Pure maths, physics, chemistry, etc.: brain-training tasks that have nothing to do with trade [Part 2] - page 15
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There is no relationship in the task given by alexeymosc. And instead of envelopes there is paper.
Yes, the problem is similar to one of the variants of the paradox of the two envelopes. The difference is that in the paradox one of the numbers is twice bigger than the other. Also, in the original paradox, the player doesn't see the number. I'm alarmed by the range from minus to plus infinity. With this formulation, the probability of any number is zero? And, in the absence of restrictions on the number above and below, it intuitively appears that the second number could be any number...
Stupid task, I don't like it. It smacks of trying to get the "client" to suck a non-existent paradox out of his hand. The most sensible answer in this fucked-up situation is: all other things being equal (same size of paper and font), if the paper is full of numbers, the larger positive number (if the comma inside the number is randomly distributed) will fit on the paper, because the minus sign, which requires space for writing, will steal one space from the set of negative numbers. So the preponderance of the set of positive numbers can be considered proved. Note the correct answer: one should always count on the fact that the number on the second piece of paper is bigger. And indeed, it's good where we're not!
;=)
Here's another simple one (3 points):
Megabrain needs to weigh a ruby urgently. He goes to the jewellers. But the first one says that his "roof" didn't balance the cup scales by making different shoulders. But he vouches for the correctness of the weights.
The second says that his "roof" made the scales absolutely accurate, with equal shoulders, but it modified the weights slightly.
Megamogg asks for the weights from the first and wants to weigh the ruby from the second, but... competitors are competitors: they refuse him. What did Megamogg do?
Comment: MM didn't buy anything, everything was done without money, purely by the power of thought.Actually, there is a solution to the chessboard :-) I proved to my 5th grade maths teacher with a protractor in hand that the sum of the sides of a triangle is NOT equal to 180 degrees...
and from the same area you can also solve with a chessboard....
No - I just had a ball like a tennis ball :-) I was crushing my fingers instead of an impact ball...
the triangle drawn on it does not have angles equal to 180 degrees :-) she said it is relevant to the topic.... that's the theme to solve the board :-)
By the way, about the two numbers on paper problem: I solved it at the beginning for a bounded segment. But the solution does not depend on its length. That's why I extended the segment to the whole real region. Haven't looked at it yet, so I don't know if it's correct or not.
Aleksander: вот этой темой и можно решить доску :-)вот этой темой и можно решить доску :-)
I doubt that geometry helps much here - especially non-Euclidean one :)
I once proved to a 5th grade maths teacher with a protractor in my hand that the sum of the sides of a triangle is NOT equal to 180 degrees...
Young man, the sides of a triangle are not measured in degrees!
Here's another simple one (3 points):
Megabrain needs to weigh a ruby urgently. He goes to the jewellers. But the first one says that his cup scales are not balanced (different shoulders), but he vouches for the correctness of the weights. The second one says that his scales are absolutely accurate, but he can't vouch for the weights. Megamizg asked for the weights from the first one and wanted to weigh the ruby from the second one, but... competitors are competitors: they refused him. What did Megamogg do?
Comment: MM didn't buy anything, everything was done without money, purely by the power of thought.It seems to me that you can get by with just one scale - with the right weights and different shoulders