Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 15
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
Andrei's got it, he knows physics well.
Mike, why are they compensated?
Here comes another one.
yes, with a problem weight of 3, don't overthink it))
I'm sorry, but the answer is wrong.
I'd like to see in figures how the heat capacity changes when density changes
alright, slippery, but let volumetric change = density changed = mass stayed the same = heat capacity stayed the same = amount of heat necessary for delta T stayed the same
Will Megamind always be able to put such a stone on a shelf on one of the edges in a stable position?
Yes, with a problem weight of 3, no need to be clever))
I'm sorry, but the answer is wrong.
I would like to see in figures how the heat capacity changes when the density changes
The change in temp is too small to consider the change in heat capacity to be significant. I don't know how to justify it.
The heat capacity has not changed: the initial and final rates are equal.
There is another effect, thermodynamic.
TheXpert: Sure. There is one proof, but I'm not sure if it counts :)
Well I was recently defended. The proof is simple.
It is interesting that in the two-dimensional case the problem is stupidly solved purely geometrically. But in the three-dimensional case it's more complicated.
By the way, there is such an invention of Hungarians - gömbötz. It's a three-dimensional convex body with a single point of stable equilibrium (and a single point of unstable equilibrium).
The change in rate is too small to consider the change in heat capacity as significant. I don't know how to justify this.
The heat capacity has not changed: the initial and final rates are equal.
There is another effect, thermodynamic.
The thermodynamic effect is relevant for gases of the freon group, so you can draw a problem on it.
For metals it is something that, in this case, is neglected
Well, I've only recently been defended. The proof is simple.
Mine's probably even simpler -- the absence of such an edge is a direct violation of the law of conservation of energy.
Ah, the geometric one is also simple. It's the face with the smallest distance from the centre of mass to the plane of the face. If the perpendicular falls outside the face, then there is a face with less distance (due to convexity) , a contradiction. CHTD.
Well, I've only recently been defended.
Do you only post the ones you've solved yourself?
Well lately, yes. Decided on about a hundred; the vast majority of them 3 or more. So you can think for yourself. There's still a few left.
But I can also post the ones I haven't solved.
But I can do the unresolved ones too.
OK, here's a problem that I've put into permanent subconscious thinking mode (weight - 3, not solved):
A megabrain in a very long text needs to replace all the letters "A" with "B" and all the letters "B" with "A". The text editor allows one arbitrary set of characters to be replaced by another in the whole text. For example, replacing "AA"->"BSAA" will cause the string "AAAAAL" to become "BSAABSAAL". How does he perform the task?
Explanation: The alphabet of the text is unknown, so we do not know any other symbols except for A, B in the text and we cannot use them to substitute in the left part. Furthermore, no other characters should be in the right-hand side of the replacement either. This is some kind of bugger, but this is exactly the condition of the problem.
I've written several "solution" options already, but all turned out to be wrong.
Another one (weight is 5, I wrote the solution a long time ago, but it hasn't been checked yet):
There is an infinite number of urns in a row, in which stones may lie. It is known that the urn with numbers n+m contains as many stones as the urn with numbers n and m in total or one more. In the urn with number 9999 there are 3333 stones. How many stones are there in the urn with number 2011?
But I'm afraid it won't interest you too much.
That's what I wrote, making a continuously stepping polyhedron that requires minimal energy to keep moving. But I was misunderstood, citing an ordinary ball as an example. True, the situation with the ball is different, but, I repeat, I was not understood.
After that I wrote the solution in the language of potential energy.
Ah, the geometric one is simple too. This face with the smallest distance from the centre of mass to the plane of the face. If the perpendicular falls outside the face, then there is a face with less distance (due to convexity) , a contradiction. CHTD.
Now that's what I like!