Problems from Another Time

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

Three men have a pile of money, their shares being 1/2, 1/3 and 1/6. Each man takes some money from the pile until nothing is left.

Money Changers

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."

Trisecting a Log

There is a log of precious wood 18 feet long whose bases are 5 feet and 2.5 feet in circumference. Into what lengths should the log be cut to trisect its volume?

Division Problem

The number 50 is divided by a certain number. If the divisor is increased by 3, the quotient decreases by 3.75. What is the number?

Logarithms: The Early History of a Familiar Function - Conclusion

The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

Alphabet Challenge

In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"

Horses and Stalls

It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.

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