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Problems from Another Time

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

What is the sum of the reciprocals of the triangular numbers?
There is a tree with 100 branches. How many nests, eggs and birds are there?
Two men starting from the same point begin walking in different directions. Their rates of travel are in the ratio 7:3.
Suppose the area of an equilateral triangle be 600. The sides are required.
A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.
A cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.
A round pond sits in a rectangular garden. Its center is inaccessible; however, you know the distances from each corner of the garden to the center of the pond: 60, 52, 28, and 40 yards. What is the radius of the pond?
Given a pendulum as shown. The height of the pendulum is two units and its horizontal width is 2 units. What is the area of the pendulum?
Three hundred pigs are to be prepared for a feast.
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.

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