Problems from Another Time

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

What is the sum of the reciprocals of the triangular numbers?

When knowing the sum of their ages along with another equation, determine how old a father and son are.

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.

Be Careful Where You Step!

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?