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Problems from Another Time

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

Multiplying Like Rabbits
Assume that the human population after the flood was 6 and that 200 years later the population was 1,000,000. Find the annual rate of growth of the population.
Lunchtime at the Fish Pond
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.
A Linear Hypocycloid
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
Triangular Numbers
What is the sum of the reciprocals of the triangular numbers?
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?

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