You are here

Problems from Another Time

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

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.
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?
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.
There is a round town 8000 feet in circumference.
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.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
Now there are six-headed four-legged animals and four-headed two-legged birds placed together.
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 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?