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?

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

Find the height of a window.

A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.

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.

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.

My age is a number consisting of two digits, 1/2 of this number is a mean proportional between these two digits, and two years hence, my age will be a third proportional to the same two digits, directly as they stand in my present age.

Thirty flasks-10 full, 10 half-empty, and 10 completely empty- are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."

There are four companies, in one of which there are 6 men, in another 8, and in each of the remaining two, 9 men. How many ways can a committee of 4 men be composed by choosing one man from each company?