Problems from Another Time

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

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?

The Sum of Its Parts

One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...

The Length of a String

Two circles, the sum of whose radii is a, are placed in the same plane with their centers at a distance 2a...

Pepper Importation

A merchant bought 50,000 pounds of pepper in Portugal for 10,000 scudi and paid a tax of 500 scudi.

Losing My Marbles?

In a square box that contains 1000 marbles, how many will it take to reach across the bottom of the box in a straight row?