Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 92

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Mathemat:
The occupiers are subtle. They can stick it any way they like. And a megamosque has to survive either way.
The occupiers have planted a flag four kilometres from the nearest point on the circumference. Ah, phew, he's not gonna make it.
 
TheXpert: The occupiers stuck a flag 4km from the nearest point of the circle.
They can be sophisticated at anything but stupidity.
 
Mathemat:
And megamozk must survive in any case.

Not necessarily.

The question is about can Megamogs always be saved by choosing the right starting point?

I mean, it's accepted that it might not save itself.

The problem is to find the maximum sum of distances, so that it is not less than 6 km.

 
sergeev: i.e. it is accepted that it may not be able to survive.
I haven't yet encountered any tasks in which a megamosk could not survive.
 
Mathemat:
I haven't yet encountered a problem where a megamosk can't survive.
But a question is a question. you're not going to prove that he'll be saved in any case and always.
 
sergeev: But a question is a question. you are not going to prove that he will be saved anyway and always.
That is exactly the very first hypothesis I would start proving. The loss of the megamosk is irretrievable.
 

(4) There are 2 blue, 2 red and 2 green balloons. In each colour, one of the balloons is heavier than the other. All the lighter balls have the same weight and all the heavier ones have the same weight. There are also scales with two cups without weights. How many weighings are minimally needed to guarantee that the heavy balls are determined?

I may be wrong but I think 3 ! First we measure two balls of the same colour to find the heavy one! Then we take the heavy ball and measure with any ball of another colour - if the other ball is balanced then it is heavy if it is light !
 
verybest:
I may be wrong but I think 3 ! First we measure two balls of the same colour to identify the heavy one! Then we take the heavy ball and measure with any ball of another colour - if the other ball is balanced then it is heavy if it yields then it is light !

If three, why bother :))) measure each colour in pairs. that's exactly three times.

 
Mathemat:
I've yet to see a task in which a megamosk could not survive.
For example, when they put coloured hubcaps on them and put them in a column, not everyone survived there
 
Mathemat:
The occupiers are subtle. They can stick it any way they like. And the megamosque has to survive whatever it takes.
In short, roughly speaking, the task comes down to proving the fact that the centre of "mass" of the flags can always be approached closer than the points where they are located.
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