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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?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
There is a number which when divided by 2, or 3, or 4, or 5, or 6 always has a remainder of 1 and is truly divisible by 7. It is sought what is the number?
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?
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
In a right triangle, the hypotenuse is 9.434 and the sum of the sides around the right angle is 13. Find the lengths of the sides around the right angle.
Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 7 months.
Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

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