Problems from Another Time

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

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.

Ladder Day Question

A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.

Walk Around the World

Suppose a person whose height is 5 feet 7 inches travels 10000 miles in the arc of a great circle. How much further will the person's head have gone compared to their feet, the circumference of the Earth being 21600 miles?

Faster Than a Speeding Horse

A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?

Logarithms: The Early History of a Familiar Function - Before Logarithms: The Computational Demands of the Late Sixteenth Century

The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

Another Numbers Game

Determine a number having remainders 2, 3, and 2 when divided by 3, 5, and 7 respectively.