Volume 40
, Issue 2

2004 The first article in this issue, by Peter Donovan, tells a fascinating story of how code breakers working at Fleet Radio Unit, Melbourne (FRUMEL) during the Second World War, were able to de-code the principal Japanese Navy operational code.

The American National Security Agency, situated between Washington and Baltimore, is said to employ more mathematicians than any other organisation.

What is a number? This seemingly banal question has plagued mathematicians for centuries who have questioned the legitimacy of irrational and negative numbers.

Junior Division

1. In how many ways can a cube be coloured with the three colours red, white and green?

Prize Winners – Junior Division

First Prize
Gidon Chaim Jones                 Moriah College

Q1161 Find all values of $x$ (real number) satisfying
\begin{align*}
\frac{x-1}{2004} & + \frac{x-3}{2002} + \frac{x-5}{2000} + \cdots +
\frac{x-2003}{2}\\
= \frac{x-2}{2003} & + \frac{x-4}{2001} + \frac{x-6}{1999} + \cdots +
\frac{x-2004}{1}
\end{align*}

Q1151. Let $p(x) = (x^{2003} + x^{2002} -1)^{2004}.$  Find the sum of the coefficients of all odd degree terms in the expansion of the trinomial $p(x).$