Problems from Another Time

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

Given a guest on horseback rides 300 li in a day. The guest leaves his clothes behind. The host discovers them after 1/3 day, and he starts out with the clothes.

A Circular Problem

Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.

On the Run

A certain slave fled from Milan to Naples going 1/10 of the whole journey each day. At the beginning of the third day, his master sent a slave after him and this slave went 1/7 of the whole journey each day.

Prove the Straight Lines

Given two circles tangent at the point P with parallel diameters AB and CD, prove that APD and BPC are straight lines.

A Dangerous Castle Indeed

A castle has n rooms each of which has 7 samurai in it.

Difference of Squares

Having been given the sum of two numbers, a, and the difference of their squares, b, find the numbers.

A Tree with Branches, Nests, Eggs and Birds

There is a tree with 100 branches. How many nests, eggs and birds are there?

Height and Distance

An erect pole of 10 cubits has its base moved 6 cubits. Determine the new height and the distance the top of the pole is lowered.

Why It Pays to Learn Math

In order to encourage his son in the study of arithmetic, a father agrees to pay him 8 pennies for every problem solved correctly and to charge him 5 pennies for each incorrect solution.

The Size of a City

A square walled city of unknown dimensions has four gates, one at the center of each side.