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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 man has four creditors. To the first he owes 624 ducats; to the second, 546; to the third, 492; and to the fourth 368.
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.
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?
A barrel has various holes in it. The fist hole empties the barrel in three days...
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.
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?
Determine the different values of x, when a certain function hits a minimum.
Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.

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