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Problems from Another Time

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

A Dangerous Castle Indeed
A castle has n rooms each of which has 7 samurai in it.
Difference of Squares
Having been given the sum of two numbers, a, and the difference of their squares, b, find the numbers.
A Tree with Branches, Nests, Eggs and Birds
There is a tree with 100 branches. How many nests, eggs and birds are there?
Height and Distance
An erect pole of 10 cubits has its base moved 6 cubits. Determine the new height and the distance the top of the pole is lowered.
A Wealth of Plantains
Twenty-three weary travelers entered a delightful forest. There they found 63 numerically equal piles of plantain fruit.
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.

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