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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 tree with 100 branches. How many nests, eggs and birds are there?
In a circle whose circumference is 60 units, a chord is drawn forming a segment whose sagitta is 2 units. What is the length of the chord?
Two men starting from the same point begin walking in different directions. Their rates of travel are in the ratio 7:3.
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?
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
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?
What is the sum of the reciprocals of the triangular numbers?
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.
Suppose the area of an equilateral triangle be 600. The sides are required.
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.

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