Volume 19
, Issue 1


There are essentially only two operations involved in the encryption of a message: substitution and transposition.

Ring a-ring a roses,
A pocketful of posies,
Atishoo, Atishoo,
We all fall down.

Over fifteen years ago, mathematics students from different countries began meeting for an annual competition called the International Mathematical Olympiad.

There were once again some interesting problems in the 1982 H.S.C. Turning first to some extreme value problems, starting with the 3 unit paper.

Q.551 Solve the system of equations
\begin{align*}u^2 + v^2 +w^2 & = 49 \\
\frac{1}{u} +\frac{1}{v}+\frac{1}{w} & = 0 \\
u - v + w & = 1\end{align*}

Q.527 On a sheet of paper we read the following 100 statements: