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Problems from Another Time

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

If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?
Imagine an urn with two balls, each of which may be either white or black. One of these balls is drawn and is put back before a new one is drawn.
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 four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
Suppose a lighthouse is built on the top of a rock; the distance between a place of observation and that part of the rock level with the eye is 620 yds.
In a forest, a number of apes equal in number to the square of 1/8 of the total number of apes are noisy. The remaining 12 apes are on a nearby hill irritated. What is the total number of apes in the pack?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
There is a four sided field.
Find the area of the elliptical segment cut off parallel to the shorter axis;
A number of 3 digits in base 7 has the same three digits...