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Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
There are a number of wonderful mathematics websites that readers of Convergence should be aware of. We describe some of them here.
You have two sums of money, the difference of which is 2 dirhams; you divide the smaller sum by the larger and the quotient is equal to 1/2. What are the two sums of money?
In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"

Problems from a 15th century French manuscript, including one with negative solutions

This is page 167 from the Exercitationes mathematicae (1657) of Frans van Schooten (1615-1660). This book contained a collection of mathematical construction problems, among much else. It was one of the books read by Isaac Newton while he was a student at Cambridge University and helped to introduce him to modern mathematics. On this page we see a construction enabling one to find the distance across a river.
What is the value of X...
Given two circle tangent at the point P with parallel diameters AB, CD, prove that APD and BPC are straight lines.
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.