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Problems from Another Time

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

Alphabet Challenge
In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"
Horses and Stalls
It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.
Be Careful Where You Step!
A ladder has 100 steps. On the first step sits 1 pigeon; on the second, 2; on the third, 3; and so on up to the hundredth. How many pigeons in all?
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Introduction
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Heron's Formula
Heron of Alexandria (c. 10 - 75 CE) wrote on many aspects of applied mathematics.
Circle and Square
Prove that a square circumscribed about a given circle is double in area to a square inscribed in the same circle.
Circumscribed Circle #2
Find the isosceles triangle of smallest area that circumscribes a circle of radius a.
In the Gentleman's Garden
A gentleman has a garden of rectangular form and wants to construct a walk of equal width half way round to take up half the garden. What must be the width of this walk?
Gun Metal
Gun metal of a certain grade is composed of 16% tin and 84% copper. How much tin must be added to 410 pounds of this gun metal to make a composition of 18% tin?
Purse of Denari
Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.

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