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Problems from Another Time

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

A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.
A copper water tank in the form of a rectangular parallelopiped 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?
Age
My age is a number consisting of two digits, 1/2 of this number is a mean proportional between these two digits, and two years hence, my age will be a third proportional to the same two digits, directly as they stand in my present age.
A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.
Thirty flasks-10 full, 10 half-empty, and 10 completely empty- are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?
Two wine merchants enter Paris, one of them with 64 casks of wine, the other with 20.
There are four companies, in one of which there are 6 men, in another 8, and in each of the remaining two, 9 men. How many ways can a committee of 4 men be composed by choosing one man from each company?
The three sides of a triangular piece of land, taken in order, measure 15, 10, and 13 chains respectively.
Given a rectangle, find the line through one vertex of minimum length that passes through the extensions of the two opposite sides.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

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