Problems from Another Time

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

In a rectangle, given the diagonal and perimeter, find the sides

Suppose that for every 4 cows a farmer has, he should plow 1 acre of land, and allow 1 acre of pasture for every 3 cows; how many cows could he keep on 140 acres?

Peano on Wronskians: A Translation

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

The Rat Race

Now there is a wall 5 feet thick and two rats tunnel from opposite sides.

The Incircle of a Triangle

The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

Numbers Game #2

Given a number, take 1/3 of the number away from itself and also remove 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Barter Transactions

Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions

Lotus in the Lake

In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span above the surface of the water.

Nuts Over Counting

A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. What is the smallest number of nuts he could have?

Two Balls, No Strikes!

Imagine an urn with two balls, each of which may be either white or black. One of these balls is drawn and is put back before a new one is drawn.