooden beam is stood vertically against a wall. The length of the beam is 30 units.
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?
What is the sum of the following series, carried to infinity: 11, 11/7, 11/49, etc.?
Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
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?
Two officers each have a company of men, the one has 40 less than the other.
Two merchants, A and B, loaded a ship with 500 hhds (hogshead) of rum; A loaded 350 hhds, and B the rest; in a storm the seamen were obliged to throw overboard 100 hhds; how much must each sustain of the loss?
A number is required; that the square shall be equal to twice the cube.
The king of France entered into a battle and was defeated. How many soldiers did he have before he was defeated?
A leech invited a slug for a lunch a leuca away.

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