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Problems from Another Time

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

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 man is walking across a bridge, when a boat passes under the bridge.How rapidly are the boat and the pedestrian separating after the boat passes under the bridge?
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?
One person possesses 7 asavas horses, another 9 hayas horses, and another 9 camels. Each gives two animals away, one to each of the others.
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?
There are two numbers whose sum equals the difference of their squares.
A set of n disjoint, congruent circles packs the surface of a sphere S so that each region of the surface exterior to the circles is bounded by arcs of three of the circles.
A four-sided town measures 1100 feet on one side and 1000 feet on the other side, on one edge 600 and the other edge 600.
An oracle ordered a prince to build a sacred building, whose space would be 400 cubits, the length being 6 cubits more than the width, and the width 3 cubits more than the height. Find the dimensions of the building.
A merchant bought 50,000 pounds of pepper in Portugal for 10,000 scudi and paid a tax of 500 scudi.

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