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Problems from Another Time

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

Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 7 months.
A father wills his estate valued at $40, 000 to his three children. Before the settlement one of the children dies. What should the other two receive?
Of the two water reeds, the one grows 3 feet and the other 1 foot on the first day. The growth of the first becomes every day half of that of the preceding day, while the other grows twice as much as on the day before.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."
The cost per hour of running a certain steamboat is proportional to the cube of its velocity in still water. At what speed should it be run to make a trip up stream against a four-mile current most economically?
Divide 100 loaves of bread among 10 men including a boatman, a foreman, and a doorkeeper, who receives double portions. What is the share of each?
If I were to give 7 pennies to each beggar at my door, I would have 24 pennies left in my purse. How many beggars are there and how much money do I have?
A horse halving its speed every day runs 700 miles in 7 days.
There is a round town 8000 feet in circumference.