Problems from Another Time

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

X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay? Two men starting from the same point begin walking in different directions. Their rates of travel are in the ratio 7:3. Determine the greatest cylinder that can be inscribed in a given cone. 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... A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity. A round pond sits in a rectangular garden. Its center is inaccessible; however, you know the distances from each corner of the garden to the center of the pond: 60, 52, 28, and 40 yards. What is the radius of the pond? The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class. In how many ways can a vowel and a consonant be chosen out of the word "logarithms?" A man agreed to pay for 13 valuable houses worth$5000 each, what the last would amount to, reckoning 7 cents for the first, 4 times 7 cents for the second, and so on, increasing the price 4 times on each to the last.
A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?