# Problems from Another Time

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

Given a wooden log of diameter 2 feet 5 inches from which a 7 inch thick board is to be cut, what is the maximum possible width of the board?
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
A man agreed to pay for 13 valuable houses worth $5000 each, what the last would amount to, reckoning 7 cents for the first, 4 times 7 cents for the second, and so on, increasing the price 4 times on each to the last. A square walled city measures 10 li on each side. At the center of each side is a gate. Two persons start walking from the center of the city. A father left$20,000 to be divided among his four sons ages 6, 8, 10, and 12 years respectively so that each share placed at 4 1/2 compounded interest should amount to the same value when its possessor becomes the age 21.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse.

A lady being asked how old she was at the time of her marriage replied that the age of her oldest son was 13; that he was born 2 years after her marriage...
If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many peaches can be bought for 100 oranges?
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students