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Problems from Another Time

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

Seven men held equal shares in a grinding stone 5 feet in diameter. What part of the diameter should each grind away?
Given a pyramid 300 cubits high, with a square base 500 cubits to a side, determine the distance from the center of any side to the apex.
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...
In a rectangle, having given the diagonal and perimeter, find the sides
Given two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.
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 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.
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?

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