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Problems from Another Time

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

Circle and Equilateral Triangle
A circle ABDC is circumscribed around an equilateral triangle ABC.  Prove that the straight line AD is equal to the sum of the two straight lines BD and DC.
If You Build It...
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?
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - A Synthesis of Mediterranean Methods
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Monkeys in a Tree
A tree 100 units high is 200 units distant from a well; from this tree one monkey climbs down and goes to the well...
Compound Interest
Suppose a man had put out one cent at compound interest in 1620, what would have been the amount in 1824, allowing it to double once in 12 years?
What Are the Odds?
Suppose that the probability of success in an experiment is a/(a+b). How many trials of the experiment are necessary to insure even odds on it happening at least once?
An Acute Problem
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.
Silver Cups
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.
Defeated in Battle
The king of France entered into a battle and was defeated. How many soldiers did he have before he was defeated?
Water Tank Minimization
A copper water tank in the form of a rectangular parallelepiped is to made. If its length is to be a times its breadth, how high should it be that for a given capacity it should cost as little as possible?

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