I really enjoy this situation which Richard Reti published at Ostrauer Morgenzeitung on
December 1921. Even thought it looks impossible, this situation ends in draw. It is a
nice example which shows the importance of thinking even in the most desperate
looking situations. Let’s have a look: Except the kings, there are only one pawn for each
in play. It seems like pretty simple. At first glance, you may think that the situation is
win for blacks. After all black king can catch up white pawn before it turns into a queen.
However, white king cannot catch the black pawn. White player can try to get close to
black pawn with king such as s/he can move the pawn. But the decision of one of these
in the first will lead to a loss. Despite that, there is such a balance in the game, first
couple moves of white can be beneficial for two plans. Thus, white can choose between,
determine to black player’s moves. This situation is an efficient proof of plain being not
always mean simple. Because if white can find the right moves, game will end up draw.
Remember that even though a couple of solutions for a problem lead to a clear misery,
there could be another solution deep down there. Therefore, never
Şg7 – h4
Şf6 – Şb6
Now, if black moves to h3, white can protect the pawn with Sd6 move and therefore
both sides can transfer in to a queen. Black’s Sdx6 move instead of h3 would not work
either. Because white can catch up the black pawn with the Sf4 move. Let’s look in to
Şf6 – h3
Şe2 – h2
Because of both sides geting a queen, game will end up tide. In every alternative white can
gets to a draw in a similar way.
Symbolical Logic and Logic Games
I believe that the logic puzzles are revolutionary for minds. Besides of interesting in researches about formal logic, I have a special interest in logic games.
Even at the moment a scientific education dictates “everything is very simple and clear, hence there could not be another way” it in fact says that everything would be more complex and in a different way.
Maybe the logic puzzles have the power of showing this to us in a simple way. In other words, they can be helpful to give a chance to people who did not study science for years understand this. Because of these features, I believe that the logic puzzles are revolutionary for minds. Particularly, I take great pleasure from working systematically on thousands of logic puzzles which masters like Sam Loyd and the author of Scientific American, Martin Gardner create
I want to introduce to you a logic question that can satisfy me as a puzzle and has an aesthetic solution.
There are three persons on an island. (Person P, T and K). One of them always tells the truth, another one tells the lie. Last person randomly tells the truth or the lie. (Little clue: You can think this as a situation that switch being open or close. You do not know if it is open or not.) Can you identify the P, T and K persons by asking three yes or no question to person or persons you chose? But another difficulty is that you do not know the language they are speaking. (Of course, they know the language you are talking, they just will answer them on their language’s.) For example, they will say “flip” for yes and “flop” for no. You do not know which one is “yes” and which one is “no”.
BEven though this problem looks easy it is actually a challenging question that requires advanced logic information. This problem has more than 10 variations and this one is the hardest and the most complex one amongst. Specially the solution of this variation requires use for advanced logical connectives. In fact, there are several articles about this problem. For example;
“Some Thoughts about the Hardest Logic Puzzle Ever”
Raymond Smullyan, The Riddle of Sheherazade (A. A. Knopf, Inc., New York, 1997).
Also, this article is the base for this problem:
George Boolos, The hardest logic puzzle ever (The Harvard Review of Philosophy, 6:62–65, 1996).
Now let me explain the solution:
First, let’s touch upon the clue. Most of the people who read this problem think that the Random one’s answers are totally random, but the clue make the situation clear. This person’s answers are not totally random, it means that the person always tells the truth or always tell the lie. Random thing in that is the person becomes the “truthful” or the “liar” in a random way. I indicate that in the clue in this way: (Little clue: You can think this as a situation that switch being open or close. You do not know if it is open or not.)
Now make a preparation for understand the answer. Consider one question: “If I ask you ‘is two plus two equals four?’ is your answer would be ‘flip’?” For one moment we think like the ‘flip’ means ‘yes’ and ‘flop’ means ‘no’. In the situation there are two opportunities. If we ask this to ‘truthful’ the answer would be ‘flip’ which means yes. Vice versa if we ask this to ‘liar’ answer would be ‘flip’ anyways. Because the liar has to say ‘flop’ to ‘is two plus two equals four?’ question, again has to say ‘flip’ for the: “If I ask you ‘is two plus two equals four?’ is your answer would be ‘flip’?” question.
Quite the opposite, if we ask the question like “If I ask you ‘is two plus two equals five?’ is your answer would be ‘flip’?” both truthful and liar would say ‘flop’.
Now think like the ‘flip’ means ‘no’ and ‘flop’ means ‘yes’. In that situation for the “If I ask you ‘is two plus two equals four?’ is your answer would be ‘flip’?” question there are two possibilities: If we ask this to truthful, answer would be flip. Because of the truthful says the truth answer for ‘is two plus two equals four?’ would be ‘flop’. So, the answer for the long question again would be flip. Vice versa if we ask this question to liar answer would be ‘flip’. Because liar will say ‘flop’ to ‘is two plus two equals four?’ and for the long question answer would be ‘flip’. Despite of that if we ask the question like: “If I ask you ‘is two plus two equals five?’ is your answer would be ‘flip’?” In this situation both answers would be ‘flop’. Therefore, if the short question is true, answer would be ‘flip’ without noticing whom to ask. And if the short question is false, answer would be ‘flop’ without noticing whom to ask.
If this part is clear enough, it will be much easier to understand the answer.
With this kind of approach, because of we could understand the trueness for the short question easily; we should ask a question that we could understand the persons names. We can start with asking “If I ask you ‘is P random?’ is your answer would be ‘flip’?” to T. If T’s answer will be ‘flip’, T is random (and answering randomly) or T is not random, and P is definitely the random. In both situation K is not the random one. If T’s answer will be ‘flop’, T is random (and answering randomly) or T is not random, and definitely P is not the random either. In both situation P is not the random one. With the knowledge of the previous question, if we ask, “If I ask you ‘are you the truthful?’ would you say ‘flip’?” to one who is not random (to P or K), because of the T is not the random one, if P or K answer as ‘flip’ it shows that the person is truthful; if the answer ‘flop’ this person is the liar. Ask “If I ask you ‘is T the random one?’ would you say ‘flip’?” to same person, If the answer is ‘flip’ T is the random one, if it is ‘flop’ the person we did not talk yet is the random one. And the last person’s identity can be found easily.
So, the answer is actually that simple!
Personal library of Gültekin in his workroom...
Beside the technic and popular Physic, Mathematic and Astrophysics science books; he has a personal library that incudes more than 5000 books predominately about Philosophy of Art, Social Anthropology, Cinema and Cinema History, Philosophy of Science, Philosophy of Politics, Word History, Philosophy of Knowledge, City History, Ancient Greek and Age of Enlightenment’s books, Literature and Literary Examinations, Photography, Music and Philosophy of Music, Philosophy of Aesthetic, Philosophy of Ethics, Social Psychology, Psychology of Education and Development, Biological Evolution, Mythology, History of Science and Mathematics, Philosophy of Logic, History of Philosophy.