Problems from Another Time

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

A fish sees a heron looking at him from across a pool, so he quickly swims towards the south. When he reaches the south side of the pool, he has the unwelcome surprise of meeting the heron.

Dimensions of a Box

The dimensions of a rectangular box in inches are expressed by three consecutive numbers. The surface of the box is 292 square inches. Find the dimensions.

A Tower on a Cliff

A cliff with a tower on its edge is observed from a boat at sea; find the height of the cliff and the tower.

Dealing in Sheep

A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received $150 for them. How many did he buy?

Horse of Course

One person possesses 7 asava horses, another 9 haya horses, and another 9 camels. Each gives two animals away, one to each of the others.

Ages of Father and Son

When knowing the sum of their ages along with another equation, determine how old a father and son are.

Stinkin' Pile of Money

Three men have a pile of money, their shares being 1/2, 1/3 and 1/6. Each man takes some money from the pile until nothing is left.

Money Changers

Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."

Trisecting a Log

There is a log of precious wood 18 feet long whose bases are 5 feet and 2.5 feet in circumference. Into what lengths should the log be cut to trisect its volume?

Division Problem

The number 50 is divided by a certain number. If the divisor is increased by 3, the quotient decreases by 3.75. What is the number?