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The fantastic pencil of Sir Alex Ferguson.


Year 2030 AD. 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?

Go to the second half to discover the solution


Let`s see the system Alex Ferguson follows:

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

13 - 03 - 15 - 20 - 08 - 10 - 11 - 06 - 12 - 07 - 09

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.:

0.1303152008101106120709 · 10 = 1.303152008101106120709

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:

2.015031410070409111224 / 10 = 0.2015031410070409111224

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

20 - 15 - 03 - 14 - 10 - 07 - 04 - 09 - 11 - 12 - 24

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:

A=01, B=02, C=03, D=04...

get its correspondent code:

'Lorem ipsum lxo ftisa er...' => A=01, B=02, C=03... => 0.1215204564121641321376873412....

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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