[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 7

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Incorrect formulation of the problem. The correct wording is that each student in the class wants to be friends with different numbers of other students. Friendship is mutual - if Petya is friends with Vasya, then Vasya will also be friends with Petya. Both sides need to have the same friendship desire, then the friendship is possible. Then the question of the problem is how many other students can be friends with each other.
 
Mathemat писал(а) >>

Now all that remains is to formalise it all.

Enough to prove that in a class where this condition is already satisfied, you can add a newcomer who will be friends with all or not with anyone, depending on the situation in the class))) If the initial configuration (class of 3 people) 1,2,1 then you can only add rogue, if 0,1,1 you can only add dude who will be friends with all. Otherwise, no way :)

 
Mathemat >>:

Так какое решение, AlexEro?

P.S. Это явно олимпиадная задача. Ни в какой обычной школе бедных детишек ей мучить не будут. А тех, кто участвует в олимпиадах (или учится в физматшколах), зта задачка только раззадорит.

Personally, I am deeply opposed to linguistic casuistry. It doesn't say "noticed that all the students in his class", it says "all his classmates". This means that the solver MUST notice this and consider two possibilities: when the number of Petya's friends does not match anyone (and find out that there is no solution, which means a contradiction in the condition, that is, Petya has delirium tremens, because it says "Petya noticed"), or when it matches (then there are exactly 24 or 25 solutions, Petya really can't have zero). I don't know about you, colleague, but at any Olympiad I did not care to look for clues in the words of the conditions.

 

"Petya has noticed that all of his 25 classmates have a different number of friends in that class."

That can't be

 
AlexEro писал(а) >>

Personally, I am deeply opposed to linguistic casuistry. It doesn't say "all the students in his class noticed", it says "all his classmates". This means that the solver MUST consider two possibilities: when the number of Petya's friends is NOT the same as someone else's (and find out there is no solution, which means a contradiction in the condition, that is, Petya has delirium tremens, because it says "Petya noticed"), or when it matches (then the solutions are exactly 24 or 25, Petya really can't have zero).

but he noticed that all of his 25 classmates.... he didn't notice anything about himself ;)

 
Mischek писал(а) >>

"Petya has noticed that all of his 25 classmates have a different number of friends in that class."

That can't be.

So you didn't notice? :)

 
How is Petya better than Vasya? Somewhere in the condition it says that he is first in order or last, but the condition says that everyone is friends with a different number of other students. Why does Peter suddenly have 13, so everyone has 13, but the condition says everyone has a different number.
 
Mathemat писал(а) >>

You shouldn't trust the author of the answer.

===

I insist on my answer: maximum 5, and so 4. The solution is intuitive (bit maths). So, if there were 16 people in the class, there could be 4 friends (2^4). And if there were 32 students, there would be 5 (2^5) friends respectively.

 

Answer my question. If there are only 5 students in the class, what are Peter's options?

With three - 0 and 1

With four - 0, 1, 2.

 
Avals >>:

но он же заметил, что у всех его 25 одноклассников.... про себя он ничего не заметил ;)

Yeah, well, that's law, not maths.

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