*This post was part of the Chalkdust 2016 Advent Calendar.*

Welcome to the 22nd day of the 2016 Chalkdust Advent Calendar. Today we have for you, a book review!

Christmas, a time of celebration, joy and meeting family you never knew you had. Regardless of how joyous Christmas can be it also is undoubtedly stressful for some. What present could I get person $x$? Why does my Christmas tree look so ugly even though I spent 2 weeks decorating it? The simple answer is because you probably drenched it in tinsel and epileptic seizure inducing lights. The mathematical answer?

“The Indisputable Existence of Santa Claus” is a recent release by Dr Hannah Fry and Dr Thomas Oléron Evans, Dr Hannah Fry who has previously written “The Mathematics of Love”. This book arranges itself as a step-by-step guide on how to prepare for the (mathematically) perfect Christmas, covering every detail from how to wrap presents according to their surface area to volume ratio, to using Markov chains as a means of perfecting the Queen’s speech.

We shall start with the big question of whether Father Christmas himself actually exists. The first chapter gives a ‘seemingly’ valid proof of Santa’s existence, from another ‘seemingly’ valid proof of how 1+1=0. You must be thinking, what? Obviously there must be a flaw in the progression of the proof somewhere, which there is, but you can discover it for yourself by reading the book.

Moving on, let’s have a look at the inconspicuous game of Secret Santa. For those unfamiliar with the concept, the classic approach to this game is simply, you write your name on a small piece of paper, fold it up and throw it into a hat. After a bit of shaking, someone picks out a piece and takes on the enormous responsibility of finding their victim, **coughs** I mean colleague, a present usually around the price range of £5. So why is this a rather inadequate way of organising this game?

Well first, you risk the chance of picking out your own name. You might think that’s easy enough a problem to solve, just put it back in the hat…But what if you were the last person? Or even the second last person? Everybody knows your name is back in the hat, and they have a greater chance of picking your name, and in some case, 2 people will have each other’s name, Secret Santa is ruined. Goodnight. The book proposes another method of making sure that no one has their own name, and no one else knows who has their name. A clever yet simple solution involving derangements, alas, Christmas is saved, now let’s hope your secret Santa isn’t a Scrooge.

My favourite chapter in this book has to be the one on the Queen’s Speech. The beginning of the chapter is an analysis of the Queen’s vocabulary score (based solely on the number of unique words in the first 35K words of her speech. Surprisingly, poor old Lizzy scored lower than her counterparts Jay-Z and Shakespeare. Well, it seems as though maths might be able to give her a hand with that, with something special called a Markov chain, that determines the next word to place in a sentence given the word before. I won’t go into too much detail as to give it away; it just so happens that earlier this week I was reading about how Markov chains are used in determining the probability of flipping a coin and getting a certain outcome which is equivalent to another outcome, so this chapter peaked my interest even further.

What is particularly good about this book is how accessible it is; at the end of every chapter there are endnotes that explain some of the maths mentioned and includes some extra reading material. The only questionable thing in this book might be the chapter about cooking turkey. They used a chicken instead. Enough said.

Overall, a great read, not too technical but with just enough maths to get you thinking. So even if your grumpy aunt Hilda despises anything to do with maths, there’s now a very slight chance she might enjoy it.

Also the amount of cracker pulling rules I’ve never heard of is remarkable. I am now going to stop pulling both ends of my own cracker, despite my competitive nature.