You are here

Problems from Another Time

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

Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?
What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

Two officers each have a company of men, the one has 40 less than the other.
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?
A number is required; that the square shall be equal to twice the cube.
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?
A leech invited a slug for a lunch a leuca away.
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.
Chuquet claimed that if given positive numbers a, b, c, d then (a + b) / (c + d) lies between a/c and b/d. Is he correct? Prove your answer