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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 tree is 20 feet tall and has a circumference of 3 feet. There is a vine that winds seven equally spaced times around the tree and reaches the top. What is the length of the vine?
A vessel is anchored in 3 fathoms of water and the cable passes over a sheave in the bowspirt which is 6 ft above the water.
A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1560. How much did he invest?
Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
Given: a circle with an inscribed equilateral triangle. The triangle has an area of 12 square units. What is the area of the circle?
A castle has n rooms each of which has 7 samurai in it.
If 80 dollars worth of provisions will serve 20 men for 25 days, what number of men will the same amount of provisions serve for 10 days?
Find two number with sum 20 and when squared their sum is 208.
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?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?

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