Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 91

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Mathemat:

That's great, thank you. I'll draw in it.

(3) In Brainiac, one in a thousand is born with superpowers. To detect them, every newborn is given a DNA test. There is a 1% chance of testing error. The son of Brainiac is recognised as superhuman. What are the odds that he isn't actually one?


Like one in a thousand is superfluous and doesn't count?
 
Mischek: like one in a thousand is excessive and doesn't count?
No, no, we do. It's quite a life-size problem with an unexpected answer.
 
Mathemat:

(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 necessary to guarantee the identification of the heavy balls?

Get two if successful or three if unsuccessful.
 
Mischek:
like one in a thousand is redundant and doesn't count?
It's a Bayesian theorem problem, for first-year students.)
 
Mathemat:

(5) The invaders once again put Megamind to the test. They stuck 30 flags in the ground in a big field and drew a circle with a radius of 100 metres. All Megamozg can do is choose a point on the circle from which to start the occupant runner. The runner runs at a speed of 10 metres per second. He should run out of the starting point, run to a flag, bring it to the starting point, run to the next flag, bring it to the starting point, etc. (pull flags out, drop them and turn around runner momentarily). If he manages to bring all flags to the starting point in 10 minutes, Megamozg gets shot. Can Megamozg always escape by choosing the correct starting point? The flags are stuck at different points.

I don't get it, are the flags stuck in a circle? inside a circle?
 
alsu:
I don't get it, are the flags inside the circle?
Flags can be placed anywhere on the field (both inside and outside the circle). The only restriction is that it is impossible to stick several flags in one point. ;)
 
ilunga:
Flags can be placed anywhere on the field (inside or outside the circle). The only restriction is that you cannot stick multiple flags at the same point. ;)
OK, it's even easier)))
 
alsu:
Okay, that's even easier)))

It's even easier to register on that website and solve problems there))

which I did =)

 
Mathemat:

(5) The invaders once again give Megamind a test. On a large field they stuck 30 flags in the ground and drew a circle with a radius of 100 meters. All Megamozg can do is choose a point on the circle from which to start the occupant runner. The runner runs at a speed of 10 metres per second. He should run out of the starting point, run to a flag, bring it to the starting point, run to the next flag, bring it to the starting point, etc. (pull flags out, drop them and turn around runner momentarily). If he manages to bring all flags to the starting point in 10 minutes, Megamozg gets shot. Can Megamozg always escape by choosing the correct starting point? The flags are stuck at different points.

Probably choose a point on a circle from which the distance to any flag is at least 100 metres.

The solution is probably the following: 10 minutes = 600 seconds, at 10 metres per second a runner can run 6000 metres, the distance to each flag consists of 2 identical segments (out and back), so 6000 metres divided by 2 gives 3000 metres, there are 30 flags on the pitch, so divide by 30 more and the distance from the starting point to each flag is 100 metres.

Something like this.

 
sergeev: It should be two for a good one or three for a bad one.

There should be one answer.

And alsu has to prove that it can't be less.

alsu:
I don't get it, are the flags stuck in a circle? inside a circle?
The occupiers are subtle. They can stick it any way they like. And the megamosque has to survive either way.
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