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Problems from Another Time

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

Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.
A lady has two silver cups, and only one cover for both. The first cup weighs 16 oz, and when it is covered it weighs 3 times as much as the second cup; but when the second cup is covered, it weighs 4 times as much as the first.
The king of France entered into a battle and was defeated. How many soldiers did he have before he was defeated?
A copper water tank in the form of a rectangular parallelepiped is to made. If its length is to be a times its breadth, how high should it be that for a given capacity it should cost as little as possible?
Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 5 months.
A number of 3 digits in base 7 has the same three digits...
Prove Chuquet's rule of average numbers.
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
Determine the dimensions for a right-angled triangle, having been given the hypotenuse, and the side of the inscribed square.
A merchant gave a university 2,814 ducats on the understanding that he was to be paid back 618 ducats per year for 9 years, at the end of which the 2,814 ducats should be considered as paid.

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