Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 51

 
alexeymosc:
My answer to the second part of the problem: 1/1025. If you don't believe me at all, let's wait for at least one more reasonable solution and compare ;)
In any case, the probability is very small. It's interesting because, for example, if you take out a coin from your purse and flip it 10 times in a row and get tails, you might mistakenly think that the coin is significantly unfair. A paradox?
 
alexeymosc:
My answer to the second part of the problem: 1/1025. If you don't believe it at all, let's wait for at least one more reasonable solution and compare ;)

I see your version, I'll stick with mine for now.

I have a counter task.

Two mega-brains are playing. The first one has two coins in his pocket. One of them is fair, the other has tails on both sides. Megamind randomly pulls a coin out of his pocket and tosses it, resulting in a tails. Then he tosses it again and covers it with his hand immediately after it falls.

What is the probability of getting heads?

What is the probability of tails?

 
alexeymosc:
My answer to the second part of the problem: 1/1025.
Uh-huh.
 
MetaDriver:

I understand your version. I stand by mine for now.

I have a counter task.

Two mega-brains are playing. The first one has two coins in his pocket. One of them is fair, the other has tails on both sides. Megamind randomly pulls a coin out of his pocket and tosses it, resulting in a tails. Then he tosses it again and covers it with his hand immediately after it falls.

What is the probability of getting heads?

What is the probability of tails?


P tails 0.833333
P heads 0.166667.
 
alexeymosc:

P Tails 0.833333
P heads 0.166667

Yes! // Grumpily: ... could have written down as simple fractions too....

But that wasn't the end of it. The mega-brains wondered what the probability was that the coin was honest, and how to tell if it was...

The first megabrain removed his hand covering the coin and... then reality recursively split into two instances.

In the first reality, the unnoticed megabrains found an eagle. They laughed and went for a beer.

But in the second reality (the other one?) two mega-brains discovered a tails. And started scratching their heads. ...

What are the odds that the coin is honest?

 
TheXpert:
It's very complicated in numbers here.

No, not really. But the diphurk is there. But on the fingers it is simple: there is a Torricelli formula, according to which water flows out of a thin hole at a speed proportional to the root of the height of the water column above.

This means that at the very end, when the water is low, it flows out at a low velocity, which will tend towards zero when the water column is zero nald.

On the other hand, there is an inflow from above (inflow) that flows in at a constant velocity greater than zero.

So there must be a pole at which the tidal velocity will be exactly equal to the tidal velocity.

I can rigorously justify it, if interested.

 
Mathemat:

But the difurcation is there.

I'm getting a decreasing exponent. i.e. not a Torricelli formula. Or am I missing something?

And in any case a margin of error has to be introduced, otherwise the drain is infinite in any case.

I can rigorously justify everything, if interested.

Interesting.

 
Mathemat:

Megamogg worked as a telephonist and one day he got a call from an office dispatcher asking him to find a buried cable. The cable was buried at a shallow depth in a straight line running exactly 5 km from where Megamogg was. Unfortunately, communication broke down and the dispatcher did not have time to clarify in which direction the cable ran. Megamogg has a metal detector that rings exactly above the cable. Can he plan his way in such a way that he is guaranteed to find the cable while walking no more than 32 km?

Just a drawing :)


 
TheXpert:

Just a drawing :)


aah, crooks, 32 is a clue ))

is it exactly 32 ?

 
MetaDriver:
The depth of the basin matters. You can't do it in numbers - there's not enough data.
It will work. Well, yes, some of the data will have to be fixed, but it doesn't affect the generality of the solution.