M. Reynolds

Consider the quadratic ${x}^{2}+x+1$ . By substituting $x=1,2,3,\cdots $ we can form a sequence

A. V. Nikov

Regular patterns and figures have always played an important part in the civilizations of mankind.

Once again, in early December 1977 the University of N.S.W. held its Summer Science School.

While exploring the peculiarities of circles we come upon an interesting phenomenon known as Simon's Line. This is formed in the following way:

In the article by Alan Fekete on Simpson's Paradox in Vol. 13 No. 3, there is apparently an error.

M. Hirschhorn

I have, since the publication of Vol. 13 No. 3, found another solution to problem 344.

**Q.369** Find a five digit number which when divided by 4 yields another 5 digit number using the same 5 digits but in the opposite order.

**Q.345** During a trial, three different witnesses A,B and C were called one after the other and asked the same questions.

A. V. Nikov

The marvellous formula of Euler, $V-E+F=2$ , can yield interesting results other than that concerning the Platonic Solids.

G. Ward

This article looks at some of the mathematics used by actuaries, and how it describes some features of our lives.

G. Karpilovsky

To solve a mathematical problem does not just mean to perform a certain number of manipulations. The most important thing is that the solution should be complete.

More on $\mathrm{tan}{1}^{\circ}$

Of the 4 suspects, one is the murderer, one is totally innocent, and the other two are witnesses.

Find a set of four different prime numbers such that the sum of every three of them is also a prime number.

**Q.381** A square cake has frosting on its top and all four sides. Show how to cut it to serve nine people so that each one gets exactly the same amount of cake and exactly the same amount of frosting.

**Q.357 **Chess-players from two schools competed. Each player played one game from every other player.

Hugh MacPherson

Several thousand years ago, magic squares were being used by Indian astrologers in their calculations of horoscopes.

S. Prokhovnik

π is an important universal constant and appears in many fields of mathematics and theoretical physics.

Brendan J. Joyce

Can you identify the next term of the series: 1,5,32,228,1675,?

Gourag Chandra Mohanty

Angle-Trisection has a history of its own. It has aroused much interest in the minds of students and teachers alike.

Recently I came across the following problem: "I have a circular fields radius 100 meters, and a goat...."

In Vol. 14 No.'s 1 and 2, the problem of finding the digits of ${1001}^{1000}$ was posed.

The solution to the cross-number puzzle given in Vol. 14 No 1 is

The standard of performance in the 1978 School Mathematics Competition was much the same as it has been for some years

A. Lenart

Suppose you are given a maze which you have to travel right through (there is an entrance and an exit)

**Q.393** Show that if $n$ is any integer greater than 2, of the fractions $\frac{1}{n},\frac{2}{n},\frac{3}{n},\cdots ,\frac{n-1}{n}$ an even number are in lowest terms.

**Q.369** Find a five digit number which when divided by 4 yields another 5 digit number using the same 5 digits but in the opposite order.