Volume 2
, Issue 2


Doubtless the above heading will be to most of our readers as cryptic as the meaning as some of the more outlandish examples of the so-called "Strine language" which have recently appeared in the newspapers.

In the October 1964 issue of Parabola, the article on the Four Color Problem called your attention to the existence of numerous unsolved mathematical problems which can be stated in quite simple non-technical terms.

J31 Prove that, given five consecutive integers, it is always possible to find one which is relatively prime to all the rest.

J21 (i) In a box there is a number of balls $c$ of different colours. What is the smallest number of balls for which we can say that, however the colours are distributed, there is at least one set of $s$ balls of the same colour? Justify your statement.

$X$ is a point inside a polygon and $AB$ is one of the sides of the polygon. Show that the perimeter of the triangle $ABX$ is shorter than the perimeter of the polygon.