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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 general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.
A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received $150 for them. How many did he buy?
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
A farmer sold a team of horses for $440, but did not receive his pay for them until 1 yr, 8 mo after the sale. He had at the same time another offer of $410 for them. Did he gain or lose by the sale and by how much, money being worth 6%/yr?
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
There is a lion in a well whose depth is 50 palms. He climbs and slips back a certain amount each day. In how many days will he get out of the well?
Given the fraction ax/ (a-x ), convert it into an infinite series.
A two door gate of unknown width is opened so that a 2 inch gap exists between the two doors.
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.

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