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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 Door and the Rod
Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.
Steamboat
The cost per hour of running a certain steamboat is proportional to the cube of its velocity in still water. At what speed should it be run to make a trip up stream against a four-mile current most economically?
Japanese Temple Problem
Given two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.
Peano on Wronskians: A Translation - Survey of Infinitesimal Analysis
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
The Cost of War
After a terrible battle it is found that 70% of the soldiers have lost an eye.
Inheritance of Three Sons
A man died leaving 3 sons, to whom he bequeathed his estate in the following manner: to the eldest he gave 184 dollars; to the second 155 dollars and to the third 96 dollars;
The Ant Race
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - A Fair Was Serious Business
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Mystery Numbers
Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27.
Provisions
If 80 dollars worth of provisions will serve 20 men for 25 days, what number of men will the same amount of provisions serve for 10 days?

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