Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 141
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
(4) The Megabrain biologist has a 10 cm long stick on which he puts ants and watches them. The ants can only run along it along its length (left or right); when they reach the end, they fall down. When two ants collide, they both immediately turn around and run in opposite directions. The stick is narrow and ants cannot go around each other without colliding. The ant's speed is 1 cm per second, the ants are moving all the time. After what minimum time is the stick guaranteed to be without ants? The initial number of ants, their positions and directions of movement can be any. The length of the ants can be neglected (considered equal to zero).
I won't even cover it with colour.
In fact, since all ants are indistinguishable from each other, we can equivalently transform the problem by assuming that the insects do not collide and turn around, but simply pass through each other like ghosts, without noticing the obstacle. Then the answer is also obvious - the time for the last of the ants to be guaranteed to reach the edge and fall does not exceed 10cm:1cm/s=10 seconds (equality is achieved if it is at the edge and crawls to the opposite edge).
alsu:
Actually, since all ants are indistinguishable from each other, we can equivalently transform the problem by considering that insects do not collide and turn around, but simply pass through each other like ghosts without noticing the obstacle.
:)
OK, yeah.
Scan
Heehee
Notebook costs 26 roubles. 50 kopecks. Now try to prove otherwise.
Hee
The correct answer is: "The whole set of positive numbers".
Another mind-boggling task about megamooks and invaders:
(5) A hundred megabrains had caps with numbers from the range 1...100 put on their heads, not necessarily different for everyone. For example, all of them may be given a cap with number 7, or half of them may be given a cap with number 20, and the other half with number 10. The main thing is not less than 1 and not more than 100. After that they were all put in a circle. Each megabrain sees 99 numbers on the heads of the others, but not his own. After that everyone writes a number from 1 to 100 on a piece of paper - the supposed number on his/her cap. Communicating and peeping is not allowed ;) They will all be let go if at least one guesses their number. What strategy should they follow if they want to be guaranteed to be let go? (The mega-brains could have agreed on a strategy beforehand).
Comment: once they've been hooded (consider it instantaneous), the megamoskis don't pass any information to each other. They just watch and count and then write their numbers.
it looks like the strategy will be as follows:
The first must look at the others and write the minimum number which they do not have.
The second should look at the others and write the minimum number they have.
The third should write the second smallest number that the others don't have.
The fourth should write the second smallest number the others have.
etc. The odd ones write what the others do not have, and the even ones write what they do have.
I can't give the strictest justification, but for the case when there are 2, 3, 4 MM, it works.
For example, there are 2 MM and they have a 0 or 1 written on their heads. The first one says the number that the second one doesn't have, and the second one says the number that the first one doesn't have. And one is bound to guess.
Here are all possible options and what they will write this strategy: 00->10, 01->00, 10->11, 11->01. Ie ustoyu guess one
But here everything is simple because there are 2 options: either the same or different numbers and check both of these options we are in the jam))
Comrade mathematicians, isn't it time to start applying your knowledge for the good of humanity?
Comrade sergeant practitioner!
We're ready to hear from you with problems that are worth our modest impractical knowledge.
Comrade sergeant practitioner!
We're ready to hear from you with tasks that are worth our modest impractical knowledge.
You've got to be kidding me. ))
He'll tell you. You can clean up the thread later.
That's one you should have fallen for. ))
He'll tell you. You can clean up the thread later.
What did you want? It was a test :), a test, so to speak. You didn't solve any of my problems. I looked up the meaning of the word "sermiyazhny" in the wiki dictionary and didn't understand anything, I guess I'm not poor.
So, have fun without me, I have another niche - I do things that pay money :) And note that it has nothing to do with mathematics, alas, today and tomorrow it is little needed in our country.
Yeah, I get it - you do things that few people want, but you get paid to do them. It has nothing to do with maths.
I'll think about it.
first option - are you spamming or something?