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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 is a tree with 100 branches. How many nests, eggs and birds are there?
Two men starting from the same point begin walking in different directions. Their rates of travel are in the ratio 7:3.
The sum of the two digits of a 2-digit number is 9. If 45 is subtracted from the number, the result will be expressed by the digits in reverse order. Find the number.
A cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.
To find three quantities x.y, and z...
A round pond sits in a rectangular garden. Its center is inaccessible; however, you know the distances from each corner of the garden to the center of the pond: 60, 52, 28, and 40 yards. What is the radius of the pond?
There are two numbers which are to each other as 5 and 6 and the sum of their squares is 2196. What are the numbers?
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?

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