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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 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?
A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.
A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?
A copper water tank in the form of a rectangular parallelopiped is to made. If its length is to be a times its breadth, how high should it be that for a given capacity it should cost as little as possible?
A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.
A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the lengths of those sides.
Two wine merchants enter Paris, one of them with 64 casks of wine, the other with 20.
There is a fish whose body weighs 8oz. Tell me how much the whole fish weighs?
The three sides of a triangular piece of land, taken in order, measure 15, 10, and 13 chains respectively.

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