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Problems from Another Time

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

Age
My age is a number consisting of two digits, 1/2 of this number is a mean proportional between these two digits, and two years hence, my age will be a third proportional to the same two digits, directly as they stand in my present age.
Two travelers, starting at the same time from the same point, travel in opposite directions round a circular railway.
Thirty flasks-10 full, 10 half-empty, and 10 completely empty- are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
There are four companies, in one of which there are 6 men, in another 8, and in each of the remaining two, 9 men. How many ways can a committee of 4 men be composed by choosing one man from each company?
A wooden beam is stood vertically against a wall. The length of the beam is 30 units.
Given a rectangle, find the line through one vertex of minimum length that passes through the extensions of the two opposite sides.
There is a right triangle where: the sum of the upright multiplied by itself twice and the hypotenuse multiplied by itself is 700 units; and, the sum of the base multiplied by itself twice and the hypotenuse multiplied by itself is 900 units.
Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.

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