Volume 44
, Issue 2

2008 Welcome to the second issue for 2008. For some forty years now the second issue of Parabola has celebrated the accomplishments of outstanding young mathematicians for their success in the UNSW School Mathematics Competition.

In my first year of teaching, I was given a formula summary sheet to be handed out to my year $11$ general mathematics class. One formula was particularly appealing.
$$2(xy+yz+xz)$$

Euclid’s Elements [of Geometry] is one of the most influential books ever written. It was first compiled in about $300$ BCE, and it reigned supreme in the classroom into living memory.

Mathematical and statistical methods are well known to underpin our highly technological society but it is perhaps less well known that mathematics and statistics are also being used as tools in the defence of human rights.

Problem 1

1. What is the angle between the long hand and the short hand of a clock at twenty minutes past four?
2. What is the next time, to the nearest second, at which the two hands of the clock have the same angle between them?

Competition Winners – Senior Division

Q1271 (suggested by Julius Guest, Victoria) Solve simultaneously
\begin{align*}
x^2 + xy + y^2 &= 189 \\
x - \sqrt{xy} + y &= 9.
\end{align*}

Q1261 A hat contains $N = 2n$ tickets, $n = 2, 3, 4, \ldots,$ each marked with a number from $1$ to $N$. (Each ticket has a different number.) In a game, players are asked to draw from the hat two tickets, read them, and replace them. Prize winners are those who draw two numbers whose ratio is $2$.