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Problems from Another Time

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

Given a number, take 1/3 of the number away from itself and add 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Given right triangle ABC where C is the right angle, ellipse O (a,b) is inscribed in it, with its major axis parallel to BC. Calculate the semi-major axis, a, in terms of AC, BC and b.
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.
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
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.
What is the value of X...
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?
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.

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