You know, even as a child, I rather liked Rumplestiltskin! It was such an exciting thing to listen how the fairy was dancing in front of the fire in the dark wood – and how it sang “Lucky me that no one knows that my name is Rumplestiltskin”. In fact, it was so exciting that I really cannot find words to describe it…

Yes, and then, a few sentences later, when the fairy self-exploded in front of the princess later in the story – that was just great! What a consistency and courage – to just self-explode! I never forgot this impressive image!

But here comes the moment of truth! This unappetizing “Rumplestiltskin Affair”. I am sure you, too read about it in the media: it is about an affair between the European upper nobility and a German Mr. Müller!

The kings and the Müllers are said to have behaved quite evilly and a lot of money was allegedly involved!

European money – of course!

To be precise, said Müller – i.e. a certain ’Soy-Bean Müller’ – who has the world leader soy bean mail-order house in his backhand, is said to have tried to make gold out of straw together with an extremely respectable European dynasty!

Mind you, this was regardless of the fact that he, Müller, does not even own straw. He only owns ’soy bean cake’. That is basically just the waste from soy flour production – but no straw!

However, for straw, the European Commission would have granted considerable subsidies from its agrarian fond. But not for cake, i.e. ’soy cake’!

Naturally, this was not good news for the soy flour mail-order house and its stock. In fact, it was actually a catastrophe. After all, stock, too, is just human, i.e. there are persons hidden behind the stock.

Persons with all their strengths and weaknesses. Just like with Müller’s small daughter Annegret who had always had a certain weakness for everything that smelled of royalty.

That is especially true for last year’s ’Vienna Opera Ball’, where she danced left-waltz with an extremely sweet young king. Left-waltz until she was dizzy and sank into the blue-blooded arms of the young king.

Due to the low stock-exchange rate, those same arms need much persuasion before they led her to the marriage altar. It did not come as a surprise that not only the love of these two doves immediately grew, but also the stock exchange rate of the ’soy flour mail-order house’. Did they grow, or what?

Consequently, it took only a few days until this activity caused a grumbling in the world of the financially potent oligarchs and a so-called ’Rumplestiltzkin ’ appeared. Nobody knew who it was and where it came from and what its name really was.

But being an industrious person, said ’Rumplestiltzkin’ had no problem getting the delegates of Romania, Bulgaria and of the newly wed kingdom to vote in her favour at the European Commission. Consequently, a majority supported the concept that ’soy-cakes’ are to be declared straw in the future and thus they are gold-coated with EU money!

It is unbelievable what Rumplestiltzkin can do and it is certainly a good thing that nobody knows its real name…

The news that the Austrian rum producer ’Straw’, too, allegedly was part of the deal in that he is said to have delivered a considerable amount of 85% ’Straw-Rum’ to the president of the European Council Junker and thus also acted in the role of Rumplestiltzkin is only one of those fake news from Russia. After all, we all know that Russia constantly aims at destabilizing the European Union!

Which, under Putin, does not come as a surprise to anybody!

The same applies to the news that the newly married ’soy flour queen’ was now allegedly impregnated by this suddenly appearing Rumplestiltzkin – rather than by the European High Nobility?

What additional shameless defamation! Those lousy Russian hackers were not even kind enough to give credit to her handsome Pilates coach in their disinformation campaign against the young queen. It is truly something that could give you offspring!

Which is exactly what happened.

But this evil pregnancy defamation is at least a good explanation for Rumplestiltzkin by all means wanting to get hold of the new-born child of the young queen, isn’t it? Of course, it is because it does not want a paternity test, and it was not at all eager to pay alimony for an entire Rumplestiltzkin life on top of having acted extremely beneficial. This is absolutely clear!

The queen was in a similar situation: she wanted to keep her new-born child without proof of paternity. And she did not hesitate to rub Rumplestiltzkin’s nose into what she wanted via twitter, along with 10 million followers!

Maybe she should not have done that. Being nobility and all! Twittering all the time! Because the Russian secret service read it all and then threatened the allegedly Russian Rumplestiltzkin with filing suit before the European Court of Law for prince robbery …

What is not really believable – and for me personally, this is rather a disappointment – is that this unknown Rumplestiltzkin is said to have angrily self-exploded afterwards. Just like the one in the fairy tale!

And they say it happened right before the blue eyes of the soy-floury queen who did not want to let go of her child. Isn’t it awful? Just self-exploding and ending up in two parts. From top to bottom. Atrocious!

After all, today, after 300 years of cultural evolution, you can do the job far more elegantly by tying an explosive from the internet to your belt!
Such a method would also have been far more media-friendly!

