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Problems from Another Time

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

Something Fishy at Customs
Two men brought their fish through customs. Find how much the fish cost, and what is the customs fee.
Weight of a Ball
If a ball 6 inches in diameter weighs 32 lbs, what will be the weight of a ball 3 inches in diameter?
Points in a Semicircle
Given a semicircle, prove that if O is the circle's center, DO=OE.
Comparing Apples to Oranges
The purchase price for an apple and an orange is 100 yen. When n oranges and n + 3 apples are bought the price is 520 yen. Find the number n of oranges and the price of one orange.
A Game of Cat and Mouse
A mouse is at the top of a poplar tree 60 braccia high, and a cat is on the ground at its foot. The mouse descends 1/2 a braccia a day and at night it turns back 1/6 of a braccia.
Investing in Apples and Pears
A merchant woman buys and sells apples and pears. How much did she invest in apples; how much in pears?
Conic Contents
Determine the greatest cylinder that can be inscribed in a given cone.
Feeling Sluggish
A leech invited a slug for a lunch a leuca away.
A Perfect Cone Sugarloaf
Three persons bought a sugar loaf in the form of a perfect cone 25 inches high and agreed to divide it...what was the slant height of each one's share?
Brazen Lion
I am a brazen lion; my spouts are my 2 eyes, my mouth, and the flat of my foot. My right eye fills a jar in 2 days, my left eye in 3, and my foot in 4.

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