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Problems from Another Time

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

Two persons sat down to play for a certain sum of money; and agree that the first who gets three games shall be the winner. After a few games they resolve to divide the stakes. How much should each person receive?
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 certain slave fled from Milan to Naples going 1/10 of the whole journey each day. At the beginning of the third day, his master sent a slave after him and this slave went 1/7 of the whole journey each day.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?
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."
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?
If you are h feet tall and walk all the way around the Earth, keeping to the same circumference, how much farther has your head gone than your feet when you complete the journey?
A horse halving its speed every day runs 700 miles in 7 days.
The square root of half the number of bees in a swarm has flown out upon a jessamine bush; 8/9 of the swarm has remained behind.