Problems from Another Time

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

The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".

But What's in the Flasks?

Thirty flasks—10 full, 10 half-empty, and 10 completely empty—are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?

'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

Frustum-Shaped Mound

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

Sugar per Pound

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

Sides of a Rectangle

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

Equal Surface and Volume

What will the diameter of a sphere be, when its volume and surface area are expressed by the same number?

Inscribed Square

Knowing the base, b, and the altitude, a, of a triangle, find the expression for a side of the inscribed square.

How Much to Buy a Horse?

Three men wish to buy a horse but none have a sufficient amount of money for the purchase; to do so, they must borrow from each other. How much money does each man have and what is the price of the horse?

Snowdrift on the Tracks

A railway train strikes a snowdrift which creates a constant resistance. How long does it take the snow to stop the train?