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Problems from Another Time

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

Two men starting from the same point begin walking in different directions. Their rates of travel are in the ratio 7:3.
A fish sees a heron looking at him from across a pool, so he quickly swims towards the south. When he reaches the south side of the pool, he has the unwelcome surprise of meeting the heron.
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?
Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?
A certain merchant increases the value of his estate by 1/3...
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.
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.
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
A square walled city of unknown dimensions has four gates, one at the center of each side.

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