Year 1990 - Volume 26
2020 - Present

David Angell

First we must introduce some musical terminology, with apologies to readers who are already familiar with it.

Ian Doust
A time series is a sequence of values x1,x2,x3,⋯ , usually representing measurements of some quantity at equal intervals of time.

Gavin Brown
Here is a problem of the sort that could possibly be set in a 4-unit paper:

David Tacon
In a recent article of Parabola (Vol. 25 No.3), Esther Szekeres showed how we could prove many geometrical results by thinking in terms of centers of mass.

Q.794 A and B are opposite vertices of a cube of side length 1 unit.

Q.782 Let Sn=1/(12-(1/4))+1/(22-(1/4))+1/(32-(1/4))+...+1/(n2-(1/4)) . Simply this expression, and show that n is large Sn is approximately equal to 2.

Tim Chambers
Everyone knows why they entered the actuarial field. The allure of what success as an actuary can bring - money, status, power - is a powerful attraction in anyone's book.

Peter Brown
Given a circle x2+y2=p , centre (0,0) radius √p , does the circle always pass through points whose co-ordinates are rational numbers?

George Szekeres
Mathematics is generally regarded as one of the few disciplines (some would say the only discipline) which is built on rock-solid foundations.

Senior Division
First Prize: \$150 and a Certificate
Le Strange, Elizabeth Teresa Sydney Church of England Girls Grammar School

The new teacher's age is an odd number which leaves the remainder 1 when divided by 3, and the remainder 9 when divided by 11. How old is the teacher?

Q.805 Solve for x and y :
√(x+y)+√(x-y)=5√(x2-y2)
2/√(x+y)-1/√(x-y)=1

Q.793 The vertices of a regular tetrahedron lie on a sphere of radius R , and its faces are tangential to a sphere of radius, r . Calculate R/r .

Michael Cowling
The subject of this paper is the mathematical theory of catastrophes. A catastrophe is a disaster. But there is, implicit in the word, the idea of a sudden change for the worse.

David Angell
We all know and have used the approximation π≃22/7. It may have occurred to you to ask why this is a worthwhile value.

Simon Prokhovnik
The geometrical proposition, named after the Greek mathematician and philosopher, Pythagoras, (~ 570-550 BC), deals with a unique property of right-angled triangles.

Q.817 Find all integers x,y such that
x(3y−5)=y2+1 .

Q.805 Solve for x and y :
√(x+y)+√(x−y)=5√(x2−y2)
2/√(x+y)-1/√(x-y)