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Problems from Another Time

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

I was employed to survey a field, which I was told was an exact geometrical square, but by reason of a river running through it, I can only obtain partial measurements.
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?
A man and his wife drink a barrel of wine at different rates. Find the rate it takes both of them together to drink the wine.
A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months absence caused by sickness, he received only $409.50. What was his board worth per month?
Having been given the sum of two numbers,a, and the difference of their squares,b, find the numbers.
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
Determine the greatest cylinder that can be inscribed in a given cone.
In a right triangle, the hypotenuse is 9.434 and the sum of the sides around the right angle is 13. Find the lengths of the sides around the right angle.
A square walled city measures 10 li on each side. At the center of each side is a gate. Two persons start walking from the center of the city.
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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