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Problems from Another Time

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

Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
A California miner has a spherical ball of gold, 2 inches in diamter, which he wants to exchange for spherical balls 1 inch in diameter. How many of the smaller spheres should he receive?
The sum of two numbers is 10 and their product is 40. What are the numbers?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
There is a four sided field.
In baking a hemispherical loaf of bread of 10" radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?
Given a triangular piece of land having two sides 10 yards in length and its base 12 yards, what is the largest square that can be constructed within this piece of land so that one of its sides lies along the base of the triangle?
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
In one day, a person can make 30 arrows or fletch [put the feathers on] 20 arrows.
What is the sum of the following series, carried to infinity: 11, 11/7, 11/49, etc.?