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Problems from Another Time

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

I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.
Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.
Determine by using algebra the number of degrees in the angle A where: cos A = tan A
Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?
On an expedition to seize his enemy's elephants, a king marched 2 yojanas the first day.
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

A railway train strikes a snowdrift which creates a constant resistance. How long does it take the snow to stop the train?
A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
One military horse cannot pull a load of 40 dan; neither can 2 ordinary horses, nor can three inferior horses.
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?

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