Problems from Another Time

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

Logarithms: The Early History of a Familiar Function - About the Authors and More Information on Sources

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

Silver and Gold

There are two piles, one containing 9 gold coins, the other 11 silver coins.

Coins

A boy gives 11 coins of equal denomination to a man, and the man finds that their total value in yen is 4 less than his age.

Looking for Bargains

One says that 10 garments were purchased by two men at a price of 72 dirhams. The garments varied in value. The price of each garment of one man is 3 dirhams more than the price for each garment of the other. How many garments did each man buy?

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Proportionality Techniques

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

Log Stuck in a Wall

Now given a cylindrical log of unknown size buried in a wall...

Lotus in the Lake

In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span above the surface of the water.

Nuts Over Counting

A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. What is the smallest number of nuts he could have?

Two Balls, No Strikes!

Imagine an urn with two balls, each of which may be either white or black. One of these balls is drawn and is put back before a new one is drawn.

Mystery Number

What number is that, which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?