[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 111

 
Richie >>:
MetaDriver, а вы как думаете. Шарики могут отталкиваться?
I was beginning to wonder... :)
 

You've got me confused again. Are we talking about a square? Is 3.3(3) a square or what? What does it have to do with dividing by 3?

Okay, I really don't understand. I'll sober up tomorrow. Bye.

 

Well, this gravitsapa hardly works on antigrave, it does not look like that:

This engine is "ablative", in it "under the action of high-voltage discharge the working body - fluoroplastic - evaporates and a thrust is generated".

 
Richie >>:
MetaDriver, да не читайте вы эту газету. У меня от неё компьютер виснет :)))


Don't breathe on him.)
 
Mathemat >>:

Richie, нужно обоснование. ОК, тогда хотя бы покажи самостоятельно, почему число из 1999 однерок не делится на 3.

2 Metadriver: достаточно. У тебя, кстати, никаких мыслей о ночной задаче насчет отрезка с концами на двух окружностях?

Следующая, вроде посложнее: Доказать, что число 111...11 (81 единица) делится на 81.

almost everyone remembers the test of dividing by 3.

and in Japan they've moved from an elective to a core discipline that makes it relatively easy to learn

to do four basic operations with four-digit numbers.

 

And this is about Swedish schoolchildren. It's much worse than the Japs.

 
Richie >>:

Какие нафиг испарения ПТФЭ? Он разлагается при нагревании свыше 400 град.С. Спокойной ночи.


Stop

A child put me on the spot with a simple question about what boilers are made of.

Well, I told him in good conscience it's a different metal, more refractory.

And he goes and asks, "What's that one made of?

I got hung up, I'm too lazy to google, it's probably a long time.


 
Mathemat >>:

А тут о шведских школьниках. Все намного хуже, чем у япошек.


And these people decide who gets a Nobel Prize and for what)
 

OK, it's not a difficult problem.

A number of 81 units 11...11 = 111111111 * (1 + 1*10^9 + 1*10^18 +...+ 1*10^72) = 111111111 * Number_1.

Number_1 = is a number consisting of 9 ones, densely diluted with zeros.

It turns out that both 111111111 and Number_1 are divided by 9, i.e. the product is 81.

 
Mathemat >>:


2 Metadriver: достаточно. У тебя, кстати, никаких мыслей о ночной задаче насчет отрезка с концами на двух окружностях?

There is, but not enough so far.

The next one is more complicated: Prove that number 111...11 (81 ones) is divisible by 81.

We divide this number by 111111111. Получаем частное 1000000001000000001000000001000000001000000001000000001000000001000000001.

We can see (according to the school principle of divisibility), that both the divisor and the quotient are divisible by 9.

Proved.

Reason: