[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 311

 
Richie >>:

MetaDriver, вам нужно больше спать и больше есть. Вы ещё заявите, что я троль, работающий на метаквоту.

It's nice to have people who know what I need to do. Somehow it's easier to make decisions in these circumstances... ) By the way, who do you work for? ;)

If you live in a second capital city, I can introduce you to a particular psychiatrist who will change your "idea of roles" :)))))

Nah. My daughter lives in number two. I'm in number three. ;(

But anyway, thank you very much for taking care of my performances. :)

 
Mathemat писал(а) >>

Well, well. That would be the answer - the root of five plus one exactly?

I believe you. I won't check it - I don't feel like writing a programme, I've been lazy since Saturday, it's been a hard week, I'm very tired.

MetaDriver wrote >>

By the way, who do you work for? ;)

I don't work for the methaquota.
And I'm not doing any psychological experiments here, my job is enough for me.
I noticed that the content of my profile annoys a lot of people, so I deleted my information.

 
409:
It is clear that starting from the first step, the sum of all vector components (4 numbers) becomes zero:
a(n) + b(n) + c(n) + d(n) = 0.
The sum of the squares is:
a(n+1)^2 + b(n+1)^2 + c(n+1)^2 + d(n+1)^2 =
( a(n)-b(n) )^2 + ( b(n)-c(n) )^2 +( c(n)-d(n) )^2 +( d(n)-a(n) )^2 =
2*( a(n)^2 + b(n)^2 + c(n)^2 + d(n)^2 ) - 2*( a(n)*b(n)+b(n)*c(n)+c(n)*d(n)+d(n)*a(n) )
But the second large bracket is strictly negative, т.is (b+d)*(a+c) = -(b+d)^2.
Hence, the sum of the squares of the components grows exponentially and the sum of the components is zero. The rest is easy.
 

Mathemat, give us a new problem. I've already solved this one in BASIC :)))
Just an interesting one, and not complicated, because I was in 8th grade 20 years ago :)))
-
hypnosis for MetaDriver: http://depositfiles.com/ru/files/kecenfelj

 
Richie >>:

Только интересную, и не сложную, а то я в 8-м классе 20 лет назад учился :)))

I need your criteria for "interesting and uncomplicated", Richie. Generally speaking, these requirements are contradictory.

The puzzles you posted earlier from Perelman were, roughly speaking, simply entertaining physics to attract interest in it. They very rarely required you to rack your brains in such a way that your brain was twisted much more than in ordinary life. But here the branch is different.

 
Mathemat писал(а) >>

I need your criteria for "interesting and uncomplicated", Richie.

It's a difficult question, I'm afraid I can't answer it.
Mathemat, when a problem is very complicated, one is no longer interested in solving it. When it is very simple, it is not interesting to solve it.
You have to find a middle ground :))

 
Mathemat писал(а) >>

The puzzles you posted earlier from Perelman were, roughly speaking, simply entertaining physics to attract interest in it. They very rarely required you to rack your brains in such a way that your brain was twisted much more than in ordinary life. But that's a different branch here.

I don't remember exactly anymore, but I think there was only one task from Perelman, spinning back pages is lazy.

 
Richie, I'm not sure I can quickly find a problem just for you. If I find one, I'll post it and specifically ask others not to interfere with the process of solving it by you. And I don't even post very complicated ones here - they're all off-board the branch.
In the meantime for others (9th):
 

What does it mean not surpassing? It means less than or equal to. 4 out of 8 is half. I think it's obvious that such a cell will be found.
That's it. Silence :))

 
Richie, I can give you an example on a five-by-five sheet of paper that doesn't meet the requirements of the task. You could probably do the same for any finite one, but you'd have to think about it.