Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 137

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Mathemat:

Another disastrous task about megamoves and invaders:

(5) One hundred megamots...

A disastrous one for the solvers... ) The worst thing is that it is absolutely useless for the poor MMs to look at each other's hubcaps: the plane of 99x100 variants that they see does not bear any information about their own number. Well, is it possible to try to understand something by the expression of the co-cap's gyrations?
 
joo:
Let the flow rate be 10 l/sec.
 
DmitriyN:
Let the flow rate be 10 l/sec.
OK. What is the cross sectional area of the nozzle?
 
joo:
OK. What is the cross-sectional area of the nozzle?
Let it be 1 square centimetre.
 
muallch: (It's a bit of a disastrous one for solvers.... )

As usual, the occupiers don't give the megamoskas any peace.

The worst thing is that looking at each other's hubcaps by the poor MMs is totally useless

Now, that's not obvious. Problem Doesn't involve any of them recognising their own number at all.

Alsu : Interesting. It seems to me that here we need to build a compressive mapping, by Banach's theorem it should have a fixed point. So if such a mapping exists, the problem is solved automatically.

You're the strong one. I've been thinking about this for quite some time too. But such strong stuff isn't necessary here.

P.S. As far as I understand, my "mapping" is not compressive. But I'm not too strong in upper algebra, so I could be wrong here.

Anyway, I haven't used this theorem in any way.

 

Mathemat:

This, however, is not obvious. Task does not at all suggest that any of them would recognise their own number.

Of course. The assumption is that MMs will agree on some algorithm for choosing a number for each, so that at least one of them will have that number in common with the Kolpakov number. And if there is no relationship of Kolpakovskie and contractual arrays, then MM need not see these Kolpakovskie numbers in the cellmates. Let them stand with their brains against each other! MM needs to come up with an unambiguous solution, i.e. essentially assign in advance who writes what number.
 
muallch: And if there is no correlation between Kolpak and contractual arrays, then there is no need for MM to see those Kolpak numbers in the cellmates.

Your "logical" conclusion is illogical. In my solution (credited) there is such a need, oddly enough.

Response:


 
Mathemat 2012.09.19 11:43 2012.09.19 11:43:00 #
Response:

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First you write: "The sum of all the numbers f(n) on the caps modulo 100 is some So", and then "since the numbers n enumerate the whole range from 0 to 99, and their sum modulo 100(So)...".

However, there is a discrepancy: in one case So is the sum (modulo 100) of all numbers in caps, and in the other case it is the sum (modulo 100) of all numbers in the range 0...99 (which, by the way, is defined and is a constant value of 50)
 
Contender:
Mathemat 2012.09.19 11:43 2012.09.19 11:43:00 #
Answer:

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First you write: "The sum of all numbers f(n) on caps modulo 100 is some So", and then "since numbers n list the whole range from 0 to 99, and their sum modulo 100(So)...".

However, there is a discrepancy: in one case So is the sum (modulo 100) of all the numbers on the caps, and in the other it is the sum (modulo 100) of all the numbers in the range 0...99 (which, by the way, is defined and is a constant value of 50)

Mathemat writes a little differently, read it carefully.

In brief and without numbers:

1) reduce all numbers on the caps by 1.

2) then the sum of all hundred numbers taken modulo 100 has value from 0 to 99

3) Each megabrain (from the first to the hundredth, as they agreed) assumes that the modulus of the sum is equal to the corresponding number (from 0 to 99). He sees 99 numbers and comes up with the hundredth (in his head) so as to get the required sum modulo. And one (and by the way only one) guesses in this way

 
ilunga 2012.09.21 13:12 2012.09.21 13:12:04 #
Mathemat wrote a little different, read carefully.

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I wrote that there is an error in the evidence because there is a substitution (So substituted)
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