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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.
Travelling Men 2
Two men start walking at the same time and travel a distance. One is walking faster and completes the journey sooner. How fast did each man travel?
Fine Parisian Wine
Two wine merchants enter Paris, one of them with 64 casks of wine, the other with 20.
Diameter of the Earth
The highest point of the Andes is about 4 miles above sea level.

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