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Problems from Another Time

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

There are four companies, in one of which there are 6 men, in another 8, and in each of the remaining two, 9 men. How many ways can a committee of 4 men be composed by choosing one man from each company?
There is a four-sided field whose eastern side measures 35 paces, its western side 45 paces, its southern side 25 paces and its northern side 15 paces. Find the area of this field.
Suppose that the propability of success in an experiment is 1/10. How many trials of the experiment are necessary to insure even odds on it happening at least once?
Two merchants, A and B, loaded a ship with 500 hhds (hogshead) of rum; A loaded 350 hhds, and B the rest; in a storm the seamen were obliged to throw overboard 100 hhds; how much must each sustain of the loss?
Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
The king of France entered into a battle and was defeated. How many soldiers did he have before he was defeated?
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
What is the perpendicular height of a cloud when its angles of elevation were 35 degrees and 64 degrees as taken by two observers at the same time...
A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.
When knowing the sum of their ages along with another equation, determine how old a father and son are.

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