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Problems from Another Time

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

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?
A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months absence caused by sickness, he received only $409.50. What was his board worth per month?
A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received $150 for them. How many did he buy?
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
A certain merchant increases the value of his estate by 1/3...
There is a right triangle where: the sum of the upright multiplied by itself twice and the hypotenuse multiplied by itself is 700 units; and, the sum of the base multiplied by itself twice and the hypotenuse multiplied by itself is 900 units.
Given the fraction ax/ (a-x ), convert it into an infinite series.
Three men wish to buy a horse but none have a sufficient amount of money for the purchase; to do so they must borrow from each other. How much money does each man have and what is the price of the horse?
Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.
What is the perpendicular height of a cloud when it's angles of elevation were 35 degrees and 64 degrees as taken by two observers?