[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 15
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Дело в том, что при этой разметке (а она подчиняется только одному принципу - у всех разное число друзей, и потому достаточно общая) Петя вообще не участвует. Он является одним из 26 учеников, абсолютно равноправным с остальными. В результате получается, что у всех не может быть разное число друзей - ряд от 1 до N-1 невозможно пронумеровать последовательно N разными числами (это в финале доказательства). Поэтому у двух учеников количество друзей должно совпадать. И эти два ученика находятся рядом в центре ряда. Так и получается, что Петя должен быть одним из этих двух. Только в этом случае все остальные имеют разное число друзей. Любые другие разметки не смогут удовлетворить этому условию.
If any "Peter" has the same number of friends as his neighbour (not matching his number in order), i.e. +1 more or 1 less than the triangular layout "should" have, THAT MEANS that EVERYONE else in that class has 1 more (or less) friends too. See? By equating Petya with his neighbour, you must immediately subtract (or add) ONE more from someone else - and this IMMEDIATELY violates triangularity of that matrix and the problem's condition in one place.
I didn't like this "Petya" at once.
The problem is rubbish.
The "solution" at the link is a rubbish.
Well done, Mathemat, for posting the problem and shaking your brains out.
I wish I could read something meaningful under that nickname for once. All you do is pout and blah, blah, blah.
Before you write something, it's a good idea to learn to understand it. At least the condition of the problem. 7th grade isn't that much.
Да, это почти так.
Если читать условие задачи ЮРИДИЧЕСКИ - то у Пети МОЖЕТ быть равное с одним другим число друзей.
Я же говорил - эта задача некорректна - при ЛЮБОМ прочтении условий. Я пожалуй могу ДОКАЗАТЬ это, причём разными способами. Но не буду..... пока.
Everyone is long gone.
Change your bald tyres
Хоть бы раз прочесть под этим ником что-нибудь содержательное. Одно только надувание щек и бла-бла-бла.
Прежде чем что-то писать, неплохо было бы научиться понимать. Ну хотя бы условие задачки. 7-й класс - это ведь не так уж много.
Informative? Please: The problem starts like this: "Petya, a pupil from a dysfunctional family, ate some hallucinogenic mushrooms and suddenly told his maths teacher that he noticed....." continue reading from page 1.
AlexEro, you still don't want to understand that the condition "there is another one in the class with the same number of friends as Peter's" does not need to be added to the conditions of the problem. It follows from the conditions of the problem while solving it. Even my efforts (I have proved that Petya is neither (0) nor (25)) admit it.
But of course, before proving that Petya is (12) or (13), both of them must be presented explicitly.
AlexEro, ты так и не захотел понять, что условие "в классе есть еще один с таким же числом друзей, как у Пети" добавлять к условиям задачи не нужно. Оно вытекает из условий задачи в процессе ее решения. Даже мои потуги (я доказал, что Петя - не (0) и не (25)) уже позволяют это понять.
Но, безусловно, перед доказательством того, что Петя является (12) или (13), нужно оба эти варианта предъявить явно.
I don't know what "arise from the conditions of the problem in the process of solving it" means. I've never encountered such a thing, and I've broken such "tricks - excuses in the course of the investigation" more than once in the courts. "The most cunning lose first". The problem setter thinks he is very clever and thinks that his phrase washed the solver's eyes (in any real firm, such a problem setter would get a black eye for such linguistic tricks).
Well, then I claim that from the same conditions of the problem it follows that Petya is friends with ALL 25 of his classmates. Otherwise, how could he 'notice' who is and is not friends with whom - for each classmate, including girls? It says "noticed".
Do you insist on examining the legal conditions of the problem? Yes? Well, then answer me, how else could Petya "notice" it, than not having ALL 25 of his classmates as friends.
How?
Ну тогда я утверждаю, что из тех же условий задачи СЛЕДУЕТ, что Петя дружит СО ВСЕМИ 25 одноклассниками.
AlexEro, this is maths, not court proceedings. How he found out about it is irrelevant to the maths problem. For example, the class teacher has been instructed from above to find out. And the class teacher is Petya's mother. Is it possible?
Or put it another way: you work somewhere, in a team. Is it difficult to notice that Seryoga is friends with Vasya, without being friends with both of them?
Secondly, the friendship relation can be replaced by any other symmetrical and non-transitive relation. I suggested it: "A met B at the disco at Aunt Masha's club". Then it won't be as tense as with friendship.
And finally, present the solution, in which Petya is friends with everyone. Of course, so that the conditions of the problem are not violated.
Mathemat, I've been meaning to ask you for a long time. What does this Petya have to do with Forex in general? You started this thread for a reason, didn't you?
What are your conclusions?
None. The topic was created for nothing. The title of the topic says in black and white: "Pure Mathematics".