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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 set of four congruent circles whose centers form a square is inscribed in a right triangle ABC where C is the right angle and serves as one corner of the square. Find their radius in terms of the sides; a,b,c, of the triangle.
A wooden beam is stood vertically against a wall. The length of the beam is 30 units.
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
Suppose a man had put out one cent at compound interest in 1620, what would have been the amount in 1824, allowing it to double once in 12 years?
A man is walking across a bridge, when a boat passes under the bridge.How rapidly are the boat and the pedestrian separating after the boat passes under the bridge?
If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circle?
One person possesses 7 asavas horses, another 9 hayas horses, and another 9 camels. Each gives two animals away, one to each of the others.
Knowing the base, b, and the altitude, a, of a triangle. Find the expression for a side of the inscribed square.
There are two numbers whose sum equals the difference of their squares.
Now there are 100 deers [being distributed] in a city. If one household has one deer there is a remainder...Find the number of households in the city.

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