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Convergence articles

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A fox, a wild-cat, and a hound pass through customs and together pay 111 coins.

One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...

A circle ABDC is circumscribed around an equilateral triangle ABC.  Prove that the straight line AD is equal to the sum of the two straight lines BD and DC.

A brief outline of policies for submission of articles to Loci.

Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By using measurments of the posts, determine, to the nearest mile, the radius of the earth.

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

There were two men, of whom the first had 3 small loaves of bread and the other, 2.

An introduction to the prime numbers in many of their aspects.

Given four integers which, if added together three at a time, their sums are: 20, 22, 24, and 27. What are the integers?

Prove that a square circumscribed about a given circle is double in area to a square inscribed in the same circle.