Problems from Another Time

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

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

A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now, supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?

Free Fertilizer

If 12 oxen eat up 3 1/3 acres of meadow in 4 weeks and 21 oxen eat up 10 acres of exactly similar meadow in 9 weeks, how many oxen shall eat up 36 acres in 18 weeks? (Hint: The grass continues to grow.)

Where Cosine Meets Tangent

Determine by using algebra the number of degrees in the angle A where: cos A = tan A

Distribution of the Mangoes

Of a collection of mango fruits, the king took 1/6; the queen 1/5 the remainder, and the three princes took 1/4, 1/3 and 1/2 (of the same remainder); and the youngest child took the remaining 3 mangoes.

Apes in a Forest

In a forest, a number of apes equal in number to the square of 1/8 of the total number of apes are noisy. The remaining 12 apes are on a nearby hill irritated. What is the total number of apes in the pack?

The Square and the Cube

A number is required; that the square shall be equal to twice the cube.

The Sum of Its Parts

One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...

The Length of a String

Two circles, the sum of whose radii is a, are placed in the same plane with their centers at a distance 2a...

Pepper Importation

A merchant bought 50,000 pounds of pepper in Portugal for 10,000 scudi and paid a tax of 500 scudi.