Get reading! There’s no time to waste. At 225 million years per rotation, the sun will only orbit the Milky Way another 22 times before it runs out of fuel. Did someone say 22? Let’s go…

## That’s a fact(orial)!

The term ‘factorial’ describes a mathematical operation where we multiply a number by all the whole numbers less than it, right down to 1.

So 3! = 3 x 2 x 1 = 6, 5! = 5 x 4 x 3 x 2 x 1 = 120 and so on.

Factorials arise most often in 'combinatorics' or the mathematics of counting and combinations. For example, how many ways can we arrange the letters ABC in order?

Well, there are 3 possible first letters. Once you’ve chosen a first letter there are two that can fill the second space. And once you’ve chose the first two letters of a “word” there is only one possible last letter.

So the 3 letters A, B and C can be arranged 3 x 2 x 1 = 3! = 6 ways. They are ABC, ACB, BAC, BCA, CAB and CBA.

The factorials get very large, very quickly.

In fact: 22! = 1,124,000,727,777,607,680,000 - which you will also notice has exactly 22 digits!!!

## The whole 22 yards and the birth of The Ashes

A cricket pitch is 22 yards long – but must have felt a lot shorter when Australian fast bowler Fred ‘The Demon’ Spofforth had a head of steam up.

The Demon was one of the first-ever tearaway quicks in world cricket and in 1882 at the Oval in England, he pretty much singlehandedly routed the home team from a seemingly unlosable position.

Needing 84 to win, England were cruising at 4-66 but then lost their last 6 wickets for 11 runs. Spofforth took 14 wickets for the match.

Afterwards, to commemorate the death of English cricket, the bails were burnt and interred in an urn and one of sport’s greatest rivalries, The Ashes, was born.

I mention this both because this is newsletter 22, and to remind everyone that Australia retained the Ashes last year … and Jonny Bairstow was absolutely, 100%, dead set, inarguably run out.

## Fascinating fast facts about 22!

As easy as 355

Many of you would remember the fraction 22/7 used as an approximation for π in high school mathematics (it’s accurate to within one part per 2500). But if you really want to impress your friends, next time the fractional approximation of π comes up in conversation, use 355/113. It is accurate to within one part per million!

The mathematics of Elvis

In the 1968 American musical action film Speedway, Elvis Presley plays Steve Grayson and drives car 7 up against Bill Bixby (Kenny Donford) in number 22. I get excited apart from the cars careening into ditches and powerpoles, because their numbers 22 and 7 alongside each other look exactly like 22/7 - Pi!!!

Alef-bet

The Hebrew alphabet contains 22 letters – Alef, Bet, Gimel, Dalet, Heh, Vav, Zayin, Khet, Tet, Yud, Kaf, Lamed, Mem, Nun, Samekh, Ayin, Peh, Tzadi(k), Qof, Resh, Shin, Tav.

There are only consonants, no vowels. Hebrew writing is read from right to left and the collection of letters is often called the alef-bet after its first two letters.

## Pentagonal numbers

In my last newsletter, we saw that 21 was a ‘triangular’ number. Well, after triangular numbers we have the ‘square’ numbers 1, 4, 9, 16…

And, after the squares, come the ‘pentagonal’ numbers, from the 5-sided figure the ‘pentagon’. The idea is the same: we keep expanding by putting another pentagon on the outside. The pentagonal numbers are the total number of points in each of the diagrams.

The diagram below shows us that the first 4 pentagonal numbers are 1, 5, 12, 22 and 35.

## TRIVIA: Win an Adam Spencer maths book!

While perusing the amazing puzzles at plus.maths.org one day, I came across this little beauty which ‘Marianne’ posted back on 1 September 2016.

There are 19 dots arranged in a hexagon, as shown in the below diagram. Your task is to label the dots with the numbers 1 to 19 so that each set of the 3 dots that lie along a triangle’s side add up to 22.

There are 4 solutions, and instead of submitting your answer as a complicated diagram, simply email me with the number you got in the middle for one solution or all four.

I’ll send a signed copy of one of my books to a couple of people who crack this (winners will be randomly drawn). Answers by Friday 15th March, 5pm AEDT please!

As Marianne herself said ... happy puzzling :)

Previous winner: In number 21 I asked, of all things, for your best 6000 calorie menu (trust me it made sense at the time!). Congratulations to Jane Whitelaw, who suggested she could power herself for a day of the Tour de France by chowing down on exactly 77 snails in garlic butter. French, easy to consume at pace, and highly calorific. Great stuff Jane. Your book prize is in the mail!

That’s all from me for now. If you'd like more geeky fun, please check out my other newsletters below, or connect with me on LinkedIn and X.

Yours in numbers,

Adam

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