The only non-trivial normal magic hexagon

3:42 pm PHT

If you arrange the natural numbers starting with 1 onto a hexagonal grid such that they fill in a hexagonal-shaped array of hexagons, there is only one non-trivial normal magic hexagon—that is, all of the numbers in every hexagonal row for all three directions sum up to the same number. This unique magic hexagon is shown above and the magic sum is 38. It has been proven in 1963 that this is the only normal magic hexagon (aside from the trivial solution of only 1 hexagon).

There are other “abnormal” magic hexagons of various sizes where the successive numbers don’t start with 1, but the one shown is the only normal one. Magic hexagons have only been studied relatively recently by mathematicians especially when compared with the vastly more popular magic squares which are known since ancient times.

That bit of mathematical trivia above is simply an elaborate way to state that I am now 38 years old. I always like to think that this is not really my real age of existence because I existed from the moment of conception. (So I have existed for 38 years and around 8+ months.) But 38 years is certainly the age of my existence as a completely separate person.

I used to have this habit of blogging on or around my birthday and I have done so for the first six years of this blog. See the posts for my 24th, 25th, 26th, 27th, 28th, and 29th birthday, most of which state some interesting mathematical trivia related to the age. I decided to restart this habit again after a long hiatus because, why not? I looked at the various mathematical properties related to the number 38 and this magic hexagon was the most interesting for me.

Anyway, aside from this little bit of blogging, I’d like to repeat what I wrote 11 years ago because it is true today as it was back then:

I’ve always thought that it’s just an ordinary day like any other. Well-wishing is always appreciated and merriment is part of the package. It’s not that I’m a prude or a killjoy, but my practical and usually unemotional mind does not attach any sort of momentousness (or portent) that many other people feel when their own annual commemoration comes.

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