Problems from Another Time

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

A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1560. How much did he invest?

A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Acceptance of Negative Solutions

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

An Inscribed Ellipse

Given right triangle ABC where C is the right angle, ellipse O (a,b) is inscribed in it, with its major axis parallel to BC. Calculate the semi-major axis, a, in terms of AC, BC and b.

Viete: Triangle II

In a right triangle, the hypotenuse is 13 and the sum of the sides around the right angle is 17. Find the lengths of the sides around the right angle.

Travelling Steamers

The steamer, Katie, leaves the wharf at New Orleans and runs an average speed of 15 mph. When Katie had gone 25 miles, the steamer R.E. Lee leaves the wharf and runs the average speed of 18 mph. How far will the Lee go before she overtakes the Katie?

Reverse the Digits

The sum of the two digits of a 2-digit number is 9. If 45 is subtracted from the number, the result will be expressed by the digits in reverse order. Find the number.

A Clothes Call

A man went to a draper and bought a length of cloth 35 braccia long to make a suit of clothes.

10 Into 3 Parts

Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.

Long Time to Fill the Tub

A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.