# Problems from Another Time

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

Three equal circumferences with radii 6" are tangent to each other. Compute the area enclosed between them.
Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
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.
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.
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?
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
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?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
A circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.
There is a four sided field.