Problems from Another Time

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

There is a garden is the shape of a rhombus whose side is 577.5 feet. Within the garden is an inscribed square flower bed whose side is 396 feet. What is the area of the garden?

Bridge Over Troubled Waters

A bridge is built across a river in 6 months by 45 men. It is washed away by the current. Find the number of workmen sufficient to build another of twice as much worth in 4 months.

Divide the Stakes

Two persons sit down to play for a certain sum of money, and agree that the first who gets three games shall be the winner. After a few games they resolve to divide the stakes. How much should each person receive?

The Cog-Wheel Revolution

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.

A Room with a View

Find the height of a window.

A Swarm of Bees

The square root of half the number of bees in a swarm has flown out upon a jessamine bush; 8/9 of the swarm has remained behind.