Year 2000 - Volume 36
2020 - Present

Frank Reid

Several years ago, a friend of mine in Germany sent me a German 10-mark banknote. It was unusual in that it featured the image and the work of a mathematician.

There is a simple approximate rule of thumb used by investors and accountants to estimate the time taken in years, n; for an investment to double with an interest rate of R; or indeed for a debt to double if left unpaid. One simply divides 72 by R to estimate the time in years.

Peter Brown

Fairly early in your study of algebra, you meet one of the most useful of algebraic techniques, the difference of two squares which enables you to write, for example x2−1=(x−1)(x+1).

Q1064. The numbers 1,2,…,16 are placed in the cells of a 4×4 table as shown in the left hand diagram below. One may add 1 to all numbers of any row or subtract 1 from all numbers of any column.

Q1057 Remember that a regular polygon has all sides equal and all angles equal.

Frank Reid

In the previous issue of Parabola I discussed the derivation of the normal distribution of measurement errors by the famous German mathematician Carl Friedrich Gauss in 1809. Gauss and the Normal Curve were featured on the front side a German banknote several years ago.

Will Smith

When people buy a home they usually have to borrow an appreciable fraction of its value from a bank or other financial institution.

Rod James
Htsi si na raitlcf ero aparobal no oht wb oerka oceds.
In the previous issue of ParabolaI am sure that, like me, your immediate reaction to the above sentence was to try to “decipher” the message

Problem 1. You have a huge pile of 1¢, 2¢, 5¢, 10¢, 20¢, 50¢ and $1 coins. Some number of coins, N say, total X ¢ . Show that you can make up$N using X coins.

Q1072. Is it possible to fill the empty circles in the diagram below with the integers 0,1,…,9 so that the sum of the numbers at the vertices of each shaded triangle is the same?

Q1064. The numbers 1,2,…,16 are placed in the cells of a 4×4 table as shown in the left hand diagram below.

Terry Tao

This will be an article about the mathematics of algorithms. An algorithm is a set of rules and instructions used to solve a real-life problem. Often this algorithm will then be run on a computer.

Jaclyn Brown and Bruce Henry

One of the focal points of the recent Sydney 2000 Olympic Games was the medal tally. We all want to know which country ‘won’ the Olympics or which country has the best athletes.

Rod James

In the previous issue of Parabola we saw how to encode (and also how to break!) monoalphabetic ciphers (i.e. we replace each letter of the alphabet by some other letter every time it occurs in the message). We now look at some more complex codes.

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.

Q1072. Is it possible to fill the empty circles in the diagram below with the integers 0,1,…,9 so that the sum of the numbers at the vertices of each shaded triangle is the same?

PRIZEWINNERS – SENIOR DIVISION
First Prize

Thomas Xia James Ruse Agricultural High Schoo