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Problems from Another Time

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

Three equal circumferences with radii 6" are tangent to each other. Compute the area enclosed between them.
A castle has n rooms each of which has 7 samurai in it.
Find two number with sum 20 and when squared their sum is 208.
A boy gives 11 coins of equal denomination to a man, and the man finds that their total value in yen is 4 less than his age.
There were two men, of whom the first had 3 small loaves of bread and the other, 2.
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
There is a four sided field.
Suppose a man had put out one cent at compound interest in 1620, what would have been the amount in 1824, allowing it to double once in 12 years?
A circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.