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Problems from Another Time

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

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.
X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?
A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?
A castle has n rooms each of which has 7 samurai in it.
Find two number with sum 20 and when squared their sum is 208.
A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.
As for a square piece of land that amounts to 100 square cubits, if it is said to you, "Cause it to make a piece of land that amounts to 100 square cubits that is round," what is the required diameter?
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
Three hundred pigs are to be prepared for a feast.
There is a regular pentagon. The length of its side is a. Find the area of the pentagon. Generalize your result for a nonagon.