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Problems from Another Time

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

Estate Will
A father wills his estate valued at $40,000 to his three children. Before the settlement one of the children dies. What should the other two receive?
Pyramid Calculation
Given a pyramid 300 cubits high, with a square base 500 cubits to a side, determine the distance from the center of any side of the base to the apex.
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.
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?

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