Year 1983 - Volume 19

Issue 3

John Loxton

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

Read the article in PDF

Peter Petocz

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

Read the article in PDF

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

Read the article in PDF

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.
 

Read the article in PDF

Q.551 Solve the system of equations
 

u 2 + v 2 + w 2 = 49 1 u + 1 v + 1 w = 0 u v + w = 1

 

 

 

Read the article in PDF

 

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

 

Read the article in PDF

John Price and Matthew Price

The game Scissors, Paper and Rock (SPR) has a long history. One famous contest took place in the pages of You Only Live Twice by Ian Fleming and resulted in our hero James Bond defeating the inscrutable Tiger Tanka.
 

Read the article in PDF

A while ago we received a short article from one of our readers, Tim Bedding about some features of this celebrated ratio.
 

Read the article in PDF

6 positive whole numbers  A , B , C , D , E   and F  satisfy  A + B = 29 , C + D = 45 , E + F = 65 , A C = 36 , B E = 312 . Find A , B , C , D , E  and  F . Show there is only one solution to the equations.
 

Read the article in PDF

This term we will contentrate on complex numbers, and solve problems from the 1981 and 1982 4-unit papers.
 

Read the article in PDF

Q.563 In the figure,  X  and  Y  are the centres of the circular arcs  A B  and  A C  respectively, and  A  is the centre of the circular arc  B C .
 

Read the article in PDF

Q.539 From the set of whole numbers  { 0 , 1 , 2 , , 999999999 }  two are selected at random. What is the probability that they differ by a multiple of 10000?
 

Read the article in PDF

John Loxton

According to Francis Bacon, perfect ciphers may be recognised by the following virtues: "that they be not laborious to write and read; that they be impossible to decipher; and, in some cases, that they be without suspicion."
 

Read the article in PDF

In 1981 and 1982 there were some 4 unit questions on the conical pendulum.
 

Read the article in PDF

Geoff Ball

The 1983 International Mathematical Olympiad was held in Paris in July.
 

Read the article in PDF

In the Junior Section of the competition there were three questions which were fairly easy, two rather difficult, and one impossibly so.
 

Read the article in PDF

Scot McPhie of Kings School Paramatta, has written asking for help in writing a programme for the Apple computer.
 

Read the article in PDF

Alex Reichel

There is much interest in the origins of science, with a view to understanding the creative process of the human mind.
 

Read the article in PDF

Q.576 The game of Yellow Pigs is a favorite pastime at Hampshire College's Summer Science Training Program.
 

Read the article in PDF

Q.551 Solve the system of equations
 

u 2 + v 2 + w 2 = 49 1 u + 1 v + 1 w = 0 u v + w = 1

 

Read the article in PDF