Problems from Another Time

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

'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

A tree 100 units high is 200 units distant from a well; from this tree one monkey climbs down and goes to the well...

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?

A General Question

Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 5 months.

Base 7

A number of 3 digits in base 7 has the same three digits...