Klaus Hnilica
Monday February 17th, 2020

(Deutsch) Caro – schnell und dünn…

Sorry, this entry is only available in German.

Klaus Hnilica
Thursday December 5th, 2019

(Deutsch) Fritz – und der Stillstand der Zeit

Sorry, this entry is only available in German.

Klaus Hnilica
Saturday November 16th, 2019

(Deutsch) Caros Rache – oder die ungewollte Spaghettisierung

Sorry, this entry is only available in German.

Klaus Hnilica
Monday November 4th, 2019

(Deutsch) Ein seltsamer Vergleich – oder?

Sorry, this entry is only available in German.

Klaus Hnilica
Tuesday January 8th, 2019

A Translation Mistake with Consequences ?

Since, after the ‘quiet time‘, we are back to ‘peaceful routine‘, it might be quite interesting to stop and think about all the evolutionary changes that even written texts can undergo. This is especially true for the book of books – the bible /1/:

For instance, in early Hebrew versions of the book Isaiah, there is a prophecy that uses the word alma when it describes the mother of a boy whose name is Immanuel (translation: God is with us).

In some languages, among them the ancient Greek, there is no translation for alma. However, a rough equivalent might be “young lady“ or “young lady who has not yet borne a child“.

When Jesus lived, however, the Jews no longer talked Hebrew. They talked Greek or Aramaeic. Consequently, the word alma became the Greek parthenos, which has a specific meaning, namely “virgin“. The biological term Parthenogenesis (“virginal conception“) is based on it: it describes a reproduction process without male contribution as we find it with some insects and reptiles.

That means that a modified translation of one single word turned a “young lady” into a “virgin” and a child into the Messiah! And the story of how Jesus was conceived suddenly changed completely. …

Matthew and Luke even turn this into a truth in their gospels. And for a billion Christians, it turns into a dogma. Which is exactly what we sing about in our Christmas Carols.

Isn’t it strange?

/ 1 / Adam Rutherford: Eine kurze Geschichte von jedem, der jemals gelebt hat
(Translated by EG)

Roland Dürre
Thursday March 15th, 2018

Landing on Antarctica (including travelling report).

Roland landing in the Antarctica.

All participants of an Antarctica expedition have to take part in a preparatory seminar prior to landing. During said seminar, they learn how seriously the world community takes the protection of the unblemished nature of the continent Antarctica.

At the same time, the entire Antarctica, and especially Southern Georgia, is one large museum where many stories of expeditions and science are told. However, it also gives profound insight into the history of this world to geologists.

There are ten rules for landing on the Antarctica and Southern Georgia. You have to strictly abide by them whenever you set foot on the Antarctica and its islands.

  • Please keep quiet!
  • Keep your distance (five metres from penguins, 15 metres from seals and birds)!
  • Do not tread on anything!
  • Never bring plants or animals!
  • Respect protected areas!
  • Preserve historic sites and monuments!
  • Do not take “souvenirs” with you!
  • Respect scientific research!
  • Think of your safety!
  • Preserve the pureness of Antarctica!

That also includes that you must not spit, sneeze or piss anywhere.

Roland on his way back to the ship.

These rules are also meant to protect the animals. I was surprised to see how seriously all participants took them and how they all rigorously kept to what was required.

I, too, got used to never treading onto a green spot. We all avoided unprotected sneezing. It was not possible to accidentally forget a paper tissue.

Thus, each landing became an impressive adventure. The light, the pure air, the wonderful nature made a huge impression on all of us. Historic buildings gave testimony of a horrible industry (waling) that, by promising people good money, had motivated many people to do a gruesome job under the hardest possible conditions far away from home. There were all kinds of remains that revealed quite a lot.

Back in Germany, it really shocked me how thoughtlessly we treat our environment and our nature both on a huge and on a small scale. Even more than before my trip, the pollution of our cyclists’ paths, streets and cities horrified me. The same was true for the gigantic soil sealing of our beautiful country. And of how we, totally without being forced to, expose ourselves to a lot of noise and polluted air in the nice residential areas of our cities.

This is where I also would like to publish a report (Bericht) on the trip for my friends. It was written and illustrated by our great editor Dr. Katrin Knickmeier. She was one (not the only) person from whom we learned so much – and I can also recommend to all of you to visit this special continent.

(Translated by EG)

Hans Bonfigt
Monday August 7th, 2017

(Deutsch) Hans im Glück, Version 2017

Sorry, this entry is only available in German.

