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Problems from Another Time

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

The number 50 is divided by a certain number. If the divisor is increased by 3, the quotient decreases by 3.75. What is the number?
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.
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 castle has n rooms each of which has 7 samurai in it.
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?
Find two number with sum 20 and when squared their sum is 208.
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?
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
Three hundred pigs are to be prepared for a feast.