Year 1974- Volume 10
2020 - Present

K. Wilkins

As you know, a prime number is any positive integer, other than 1, which has exactly two distinct factors (itself and 1). Thus the set of primes starts 2,3,5,7,11,…,

P. Diacono

Contributed by P. Diacono of St. Joseph's College

S. D. Saunders

Many of the articles in Parabola pose problems which invite the reader to invent original solutions. But, in the absence of a helpful hint, how does one set about arriving at such a solution?

In Problem O230 I noticed that those positions where the second player can force a wing are all Fibonacci numbers.

K. Wilkins

Selected for this issue are two 2-player games.

"An Introduction to Computer Programming" by Training and Personnel

J231 A man goes to an auction with $100 and buys exactly 100 animals. J221 Find a 2-digit number $AB$ $AB$ such that $\left(AB{\right)}^{2}-\left(BA{\right)}^{2}$ $(AB)^2 - (BA)^2$ is a perfect square. At some stage of our school life, most of us would have sent or received coded messages from our classmates. General mathematical principle: To investigate a complicated situation apply simplifying transformations, investigate the simplified situation, and try to transfer this information back to the original situation. I have been doing some work on the n'th prime number, but was impeded for some time because of the lack of prime numbers. W. Moore This game is a contest between two gladiators in an arena consisting of a 20 × 20 grid. Determine all ordered triples $\left(a,b,c\right)$ $(a,b,c)$ of natural numbers, $a\ge b\ge c$ $a\geq b\geq c$, such that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$ Prove that you have found all solutions "Excursions in Geometry" by C.S. Ogilvy J241 By inserting brackets in $1÷2÷3÷4÷5÷6÷7÷8÷9,$ the value of the expression can be made equal to $7/10$$7/10$. How? J231 A man goes to an auction with$100 and buys exactly 100 animals.

W. Moore

Anybody who knows where he is going is happy, unhappy people wander aimlessly in circles.

P. Diacono

Contributed by P. Diacono of St. Joseph's College.

Mark Durie

This note reports on some work which arose out of a discussion of unit or Egyptian fractions.

J. Mack

It is a matter of observation that paint tins are depressingly similar - they are all right circular cylinders of finite height.

Recently I've bought a tiny calculator and discovered the following ways of doing rapid calculations:

W. Moore

The game of three dimensional noughts and crosses is played on four layers of 4×4 grids, as shown in Figure A.

For the first time ever, in this division, the first prize winner, Alan Fekete, solved every part of every question correctly.

"Tricks Games and Puzzles with Matches" by Maxey Brooks

J251 Framer Jones grew a square number of cabbages last year. This year he grew 41 more cabbages than last year and still grew a square number of cabbages.  How many did he grow this year?

J241 By inserting brackets in

$1÷2÷3÷4÷5÷6÷7÷8÷9,$

the value of the expression can be made equal to $7/10$$7/10$. How?