Volume 57
, Issue 3

2021

Dear Readers, welcome to this issue of Parabola; please enjoy!

I thought I would share with you a few facts about squares - some well known, and others perhaps not so well known.

A gem for teaching probability to STEM students is the game of Egg Russian Roulette. The first person who has cracked two raw eggs on their head loses the game.

What is the greatest product of $n$ numbers with some fixed sum?
What is the least sum of $n$ numbers with some fixed product?
These questions are answered, and applications are given.

In this note, we determine the curve that is the set of points all of which are the third vertex of all triangles with a given side and a given incircle tangent anywhere to that side.

In this paper it is shown that a Bilinski dodecahedron is an isohedral space-filling tessellating polyhedron, thus bringing the number of these to five.

This article presents a quick and easy method of finding $\pi$ using both the methods of ancient mathematicians and basic calculus.

This paper proves three elegant integer identities by algebraic proofs and by picture proofs.

During the 1910s, A.J. Kempner proved that the harmonic series - which is divergent - became convergent when all terms relating to numbers containing 9 as at least one digit were removed. We seek to do the same thing here but generalize the result to all bases.

Q1664 Let $a,b,c,d$ be four prime numbers for which $5 < a < b < c < d < a + 10$.
Prove that $60$ is a factor of $a + b + c + d$ but $120$ is not.

Problems 1651–1660 are dedicated to the editor of Parabola, Thomas Britz, and his partner Ania, in celebration of the arrival of their twin sons Alexander and Benjamin.

The problems and solutions from the 59th UNSW School Mathematics Competition.

The winners of the 59th UNSW School Mathematics Competition.
Congratulations to you all!