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Problems from Another Time

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

The Cog-Wheel Revolution
Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?
The Recruiting Officers
Two officers each have a company of men, the one has 40 less than the other.
The Time It Takes To Eat a Goat
A lion, a wolf and a fox each take a certain amount of time to eat a goat separately. How long would it take all these animals together to eat the goat?
Maxes and Mins
Determine the different values of x, when a certain function hits a minimum.
Two Numbers
Find two numbers with sum 20 and when squared their sum is 208.
A Room with a View
Find the height of a window.
Money Makes the World Go Around
You have two sums of money, the difference of which is 2 dirhems; you divide the smaller sum by the larger and the quotient is equal to 1/2. What are the two sums of money?
Logarithms: The Early History of a Familiar Function - Parallel Insights and the Reception of Mathematical Ideas
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
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?

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