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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
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 man hired a horse in London at 3 pence a mile. He rode 94 miles due West to Bristol then due north to Chester, whence he returned toward London for 66 miles, which put him in Coventry.
A tree is 20 feet tall and has a circumference of 3 feet. There is a vine that winds seven equally spaced times around the tree and reaches the top. What is the length of the vine?
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.
A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1560. How much did he invest?
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.
Given: a circle with an inscribed equilateral triangle. The triangle has an area of 12 square units. What is the area of the circle?
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
If 80 dollars worth of provisions will serve 20 men for 25 days, what number of men will the same amount of provisions serve for 10 days?

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