FIRST HALF

Year . **Sir Alex Ferguson** is still the **coach** of **Manchester United**.

In **full possession** of his football **faculties**, he has won for last three Premier Leagues for the **Manchester United**. However, his **memory** is no longer what it was. And this is the problem.

Faithful servant of his tradition, he still **decides** the **line-up** for the next match, after the end of the **last training** the day before. But given the limitations of their **memory**, **Sir Alex** started **noting** it down in a **notebook** he kept in his office at **Old Trafford**. However, he began to notice that someone was **spying** this book, and that his rivals knew in advance the **starting line-up** of **Manchester United** and took advantage of it.

He therefore decided to **change** the system, and write the line-up on his **computer**. But the same thing happened again, someone managed to get into his computer and **steal** data.

But one day he decided to make **a very precise mark in a pencil** (still in production in 2030) of his office, and he **never** had **problems** again with that.

Can you imagine how a simple mark could make him remember the lineup?

Let`s see the system **Alex Ferguson** follows:

At first, he lists the **shirt numbers** of the players who will play:

Then, he forms with the **decimal part** of the number below:

Afterwards he obtains a number, multiplying it by the **pencil length**, in this case **10 cm.**:

And just at that **point of the pencil**, in the **cm. 1.303152008101106120709**, he practices an **incision**.

Obviously, he did not it **manually** (his **eyesight** was not up to that sort of thing any more), but with a small **'i-ncisor'** **device** created in the 20's. This device also allowed him to **read** the following day the **exact point** of the pencil where the **cut** had been practiced.

So, if the incision was made in the **cm. 2.015031410070409111224**, we can **obtain** from it the lineup as follows: we divide the number by the length of the pencil:

We despise the integer (zero), and take the decimal part two by two numbers:

And so we have the lineup.

This **i-ncisor** can record not only the lineup of a team, but also write a whole **library**. You just have to **encode** any text or book you want:

get its correspondent **code**:

and then move the number to any support with an i-ncisor accurate enough.

This system would allow us to **save** any phrase, any writing, any newspaper, or **any text, image or video** you can think by coding and marking it in a simple pencil.

This problem is linked to the **Chapernowne constant**. This is a number formed by the concatenation of all the natural numbers, ordered as follows:

This number contains each and **every** one of the existing **natural numbers**.

For example, sooner or later we'll find the number **4985045:**

... or any other number that comes to mind.

And we will find the coded sequence of the last issue of our favorite **newspaper**:

We can also find the coding of **tomorrow's newspaper**, or the newspaper that tells the end of the last **club world cup**. And there is another coding with a newspaper exactly like last one, but in which our **favourite club** was the winner. And another in which also **you** were the player who scored the **goal** that gave the **victory** to your team.

And moreover, we can also find the sequence of the encoded **photo** in which **you're scoring the goal** that gave your country the World Cup Championship ... And **anything else** you can **imagine**, everything has a place in this single number, since all the numbers are contained in it.

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