Problems from Another Time

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

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...

Chuquet's Rule of Average Numbers

Prove Chuquet's rule of average numbers.

Look Out Below!

Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...

Radii of Three Circles

Determine the radii of three equal circles described within and tangent to a given circle, and also tangent to each other.

Numbers Game #1

The sum of two numbers is 10 and their product is 40. What are the numbers?