Year 2019 - Volume 55
2020 - Present

Thomas Britz

Dear Readers, welcome to this year's first issue of Parabola!
In it, I am excited to bring you interesting and excellent articles, problems, and comics.

Trevor Tao

Are players of popular online games like Spider Solitaire justified in suspecting that some games are rigged? This article shows that random walks can be used to settle accusations of bias.

Martina Štěpánová

This article presents Adams' Circle, a 176-year old but yet little-known circle closely related to any triangle, and further presents new and beautiful geometrical research.

Anthony Wang

This article describes how to count the number of paths across an obstructed grid. It turns out that this number of paths is fundamentally connected to the Inclusion-Exclusion Principle and Pascal's Triangle.

Robert Schneider

An odd comic about even numbers.

David Angell

Q1583 Coins are placed in an n×n array, alternately heads up and tails up. At each move, you are allowed to turn over all coins that form one connected region. How can you get all the coins heads up in the minimum possible number of moves?

David Angell

Q1571 Find positive integers a,b,c such that a≤b≤c and 1a+1ab+1abc=526.

Thomas Britz

Dear Readers, welcome to this issue of Parabola!
In it, I am excited to bring you interesting articles, addictive problems, and pretty punny comics.

Johnny Wong

Living with others, you might sometimes have to wait to use the bathroom. The fewer bathrooms or more people, the longer you'd have to wait. But can we mathematically calculate how long we can expect to wait every day? One approach is to use so-called Markov chains.

Marius-F. Danca, Guanrong Chen, and Nikolay Kuznetsov

The problem of the aircraft squadron is that of determining how far some aircraft from a squadron can fly if the aircraft are able to share fuel, and which fuel-sharing strategy might work best?

Bodhideep Joardar

Ancient Babylonians used Pythagorean triples to conduct real-life calculations but, although that was nearly 4000 years ago, these triples have not been greatly studied.

Robert Schneider, Michael Klipper and Mike Chapman

Laugh and wince at these punny comics.

David Angell

Q1591 For f(x)=x4+2x3−7x2+11 , find a line which is tangent to the graph y=f(x) twice.

David Angell

Q1583 Coins are placed in an array, alternately heads up and tails up. At each move, you are allowed to turn over all coins that form one connected region. How can you get all the coins heads up in the minimum possible number of moves?

Thomas Britz

The focus of this issue is the interplay between fun games and serious maths. Accordingly, this issue offers twice the number of fun and challenging problems for you to solve.

Trevor Tao

This is a simple introduction to dynamic programming, by way of a mathematical analysis of the game Connect Four.

Heidi Olsen

Monopoly® is a common household game where players attempt to bankrupt an opponent by buying properties, gaining profits, and taking control of the game board. Which properties give the best winning strategies?

Rishabh Poddar

A magician asks you to think of a number and then to perform some arithmetic operations on it. As if by magic, the magician then tells you which number you have calculated. This article provides variations of this magic trick and thereby provides an intuitive introduction to number theory.

Mike Chapman and Robert Schneider

A fresh comic for your amusement!

David Angell

Q1605 Calculate the constant term when the expression (1+x+1/x)10 is expanded and like terms collected.

David Angell

Q1591 For f(x)=x4+2x3−7x2+11 , find a line which is tangent to the graph y = f(x) twice.

Denis Potapov

The problems and solutions from the 58th UNSW School Mathematics Competition.

Denis Potapov

The winners of the 58th UNSW School Mathematics Competition. Congratulations to you all!