# Problems from Another Time

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

A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
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?
In order to encourage his son in the study of arithmetic, a father agrees to pay him 8 pennies for every problem solved correctly and to charge him 5 pennies for each incorrect solution.
A horse halving its speed every day runs 700 miles in 7 days.
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 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.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
Rabbits and pheasants are put in a basket.
Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse.

Two persons sat down to play for a certain sum of money; and agree that the first who gets three games shall be the winner. After a few games they resolve to divide the stakes. How much should each person receive?