Year 2001 - Volume 37
2020 - Present

Professor Szekeres was responsible for starting Parabola in 1964 (before High School students of today were born!)

Professor Ian Sloan is one of Australia’s most accomplished mathematicians. Australian born, Ian completed his schooling in Ballarat in Victoria.

Peter G. Brown
In this article I want to present some simple ideas for obtaining interesting identities related to the binomial co-efficients (n/r) which turn up in the 3-Unit course.

Peter Cooke
In probability theory and in everyday language we use the word ‘random’ and, for many of us, our first encounter with the word would have been in drawing a name at random from a hat.

Q1092. Carl Frederick Gauss, born in Braunschweig in 1777 and who died in Göttingen in 1855, was one of the greatest mathematicians of all time. Assuming that each letter in the following sum represents a different digit find all possible solutions for A,C,G,L,R,S and U .

Q1082 There are 25 people sitting around a table and they are playing a game with a deck of 50 cards. Each of the numbers 1,2,…,25 is written on two of the cards.

Rob Womersley
The Travelling Salesman Problem (TSP) is to find a tour of n cities which minimizes the total cost of the tour.

George Szekeres
Amongst all closed curves with given length (or perimeter) L , which one encloses the largest area?

Jim Franklin
John Blatt was born in Vienna in 1921, into an intellectual and musical family characteristic of interwar Jewish Vienna. His father was a well-to-do physician. The family fled the Nazis in 1938 and settled in the U.S.

Travelling from Goulburn to Canberra at a uniform speed I noticed a distance marker showing a two-digit distance from Goulburn. Thirty minutes later another marker showed a distance with the previous two digits reversed, and another thirty minutes later another marker with the original two digits separated by a 0.

Q1098. Consider the 2000 -digit number which begins with 1000 4 ’s, next has 999 8 ’s and ends in a 9 . Find its square root.

Q1092. Carl Frederick Gauss, born in Braunschweig in 1777 and who died in Göttingen in 1855, was one of the greatest mathematicians of all time. Assuming that each letter in the following sum represents a different digit find all possible solutions for A,C,G,L,R,S and U .

Bruce Henry
I drive about an hour each way to work each day through heavy commuter traffic. Some days I can do the trip in under forty minutes whereas on other days it may be closer to two hours.

John D. Steele
Everyone reading this article will be familiar with calculators. One of the problems we face using them is that they have a limited precision: usually 8 digits, sometimes 10 .

Anand Kumar
In this paper we note the following property shared by all positive integers.

Anne Thomas
Henri Poincaré was born in 1854 in Nancy, France. At school he was one of the top students in every subject, and his mathematics teacher described him as a “monster of mathematics”.

Two of our readers have made comments about some matters in earlier issues of Parabola.

Q1105. A hollow square is an arrangement of dots in a square with a central square left blank. For example here are thirty two dots arranged in a hollow square.

Q1098. Consider the 2000 -digit number which begins with 1000 4 ’s, next has 999 8 ’s and ends in a 9 . Find its square root.

PRIZEWINNERS – SENIOR DIVISION
FIRST PRIZE
Maiyuran Perumynar Arumugam James Ruse Agricultural High School