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Problems from Another Time

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

A guest on horseback rides 300 li in a day. The guest leaves his clothes behind and the host rides off to catch up with the guest once he discovers the clothes. Assuming the host rides without stop tell how far he can go in a day?
I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.
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."
Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.
Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?
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.
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?

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