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Problems from Another Time

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

Loaves and Bishops
A certain bishop ordered that 12 loaves be divided among his clergy.
Loaf of Bread
In baking a hemispherical loaf of bread of 10" radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?
Crown of Metal
Make a crown of gold, copper, tin, and iron weighing 60 minae: gold and copper shall be 2/3 of it; gold and tin, 3/4 of it; and gold and iron, 3/5 of it. Find the required weights of gold, copper, tin, and iron.
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript
Problems from a 15th-century French manuscript, including one with negative solutions.
Circular Cone
The frustum of a circular cone has height 15.
Walk Around the Triangle
If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?
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.
In the Gentleman's Garden
A gentleman has a garden of rectangular form and wants to construct a walk of equal width half way round to take up half the garden. What must be the width of this walk?
Gun Metal
Gun metal of a certain grade is composed of 16% tin and 84% copper. How much tin must be added to 410 pounds of this gun metal to make a composition of 18% tin?
Purse of Denari
Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.

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