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Problems from Another Time

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

Sugar per Pound
What proportions of sugar at 8 cents, 10 cents and 14 cents per pound, will compose a mixture worth 12 cents per pound?
Sides of a Rectangle
Given a rectangle, find the line through one vertex of minimum length that passes through the extensions of the two opposite sides.
Equal Surface and Volume
What will the diameter of a sphere be, when its volume and surface area are expressed by the same number?
Inscribed Square
Knowing the base, b, and the altitude, a, of a triangle, find the expression for a side of the inscribed square.
How Much to Buy a Horse?
Three men wish to buy a horse but none have a sufficient amount of money for the purchase; to do so, they must borrow from each other. How much money does each man have and what is the price of the horse?
Snowdrift on the Tracks
A railway train strikes a snowdrift which creates a constant resistance. How long does it take the snow to stop the train?
A River Runs Through It
Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
A General Question
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.
Base 7
A number of 3 digits in base 7 has the same three digits...
Chuquet's Rule of Average Numbers
Prove Chuquet's rule of average numbers.

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