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Problems from Another Time

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

Logarithms: The Early History of a Familiar Function - Appendix: Student Tasks
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
A Family Problem
A man, woman, and two boys desire to cross a river, but their boat has weight restrictions!
Parallelepiped Chimney
The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".
But What's in the Flasks?
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?
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Background: The Abbaco Tradition
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Monkeys in a Tree
A tree 100 units high is 200 units distant from a well; from this tree one monkey climbs down and goes to the well...
Compound Interest
Suppose a man had put out one cent at compound interest in 1620, what would have been the amount in 1824, allowing it to double once in 12 years?
What Are the Odds?
Suppose that the probability of success in an experiment is a/(a+b). How many trials of the experiment are necessary to insure even odds on it happening at least once?
An Acute Problem
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.
Silver Cups
A lady has two silver cups, and only one cover for both. The first cup weighs 16 oz, and when it is covered it weighs 3 times as much as the second cup; but when the second cup is covered, it weighs 4 times as much as the first.

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