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Problems from Another Time

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

There is a lion in a well whose depth is 50 palms. He climbs and slips back a certain amount each day. In how many days will he get out of the well?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.
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.
A copper water tank in the form of a rectangular parallelopiped is to made. If its length is to be a times its breadth, how high should it be that for a given capacity it should cost as little as possible?
A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.
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?
Divide 100 loaves of bread among 10 men including a boatman, a foreman, and a doorkeeper, who receives double portions. What is the share of each?

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