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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 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?
Of the two water reeds, the one grows 3 feet and the other 1 foot on the first day. The growth of the first becomes every day half of that of the preceding day, while the other grows twice as much as on the day before.
What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
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?
A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.
Two officers each have a company of men, the one has 40 less than the other.
As for a square piece of land that amounts to 100 square cubits, if it is said to you, "Cause it to make a piece of land that amounts to 100 square cubits that is round," what is the required diameter?
A number is required; that the square shall be equal to twice the cube.
There is a regular pentagon. The length of its side is a. Find the area of the pentagon. Generalize your result for a nonagon.
A leech invited a slug for a lunch a leuca away.

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