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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.
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
Suppose a man had put out one cent at compound interest in 1620, what would have been the amount in 1824, allowing it to double once in 12 years?
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."
A circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.
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?
Gun metal of a certain grade is composed of 16% tin and 84% copper. How much tin must be added to 410 lbs. of this gun metal to make a composition of 18% tin?
A horse halving its speed every day runs 700 miles in 7 days.
Now there are six-headed four legged animals and four-headed two-legged birds. Find the total number of animals and birds.

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