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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.

Creating expressions/formulae. Generalising. Manipulating algebraic expressions/formulae. Number theory. Visualising. Patterned numbers. Inequality/inequalities. Topology. Dynamical systems. Mathematical reasoning & proof.