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Problems from Another Time

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

Find the height of a window.
Now a pile of rice is against a wall, it has a base perimeter of 60 feet and a height of 12 feet.
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.
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.
What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
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?
A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.
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?
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?
Given a rectangle, find the line through one vertex of minimum length that passes through the extensions of the two opposite sides.

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