# Problems from Another Time

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

Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
An official asks a woman why she has so many bowls to wash. The woman explains that she had dinner guests who ate meat, rice, and soup. Judging by the number of bowls, how many guests were there?
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?
Given a rectangle, find the line through one vertex of minimum length that passes through the extensions of the two opposite sides.
Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
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.
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
Three men wish to buy a horse but none have a sufficient amount of money for the purchase; to do so they must borrow from each other. How much money does each man have and what is the price of the horse?
A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.
What is the perpendicular height of a cloud when it's angles of elevation were 35 degrees and 64 degrees as taken by two observers?