Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 8

 
Mischek:

What? Again?

You're drawn to the pyramids, you are. Subconsciously. Just not to the top, because you're scared.)

You'll get glitchy there.)

But when you come in from afar, you're a sly one.

...you're going to the wall newspaper... )

 
Integer:
The conversation is about the Egyptian Primidas.

yeah, that's right.

they have ad=2db?

 
I drew it. all corners are marked.
 

That's it. We got it.

The real pyramids don't have angles of 60 degrees - firstly, and they don't face the poles, but sides - secondly.

Thanks, everyone.

 
Mischek:

Leha, there's this... mamememe commercial.

I've got him figured out.

That's how it is - you run away from a quarter and they catch up with you here too.

So, no one wants to cut the circle - fine. And the problem of two commands seems to have been put on the back burner.

OK, here's another one (4 points):

There are 200 safe deposit boxes in a bank vault. Three of them contain diamonds: the first one contains 35 diamonds, the second 69 and the third 91. The rest of the boxes are empty. The robber managed to break into the bank and get into the vault, but he could not just take the diamonds: the vault was equipped with an alarm system which would make him very unhappy if the alarm was triggered. He manages to partially block the security system and is able to perform the following operations without causing an alarm: 1) move all diamonds from any one cell to any other; 2) move exactly half of the diamonds from any selected cell to any other; 3) take a diamond from any cell, if there is one there. The above operations can be performed an unlimited number of times and in any sequence. How many diamonds can the robber steal?

 
Mathemat:

OK, no one wants to cut the circle - but that's OK. And the task about two teams seems to have been put on the back burner.

It needs a deep dive, so I'll pass.

OK, another problem (4 points):

How many diamonds can the robber steal?

I suspect that all :) but I will have to suffer.
 
That's right, MD. I'm even a little surprised, as I didn't expect you to prove it rigorously.
 
MetaDriver:

Thus, the robber has no chance of creating even one group of diamonds, with the number being any degree of two.

Mm-hmm. I somehow cleverly managed to get 19.
 
Mathemat:
That's right, MD. I'm even a little surprised, as I didn't expect you to prove it strictly.
I didn't expect it myself. I guess I've gradually developed a taste for it over the life of this thread. :)
 
TheXpert:
Mm-hmm. I've somehow managed to get 19 in some clever way.

Come on, show me, I must have got it wrong somewhere along the way. It's no wonder, there are a lot of variants branching out there.

But according to my theory there should not be 19, and I don't see any holes in the theory. I'm not arguing, maybe I'm just blind. Show me.

Reason: