Volume 36


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.

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.

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 $1, 2,\ldots , 25$ is written on two of the cards.

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


First Prize
Thomas Xia                James Ruse Agricultural High School