Year 2004 - Volume 40
2020 - Present

In the first article in this issue, by Michael Hirschhorn, you will learn about the harmonic series ∑k=1∞1k.

Michael D. Hirshhorn
If you study series, one of the first divergent series you will meet is the harmonic series, 1+12+13+14+ ⋯ =∑k=1∞1k.

Seán Stewart
Sometime in your senior mathematics course you will have come across arithmetic and geometric sequences.

Bruce Henry
My first experience with an algebraic manipulation package was about twenty years ago, toward the end of my PhD in theoretical physics.

Q1151. Let p(x)=(x2003+x2002−1)2004. Find the sum of the coefficients of all odd degree terms in the expansion of the trinomial p(x).

Q1141. In the 2003 cricket XI there were 7 boys who had been in the 2002 XI, and in the 2002 XI there were 8 boys who had been in the 2001 XI. What is the least number who have been in all three XIs?

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.

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

Daniel Chan
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 (x−1)/2004=(x−2)/2003+(x−3)/2002+(x−5)/2000+⋯+(x−2003)/2+(x−4)/2001+(x−6)/1999+⋯+(x−2004)/1

Q1151. Let p(x)=(x2003+x2002−1)2004. Find the sum of the coefficients of all odd degree terms in the expansion of the trinomial p(x).