Problems from Another Time

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

Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?

The Recruiting Officers

Two officers each have a company of men, the one has 40 less than the other.

The Time It Takes To Eat a Goat

A lion, a wolf and a fox each take a certain amount of time to eat a goat separately. How long would it take all these animals together to eat the goat?

Maxes and Mins

Determine the different values of x, when a certain function hits a minimum.

Two Numbers

Find two numbers with sum 20 and when squared their sum is 208.

Four Integers

Given four integers which, if added together three at a time, their sums are: 20, 22, 24, and 27. What are the integers?

Golden Spheres

A California miner has a spherical ball of gold, 2 inches in diameter, which he wants to exchange for spherical balls 1 inch in diameter. How many of the smaller spheres should he receive?

Money Makes the World Go Around

You have two sums of money, the difference of which is 2 dirhems; you divide the smaller sum by the larger and the quotient is equal to 1/2. What are the two sums of money?

Logarithms: The Early History of a Familiar Function - Parallel Insights and the Reception of Mathematical Ideas

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

Loaves and Bishops

A certain bishop ordered that 12 loaves be divided among his clergy.