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Problems from Another Time

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

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.
Two persons sat down to play for a certain sum of money; and agree that the first who gets three games shall be the winner. After a few games they resolve to divide the stakes. How much should each person receive?
What is the value of X...
A certain slave fled from Milan to Naples going 1/10 of the whole journey each day. At the beginning of the third day, his master sent a slave after him and this slave went 1/7 of the whole journey each day.
On a day in spring a boy has gathered cherry blossoms under a cherry tree. Nearby a poet is reading some of his poems aloud. As he reads, the boy counts out the cherry blossoms, one blossom for each word of a poem.
There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
If you are h feet tall and walk all the way around the Earth, keeping to the same circumference, how much farther has your head gone than your feet when you complete the journey?
There is a four sided field.

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