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Problems from Another Time

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

Base 7
A number of 3 digits in base 7 has the same three digits...
Chuquet's Rule of Average Numbers
Prove Chuquet's rule of average numbers.
Look Out Below!
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
Radii of Three Circles
Determine the radii of three equal circles described within and tangent to a given circle, and also tangent to each other.
Numbers Game #1
The sum of two numbers is 10 and their product is 40. What are the numbers?
University Payment Plan
A merchant gave a university 2,814 ducats on the understanding that he was to be paid back 618 ducats per year for 9 years, at the end of which the 2,814 ducats should be considered as paid.
Logarithms: The Early History of a Familiar Function - About the Authors and More Information on Sources
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Silver and Gold
There are two piles, one containing 9 gold coins, the other 11 silver coins.
Coins
A boy gives 11 coins of equal denomination to a man, and the man finds that their total value in yen is 4 less than his age.
Looking for Bargains
One says that 10 garments were purchased by two men at a price of 72 dirhams. The garments varied in value. The price of each garment of one man is 3 dirhams more than the price for each garment of the other. How many garments did each man buy?

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