# 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?
Chuquet claimed that if given positive numbers a, b, c, d then (a + b) / (c + d) lies between a/c and b/d. Is he correct? Prove your answer
Determine a number having remainders 2, 3, 2 when divided by 3, 5, 7 respectively.
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?
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Two travelers, starting at the same time from the same point, travel in opposite directions round a circular railway.
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.
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.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions