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Problems from Another Time

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

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.
Square
The square of a certain number multiplied by itself and by 200 is 446,976. What is the number?
An Apple a Day
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.

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