Just for Bruce McAvaney: these numbers are special

This article is very entertaining for anyone who’s a fan of both maths and the Simpsons. It covers a variety of exotic maths identities like perfect and narcissistic numbers, Fermat’s last theorem, Mersenne primes.

Inspired by this, on AFL grand final day, what better way for the New Statsman to celebrate? Than by revealing the AFL’s own long-pondered but never revealed exotic numbers: AFL Products and AFL Powers.

AFL Product numbers exist in pairs, where the score achieved by a combination of goals and behinds is the same as if the goals are multiplied by behinds; AFL Powers exist where the goals raised to the power of the behinds, or vice versa, also yields the score achieved. (For international readers: AFL scoring is explained here.)

AFL Product: 6G + B = G x B

0.0 (0), 0x0 = 0

2.12 (24), 2×12 = 24

3.9 (27), 3×9 = 27

4.8 (32), 4×8 = 32

7.7 (49), 7×7 = 49

AFL Goal Powers: 6G + B = GB

2.4 (16), 24 = 16

AFL Behind Powers: 6G + B = PB

0.1 (1), 10 = 1

2.4 (16), 42 = 16

5.2 (32), 25 = 32

These are the only existing pairs for any score under 300.300 (2100).

The sharp-eyed amongst would have noticed evidence of another interesting maths identity making an appearance: 24 = 42 is the only known instance where xy = yx, x ≠ y, x and y are integers > 0.

Why write this article? Because the Hunters and Collectors are the grand final half time show. Sigh.


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