Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 161

 
C-4: This begs the question: What happens to the water in the bottle?

Nothing much. Rather option 1. The weaker the water will flow out, the closer the water level is to the crack.

Perhaps the crack is so small that water will not flow out because of surface tension.

 

Happy New Year everyone!!! By the way, I found a reference answer to the matchmaking problem. But I can't post it here, you know, palaver and so on. So if anyone needs it very much, write to me in person, I'll show you.

However, there is some useful information which can be used to solve this problem. You can read it:

http://www.genfunc.ru/theory/catalan/

 
Road_king: However, there is some useful information which may help to solve the problem. You are welcome to read it:

http://www.genfunc.ru/theory/catalan/

Still need to remember what those Catalan numbers are. I have already forgotten. And if there are facts associated with them, you'll have to prove them too, for sure.

P.S. Yes, something like that should have popped up, I have the relevant reasoning. It's just a little bit missing.

 

Mathemat, did you know them? I wonder if these numbers are taught in school, for real? I don't remember any of them. There, at the link, you can immediately see the article at the end - "Wandering on a half-straight line". In fact this problem is identical to the given one. And the answer comes out the same for the general case. Only it is necessary to clearly understand why it is so. They still do not want to give me credit, saying that I do not understand what is written in these materials, and when you rewrite it turns out to be nonsense. All in all, what I'm missing is a clear answer to the question:

"What is Catalan's nth number equal, and why?"

How do you find the answer and justify it? Then it's done. Or rather, the answer is found, we need to explain why.

 
Road_king: Mathemat, did you know them? I wonder if these numbers are taught in school, for real? I don't remember any of them.

So what, but I graduated from "Kolmogorov's" FMSh № 18 at Moscow State University. There was a lot more than school in physics and mathematics; even if these numbers were not given there, I myself was quite an inquisitive young man.

 

Sorry for the intrusion, a question for mathematicians.

Why do online calculators that convert from one number system to another limit the base of the number system? (32 or 36 usually). I.e. you can convert from 10 to 12 figures, but not to 60 figures.

And can anyone suggest a formula for Excel to convert numbers from 10 to 12 and 60-cimal, and vice versa.

Or where to read, google doesn't understand me this time.

 
Silent: Why do online calculators that convert from one number system to another limit the base of the number system? (32 or 36 usually). I.e., a number from 10 to 12 can be converted to 12, but cannot be converted to 60.

First, list all the digits of the hexadecimal numeral system by name.

Finding the algorithm yourself is not difficult - just generalize it from the examples given on the web.

If this is difficult for you - bear with me, we'll do it tonight, I hope. But first let's agree on the notation of all 60 digits :)

 
Mathemat:

First, list all the digits of the hexadecimal c.c. by name.

Finding the algorithm yourself is not difficult - just generalize it from the examples given on the Internet.

If this is difficult for you - bear with me, we'll do it tonight, I hope. But let's first agree on the notation of all 60 digits :)

0-9a-zA-Z 26*2+10=62
 
Mathemat:

First, list all the digits in hexadecimal c.c. by name.

Finding an algorithm yourself is not difficult - just generalize it from the examples given on the web.

If this is difficult for you - bear with me, we'll do it tonight, I hope. But first let's agree on the notation of all 60 digits :)

Ah, there are no unique common signs for number systems with a base greater than digits + letters. I don't get it.

No, the algorithm's a mess. I'll try it, of course. I'll end up counting in columns, for crying out loud.

Let it be ASCII.

0123456789
abcdefghij
klmnopqrst
uvwxyzABCD
EFGHIJKLMN
OPQRSTUVWX

So the Sumerians had a decimal system, with an extra base of 60. Decimal/60 decimal, that's what it was. Boo.

 
felidae:
0-9a-zA-Z 26*2+10=62

I first thought it was an example of system-to-system transfer :)

Thanks, you can do it that way.

Reason: