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Problems from Another Time

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

Given a number, take 1/3 of the number away from itself and add 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?
Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?
If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?
A certain merchant increases the value of his estate by 1/3...
Imagine an urn with two balls, each of which may be either white or black. One of these balls is drawn and is put back before a new one is drawn.
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
Suppose a lighthouse is built on the top of a rock; the distance between a place of observation and that part of the rock level with the eye is 620 yds.
A square walled city of unknown dimensions has four gates, one at the center of each side.
In a forest, a number of apes equal in number to the square of 1/8 of the total number of apes are noisy. The remaining 12 apes are on a nearby hill irritated. What is the total number of apes in the pack?
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

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