# Problems from Another Time

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

A ladder has 100 steps. On the first step sits 1 pigeon; on the second, 2; on the third, 3; and so on up to the hundredth. How many pigeons in all?
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months absence caused by sickness, he received only$409.50. What was his board worth per month?
Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
If I were to give 7 pennies to each beggar at my door, I would have 24 pennies left in my purse. How many beggars are there and how much money do I have?
In a right triangle, the hypotenuse is 9.434 and the sum of the sides around the right angle is 13. Find the lengths of the sides around the right angle.
A horse halving its speed every day runs 700 miles in 7 days.
Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students