Problems from Another Time

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

A father wills his estate valued at $40,000 to his three children. Before the settlement one of the children dies. What should the other two receive?

Pyramid Calculation

Given a pyramid 300 cubits high, with a square base 500 cubits to a side, determine the distance from the center of any side of the base to the apex.

A Wealth of Plantains

Twenty-three weary travelers entered a delightful forest. There they found 63 numerically equal piles of plantain fruit.

The Door is Ajar

A two door gate of unknown width is opened so that a 2 ts'un gap exists between the two doors.

Rifle Ball Through a Three-Inch Plank

A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.

Two Circles

Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?

Peano on Wronskians: A Translation - On the Wronskians

How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students

Traveling on a Train

Two travelers, starting at the same time from the same point, travel in opposite directions round a circular railway.

Bargain Houses

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.

Weights and Measures

A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?