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Problems from Another Time

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

An official asks a woman why she has so many bowls to wash. The woman explains that she had dinner guests who ate meat, rice, and soup. Judging by the number of bowls, how many guests were there?
If 12 cattle eat up 3 1/3 acres of meadow in 4 weeks and 21 cattle eat up 10 acres of exactly similar meadow in 9 weeks, how many cattle shall eat up 36 acres in 18 weeks? (Hint: The grass continues to grow.)
If a ball 6 inches in diameter weighs 32 lbs, what will be the weight of a ball 3 inches in diameter?
Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
Find the two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
How high above the earth must a person be raised that he [or she] may see 1/3 of its surface?
A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.
Two men start walking at the same time and travel a distance. One is walking faster and completes the journey sooner. How fast did each man travel?
In a square box that contains 1000 marbles, how many will it take to reach across the bottom of the box in a straight row?

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