Problems from Another Time

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

A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months' absence caused by sickness, he received only $409.50. What was his board worth per month?

Out to Pasture

Two men rent a pasture for 100 lire on the understanding that two cows are to be counted as being equivalent to three sheep. The first puts in 60 cows and 85 sheep; the second 80 cows and 100 sheep. How much should each pay?

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Appendix A: The Land of 'Oc'

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

Lucky Seven

There is a number which when divided by 2, or 3, or 4, or 5, or 6, always has a remainder of 1, and is truly divisible by 7. It is sought what is the number.

Hogsheads of Rum

Two merchants, A and B, loaded a ship with 500 hhds (hogsheads) of rum; A loaded 350 hhds, and B the rest; in a storm the seamen were obliged to throw overboard 100 hhds; how much must each sustain of the loss?

Height of the Clouds

The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?

Bicyclists on a Track

Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider

To Each His Due

A man has four creditors. To the first he owes 624 ducats; to the second, 546; to the third, 492; and to the fourth 368.

Three Vertical Posts

Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By using measurments of the posts, determine, to the nearest mile, the radius of the earth.

A Circular Problem

Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.