Author Archives: apgoucher

Hunter Spink gave me an interesting problem about a beach ball inscribed in a wire tetrahedron, since its most elegant solution uses techniques explored in the tenth chapter of Mathematical Olympiad Dark Arts. Rather than give you the problem now, … Continue reading →

Alexander Betts (nee Luke) posed an interesting problem in combinatorial geometry for the Romanian Masters of Mathematics 2011: We have a finite set S of n points in the plane, {A1, A2, …, An}, such that (for all i and j) the … Continue reading →

It’s Guy Fawkes Night now and I’ve had to update the seasonal banner yet again. There are a few late items of news I would like to mention: Firstly, thanks go to everyone who has sent me feedback regarding MODA; I have … Continue reading →

The P versus NP conjecture essentially asks whether any problem whose solution can be easily verified can also be easily solved. Here, ‘easily’ technically means ‘computed in polynomial time on a Turing machine’. If you think for a moment, it … Continue reading →

Feeling that Complex Projective 4-Space isn’t sufficiently seasonal, I was compelled to alter the colour scheme of the banner to reflect the fact that today, the 31st October, is All Hallows’ Eve, popularly abbreviated to Hallowe’en. Anyway, I actually prefer … Continue reading →

Quite a lot of interest originated from the following puzzle of unknown origin: Given two pieces of rope which burn in precisely 1 minute, time an interval of 45 seconds (3/4 minutes). The rope is not necessarily uniform, so you’re … Continue reading →

We’re quickly approaching Ebenezer Scrooge’s favourite time of the year, Greenwich Mean Time. This brief post serves as a reminder to anyone who has forgotten about the temporal adjustment due to spending too little time in real Euclidean 3-space. Of course, if … Continue reading →

We’ll begin with an intriguing set of three interlinked rings, the Borromean rings. They can’t be realised as solid circular tori, but ellipses work just fine. Here is a visualisation: If you remove any one of the three rings, the … Continue reading →