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Problems from Another Time

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

Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
What is the sum of the reciprocals of the triangular numbers?
If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?
Given a guest on horseback rides 300 li in a day. The guest leaves his clothes behind. The host discovers them after 1/3 day, and he starts out with the clothes.
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 bridge is built across a river in 6 months by 45 men. It is washed away by the current. Required the number of workmen sufficient to build another of twice as much worth in 4 months.
The triangle ABC has a right angle at C. Show that 1/ED=1/AC+1/AB
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
Three hundred pigs are to be prepared for a feast.

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