Volume 51
, Issue 2

2015

this is my last message to you as Editor of Parabola.

this is my first message to you as Editor of Parabola.

When learning the intuition behind definite integration, calculus students often learn how to find the area under a curve by using a Riemann sum.

Ever thought of batting in cricket as a life and death struggle against hostile forces? It always seemed that way when I batted anyway.
Well you might be more accurate than you think in looking at it that way.

An enclosure of length $1$ unit is constructed around two adjoining walls of unlimited length. It is made of $n \geq 2$ straight sections, referred to as an $n$-enclosure, designed so as to maximise the enclosed area $A_n(\omega)$, where $\omega \leq \pi$ is the angle formed by the walls.

Competition Winners - Senior Division
Seyoon Ragavan   Knox Grammar School   1st prize

Competition Winners - Junior Division
Richard Gong   Sydney Grammar School   1st prize

Junior Division - Problems and Solutions
Solutions by Denis Potapov, UNSW Australia.

Problem 1

Q1481  Prove that if the denominator $q$ of a fraction $p/q$ is the number consisting of $n$ digits, all equal to $9$, and if $p$ is less than $q$, then $p/q$ can be written as a repeating decimal in which the repeating part has length $n$ and contains the digits of $p$, preceded by a sufficien

Q1471  Find the positive integer which has $7$ proper divisors, with the sum of the proper divisors being $673$.  (Proper divisors are all divisors except the number itself: for example, the proper divisors of $20$ are $1,2,4,5,10$.)