I was just amazed by this article when I first read it.
The question that leads into the article just felt unrealistic and, if it was possible to answer it seemed like the maths would be so difficult:
"How many high points, low points and passes are there on the island of Crete? I don't know...but I know a formula which, given the no. of high and low points, tells me the number of passes."
How wrong could I have been.
The article is readable, accessible and so clever. Such simple ideas can lead to a result that seems too "real world" to be possible.
I struggled a bit with some of the visualising but it was worth it.
I recommend it as a good read and, like many very clever ideas, the maths is simple and incidently makes some sense of maxima and minima if you are interested...
Thank you Tom for a really good read!