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Problems from Another Time

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

Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
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.
A gentleman has a garden of rectangular form and wants to construct a walk of equal width half way round to take up half the garden. What must be the width of this walk?
Age
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?
Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?
A certain merchant increases the value of his estate by 1/3...
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?
Given a rectangle, find the line through one vertex of minimum length that passes through the extensions of the two opposite sides.
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.

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