[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 302

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And the solution method, MetaDriver? There is no calculator at the Olympiad. The selection - you know, it's not nice somehow...
Richie, who told you that "such problems are solved in grades 9-10"? In ordinary schools they don't, but at olympiads they do.
 
Mathemat писал(а) >>
Richie, who told you that "such problems are solved now in 9-10 grades"? In ordinary schools they don't, but they do at olympiads.
That makes me happy. What happens to kids who can solve such problems? For a long time I have wanted to meet a young man or a girl in order to use him (or her) in my self-interest, but I don't see any.
 
What happens to them... Some go into science (very few), some into programming at a decent firm like Melkosoft, and some just drink themselves to death. Life's fate is about the same as that of other, ordinary people...
You know what times are like. But there are still some of them, and there are no fewer of them.
 
I didn't say I had made up my mind. I just wanted to see the minimum... So I threw in a script... me too, crime.... :)
But I hand-checked the dividers honestly. Even without Excel. :)
I'll decide now.
Files:
divi.mq5  1 kb
 
Come on, you're making excuses. You know the value of your decision yourself...
 

Some people liked the programming olympiads better than the maths ones ;)

 
Programming is also good. Russian olympiadists are among the strongest in the world, if not the strongest...
 
And don't talk me into it. If I want to, I'll make excuses!
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I did a little research on the problem.
I figured out that the number must satisfy the equation: ( (11 * 13) * N + 12) % (2*3*5*7) == 0 // ( 143 * N + 12)% 210 == 0
The solution, in fact - the number (( 11 * 13) * N + 12) - 10, i.e. what is in brackets should be exactly in the middle of the range we are looking for.
The problem is how to find N. So far I don't know how to crack it analytically. It does not seem to be possible to find N... at least in our monastery they think so...
 
I'm thinking about the middle of the range, too. But I'm doing it the old-fashioned way, with factorials. Have you forgotten Wilson's theorem? Well, it's just in case: p is prime <=> (p-1)! = -1(mod p). Just in case it may come in handy...
This theorem children should know, although the school does not give it.
P.S. I solved the problem on a piece of paper without a calculator! But the number came out very big(197*10! in the centre and 10 on top and bottom).
By the way, your solution is just given in the problem book. 9450 in the centre. But you need much less than the program on "five" to justify it. Note that
9449 % 11<br / translate="no"> 9450 % 2, 3, 5, 7
9451 % 13
i.e. both numbers at the bottom and top of 9450 are divided by 11 and 13 respectively. It remains to find a way to prove it without involving complex computational methods. I don't need to prove anything else :)
My 10! and 197 came about quite logically, just from these requirements.
 
Richie >>:

Не может того быть, чтобы такие задачи сейчас в 9-10 классах решали. Я, что так сильно отстал?
Дайте мне ссылку на 9-10 классника, который это решать может, хочу познакомиться.

I can give you a link for those who can't:))))))
http://www.profi-forex.org/country_traders/entry1003142342.html

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