# Problems from Another Time

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

A certain merchant increases the value of his estate by 1/3...
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?
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
A square walled city of unknown dimensions has four gates, one at the center of each side.
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?
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 fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?
There are two piles, one containing 9 gold coins, the other 11 silver coins.
A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.