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 - Background: The Abbaco Tradition

Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions

There is a mound of earth in the shape of a frustum of a cone.

What proportions of sugar at 8 cents, 10 cents and 14 cents per pound, will compose a mixture worth 12 cents per pound?

Given a rectangle, find the line through one vertex of minimum length that passes through the extensions of the two opposite sides.

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...