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Problems from Another Time

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

On a day in spring a boy has gathered cherry blossoms under a cherry tree. Nearby a poet is reading some of his poems aloud. As he reads, the boy counts out the cherry blossoms, one blossom for each word of a poem.
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.
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
In a rectangle, having given the diagonal and perimeter, find the sides
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
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.
There is a four sided field.
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.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
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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