[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 10
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ah, it's simple)
min-minimum number of friends a classmate has.
max-maximum number of friends a classmate has.
the two options are 0-24 and 1-25.
Pete's friends = (min+max)/2
12 or 13.
oops, there may be an even number of classmates)You've got six men, Figaro. That's the configuration: {"1","5","4","3","2"}|"3". Yeah, that's right.
друзей у Пети=(min+max)/2
12 или 13.
Why is that?
You've got six men, Figaro. That's the configuration: {"1","5","4","3","2"}|"3". Yeah, that's right.
Yeah, well, with Petey 6, by the way, if you have Petey 7, you get 3, too. And that confuses me.
You don't even have to draw a picture for 4+1, there's only 5 links.)
Oh, that's it! You, colleagues, also check the possibility of building friendly relations according to the problem's conditions and try to prove that:
- if you read the conditions of the problem very carefully and meticulously,
- if you notice that the stager hints at the coincidence of Petya's friends with the number of friends of another classmate,
- Assuming that such a situation is possible at all,
THEN FOR COMPLETE CORRECT PERFORMANCE GRAFF OF FRIENDS in class MAY BE SUSPENDED that the number of friends of unique Peter (who coincides with Vasya, otherwise the problem - lame), - must be any other than 12 or 13.
Am I following the right direction of your thoughts? If you got it right, then... Why do you need such a complication?
Petya is any student in the class. The task is to find the maximum number of friends any student has, so that the condition of the problem is met.
- если заметить, что постановщик намекает на совпадение Петиных друзей с числом друзей одного другого одноклассника,
This is not what the stager is hinting at. It follows from the analysis of the problem, but it's not in the condition of the problem.
Otherwise it is correct. And don't read it too fastidiously. The problem has clear conditions which allow for a solution.
Richie >> Petya is any pupil of the class. The problem is to find the maximal number of friends of any pupil, so that the condition of the problem is satisfied.
Petya is not any pupil, but exactly Petya. Almost everyone else's view of the class is different.
And the maximal one is already found out: it is either 24 or 25. This still doesn't solve the problem, because Petya can't have 24 or 25.
Петя - это любой ученик класса. Задача в том, чтобы найти максимальное количество друзей у любого ученика, так, чтобы выполнялось условие задачи.
Graphs are taught in the 3rd or 4th year of a mechmatics course. To show friendships and to prove that POSSIBLY FOR correctness of the graph - an outcast unique Petya (aka Vasya) must have 12 or 13 friends - it is necessary to construct a graph. If you don't build the graph, then my reasoning about "numbering" students by their friends' numbers is quite enough.
The "solution" at the link does not show at all, why exactly Petya (aka Vasya) must be in the middle of the sorted numbers removed from both sides of the sequence. There is no causal connection between finding Petya and Vasya in the middle and the conditions of the problem.
And the maximum is already figured out: it is either 24 or 25. That doesn't solve the problem yet.
I wrote: so that the condition of the problem is fulfilled. With 24 or 25 it will not be fulfilled.
Значит не заметил? :)
It's all worked out.
I've got Petya kind of on the outside looking in on a class of 25
It's a good formulation, it's confusing.
It would be easier and not more interesting if it were like.
"In a class of N, everyone has a different number of friends.
Except for Lesha and Vitya.
How many friends does Lyosha Matemata have?"
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Regardless of N, there will always be two people with the same number of friends