And we all would have certainly been able to download the atrocious event in no time through our smartphones from some video supervision camera or other immediately after Rumplestiltzkin’s self-explosion. In other words: we would all have been there – in fact, all Europe would have been there!

Thee usual stereotypical condemnation of the deed by all the politicians, too, would have been noticed by far more citizens – than this silent, ego-maniac ’Rumplestiltzkin self-exploding’!

Even the IS did not find it worthy of claiming responsibility!

It really is a pity! What a pity that Rumplestiltzkin failed so miserably! Everybody would have benefited from a proper explosion? I mean You, You and You! All of Us! Europe would have been truly united by such an explosion! At long last, what belongs together would have come together. What a pity …

KH
(Translated by EG)

Roland Dürre
Monday April 17th, 2017

Solution

Two weeks ago, I formulated a Logelei I very much like. I also considered it extremely hard to solve. Well, one email I received had the correct answer.

Here is the solution to the problem I gave you on April, 2rd, 2017. I copied the formal part of the solution from the winner: Jörg.
The question was:

How can the criminals make sure that they all survive?

And the solution is surprisingly simple!

Jörg – the winner!

The 10 gangsters have to assign a number between 0 and 9 to every one of them, for instance by counting them down!

As soon as a gangster will see the nine images of all the other nine gangster, he will do the sum of all the numbers on these images and then add “his” number to the sum.

Then he applies the operation modulo 10 to the result and calls the resulting number. Every gangster does this during her or his interview.

This is how you can make sure that exactly one of the gangsters will give the number on his/her picture. The others will, of necessity, say a wrong number – but that is irrelevant, since it will suffice if one of them gives his correct number. That means they all will survive.

Well, as you see, you must never give up hope – once in a while, even mathematics can help.
Here is the formal description of the solution (after Dr. Rothermel).

• Let the number of gangsters be: N
• Let zi be the number assigned to the gangster I (not known to him). It is not necessarily unique and it is part of the set {0, 1, …, N-1} of which a minimum of one needs to be told in the end..
• Let S be the sum of all pre-defined numerals S = Σ zi
The gangsters agree upon the following procedure:
1. Initially, each of them gets a personal, unique number i (known to him/her) assigned to her/his picture from the set {0, 1, …, N-1}.
2. During the interview, every gangster builds the sum of all the numbers he/she can see – that is the (definite) total sum S minus his own (not known to him) numeral zi , i.e. S – zi . That is the only information at his disposal.
3. Since the gangsters are only interested in the numbers in the range {0, 1, …, N-1}, they will modulo N or the congruency relation ≡ N. Now each gangster will calculate an integer x such that:
x ≡ N i – (S – zi ) or
x = ( i – (S – zi )) mod N (I)
With this procedure, exactly one gangster will get his correct zi!

Proof:

S is congruent with a number s from the set {0, 1, …, N-1} or S ≡ N s, consequently, you can also write (I) as:
x ≡ N i – (s – zi )
Since no two N i’s are identical, one of them equal s, consequently, we have for one gangster:
x ≡ N zi.
both x and zi belong to the set {0, 1, …, N-1} which means they are not only congruent, but identical:
y = zi,
and that means this gangster will have the correct number for himself.
(Solution and proof by Dr. Jörg Rothermel)
Now I would recommend that you read the problem  again and ponder it a little bit.

RMD
(Translated by Evelyn)

Roland Dürre
Wednesday April 12th, 2017

Another Logelei!

Since my last Logelei gave many people some joy (and brought others close to desperation), here is another one. However, it is
Basically very simple!

A house owner has a square-shaped patio paved with 64 simple square-shaped tiles (each measuring 30 cm x 30 cm). He wants to put 31 domino stones (he already bought them) over them. They are twice as big as the tiles, that is, their width is twice their length, i.e. 60 cm x 30 cm.

His special desire is that the two opposing corners should be left untouched by the domino stones. He wants cubic tiles with a very special symbol at those corners. He already bought the two of them (just as big as the original ones, i.e. 30 cm x 30 cm). Naturally, for aesthetic reasons, the domino stones cannot be halved.

He assigns the task to a craftsman. The craftsman is happy to do the job and starts his work. He leaves a corner open and starts positioning the domino stones.

Now here are the questions:
Will the craftsman manage to do it?

If yes, how?
or
If not, why not?0

I will publish the solution two weeks from now – and until then, I look forward to many  emails  suggesting a solution!

Here is some help: I, too, have a square-shaped patio 🙂

In 1968, Werner gave me this question while we were watching a boring soccer match in the Rosenau Stadium. He was five years my senior and already studied mathematics at TUM at the time. I was still a pupil at the Jakob-Fugger-Gymnasium. Unfortunately, I do not know the original source of this logelei, either.

RMD
(Translated by Evelyn)