The Number Devil~ Introductory on "Vroooom!"

Greetings fellow pupils!

As you may or may not know already, I am the Octopi, an aspiring mathematician. This blog is mainly to enlighten audiences with simple mathematical concepts that can be easy to comprehend. As an introductory to my posts, I will expose you to a fun, child-friendly book that is (surprisingly…) based on mathematics!

Meet the Number Devil:

As a young octopus, I came across this book when my older sibling had advised me to read this book, and I was highly likely to learn a thing or two about math along the way. I’ve re-read it over the years, and the way the author (Hans Magnus Enzenburger) portrays commonly boring topics, such as factorials, Fibonacci numbers, exponentiation, and permutation.

(Not to spoil anything) This book is primarily based on a young boy, Robert, who is being increasingly bored about mathematics in school, leading to anxiety. He experiences recurring dreams until he meets a devil-like creature in his dreams, called the Number Devil. During his sleep, the Number Devil educates him about various mathematical principles centered on numbers, and eventually gets Robert more and more interested into mathematics.

Boring, hey?

Just kidding. Imagine having a mentor that could visit you during the life and teach you some of some amazing adventures!

1! 2! 3!

4! 5!

6!

…

Ah. You might be wondering why I’ve been shouting consecutive natural numbers in exclamation, but the typically used exclamation mark is also representing the factorial (!) sign.

For example, 4! = 4 * 3 * 2 * 1. (NOTE: “*” means Multiplication)

Or, as expressed by a variable, x! = x * (x-1) * (x-2) * (x-3)…*1

Let’s just go over some simple factorials, starting from 1.

1! = 1

2! = 2

3! = 6

4! = 24

5! = 120

6! = 720

…

How did the result of these factorials move from 1, all the way to 720? This concept of how quickly the factorials accelerated were called “Vroom!” by the Number Devil. It has given children a simple way to remember the overall concept of these factorials by the sound of a vehicle.

Of course, factorials aren’t JUST the sound of a car racing down the road: in fact, probability problems can be commonly solved by factorials, in a situation called permutation. What is it, you may ask?

Here’s a simple mathematics problem: If you were given 3 oranges and picked two at random to eat later, how many combinations would you have (assuming order does NOT count)?

…

…..

…

Get it yet?

Simply, your answer should be 3. For questions like these, many people find a diagram incredibly helpful.

Okay. NOW let’s say you were given 15 oranges and you could pick 10 at random.

So, I have included several samples. The grey triangles also represent a possible combination of 10 oranges, but there’s much too many to portray with a couple of markers. It’s also incredibly tricking listing each method, because the number of oranges you’re choosing is so large. It’s hard to keep track of all these combos by just a few lines.

This is permutation. For larger probability questions such as these, using the “Choose” formula can get your answer within half a minute (provided you have a calculator for the final step).

This Choose formula is denoted by nCx, where n is the total number of items, and x is the number of items you wish to take out of the set of items.

The formula is:

nCx= n! / x! * (n-x)!

Or, using the example above:

15C10= 15! / 10! * (15-10)!

You may think this made the situation quite a little harder, but using a simple crossing out method the result will simplify it to a quite small multiplication statement:

So, there are a total of 3003 possibilities, which is quite a considerably large number, and would’ve taken a lot of time to reach that answer by counting each individual way.

There are many other applications of factorials in the mathematical world, such as factors in algebra and calculus.

This is all I shall explain today. Be sure to read the Number Devil sometime, and find out the Number Devil’s actual name… without using Wikipedia.

~The Octopi