Roland Dürre
Saturday April 22nd, 2017

Solution to Problem 2

On April, 12th, I published a second Logelei in the IF

The question was:
Can you position 31 domino stones (each of which is as big as two tiles) in a square area that consists of 64 square tiles such that two opposing corners remain free?

The task is easy as soon as we (mentally) colour the area that consists of 64 tiles like a chess board (Auszeit).
Then we know that one domino stone – as big as two fields (tiles) – will always cover a black field and a white field.

But we will also instantly see that the two opposing fields have identical colours.

So what does this tell us?
If you try to solve this problem by trial and error, you quickly run the danger of making a mistake. However, if you use a simple construct to help you (such as colouring the field like a chess board), the solution will immediately be clear.

You only have to have the right idea!

(Translated by EG)

I am taking time out (Auszeit). This article has been written in advance and will be automatically published (two weeks after the problem was formulated).

Roland Dürre
Monday April 17th, 2017


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!


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.

(Translated by Evelyn)

Roland Dürre
Monday April 3rd, 2017

A Very Special Task!

The Solution will be Supplied Later!

A short time ago, a good friend of mine came up with a brainteaser. He did not know the source, otherwise I would gladly have cited it. My friend was not able to solve the problem, neither was I. But it is a truly exciting scenario. And it has a surprisingly simple solution, including a beautiful mathematical reasoning. It also gives us a nice metaphor for our lives.

Among other things, it shows that mathematics can also, once in a while, be quite useful. Here is the story:

Here is a female criminal. On her card, the number 1 is written. But she does not know this. After all, she only knows the nine other images with their numbers.

A – not dislikeable – gang of 10 persons constantly violates the prevailing moral concepts in an outrageous manner. The gang members are creative and wise – this is how, with great finesse, they remain unmolested by the arm of the law for their abominable activities. That is lucky for them, because the legal penalty for their crime is death by strangulation.

In the public perception, the gang soon has a legendary reputation, and is idolized by quite a few simple people. For the authorities, this development is totally unacceptable. Consequently, the increased manhunt of the authorities, along with a growing arrogance and flippancy among the gang members led to the capture of the group.

All 10 gang members are quickly sentenced to death due to their abominable behaviour in a show trial. However, there is a way for the ten comrades in crime to save their lives – through an appeal for clemency. The head of state who decides upon said appeal is a very prudent and well-meaning woman. She is very wise; there are even some rumours insinuating that she may to some extent sympathise with the gang.

Actually, she works hard to come to a fair decision. She hands down a conditional amnesty (a little like a “Judgement of God”):
Before the verdict is executed, the ten members are permitted to see each other once more. There is a farewell meeting, the ten gangsters can spend the afternoon before their execution together and without supervision.

Here is a male criminal. On his card, the number 2 is written. But he does not know that. After all, he only knows the nine other images with their numbers.

As the meeting starts, the gangsters are told how the amnesty will work. A picture of each of the members is taken (two of them can be seen here). On each of those pictures, a number from the set 0 – 9 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is drawn. Each number can be used several times. Consequently, it is possible that the same number is written on all the pictures. Or that only some numbers are used, for instance {1, 2, 3)}. Or maybe only the even or uneven numbers. Whatever. But perhaps all numbers have been used. Nothing is impossible.

After the meeting, each of them is taken into solitary confinement until the time of execution. Each of the ten gang members is shown the nine pictures of the other nine members – but not his own one. And then they ask him the number on his own photo. And if even one of the gangsters gives a correct answer for the number on his card – all of them will get the amnesty.

Initially, you will think that the gangsters have quite a good chance to avoid their punishment and enjoy clemency over justice. And there is no doubt that their situation will have improved. After all, chances are not too bad that one of the ten will guess correctly and thus free them all.

But it is nowhere near as easy as that. Matters may turn out poorly. And there is one thing the wise regent forgot (or perhaps not): by applying a simple agreement, the ten gangsters can make sure that one of them will inevitably say the right number, as written on his picture. And this is how he can guarantee that he and his comrades will enjoy the amnesty.

It is a small problem: what agreement makes it possible for the gang to use the meeting that was meant as a farewell to make sure that “their heads” are out of the sling with a 100% chance?

I will publish the solution in a few weeks – and until then, I look forward to having many email solutions sent to me!

(Translated by EG)