Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 147

 
Шесть мегамозгов входят в совет директоров компании, которая получила прибыль в виде 100 акций стоимостью 1 млн. долларов каждая. Среди директоров есть линейная иерархия: от самого главного до самого "младшего". Прибыль делится следующим образом: главный директор предлагает, кому сколько дать акций, потом каждый голосует, "за" или "против". Если по меньшей мере половина директоров проголосует "за", они поделят акции так, как предложил главный, если же нет — главный мегамозг исключается из совета директоров, главным становится следующий по иерархии и делёжка начинается с начала по тому же принципу. Процесс продолжается до тех пор, пока какой-то план не будет принят. Как должен предложить разделить 100 акций главный мегамозг, чтобы получить максимальную прибыль? (Все мегамозги жадные, мыслят очень логично, и никто не хочет терять место в совете директоров).

In my opinion, all brains benefit from removing as many brains as possible, and since you need at least half of the votes, you will end up with 2 brains left, the main one will get all of them.

5 eliminate 1=>4

3 exclude 1=>3

2 exclude 1=>2

and of these two, the main one takes all, as his FA is equal to half

 
lazarev-d-m:

In my opinion, all brains benefit from removing as many brains as possible, and since you need at least half of the votes, you will end up with 2 brains left, the main one will get all of them.

5 eliminate 1=>4

3 exclude 1=>3

2 exclude 1=>2

and of those two, the main one takes all because his FA is half.

You have misunderstood the condition.

Main(most important of six) must be offered an option that excludes reduction of directors, because he will be the first to leave if they vote against.

The idea of bringing the task to two is correct, but unfortunately not elaborated enough by you.

It seems to me unlikely, because you can get cubes in the final result if you divide the cube in half on all axes, otherwise you will get cubes and parallelepipeds.
You need a sufficiently rigorous justification, and yours is too vague.
 

The next one just counted:

(4) On the eve of Mega Brain Day, the administrator of the Mind Games club sent out the following message to ten randomly selected participants: "The site administration notifies you and nine other participants that each of you will receive a cash prize (the same for all), but on the condition that one of you (and only one!) sends a reply message within a week. After receiving the message, the nominees do not communicate with each other. What should they do to maximise their chances of winning prizes?

 

Шесть мегамозгов входят в совет директоров компании, которая получила прибыль в виде 100 акций стоимостью 1 млн. долларов каждая. Среди директоров есть линейная иерархия: от самого главного до самого "младшего". Прибыль делится следующим образом: главный директор предлагает, кому сколько дать акций, потом каждый голосует, "за" или "против". Если по меньшей мере половина директоров проголосует "за", они поделят акции так, как предложил главный, если же нет — главный мегамозг исключается из совета директоров, главным становится следующий по иерархии и делёжка начинается с начала по тому же принципу. Процесс продолжается до тех пор, пока какой-то план не будет принят. Как должен предложить разделить 100 акций главный мегамозг, чтобы получить максимальную прибыль? (Все мегамозги жадные, мыслят очень логично, и никто не хочет терять место в совете директоров).

Another option would be to

1) In order to stay "in power", the main brain has to persuade 2 more people to vote for it.

2) It is necessary to offer better conditions than if we had to divide the same amount of shares, only five of us.

3) therefore it is necessary to give 98 shares to the first, one share to the second and one share to the last, because the next brain after the main brain is in the same precarious position, so the distribution is necessary, for the main (1) - 98 shares, the next (2) - 1 share, (6) - 1 share.

The second in this situation also maximizes the profit, because he will also have to distribute the finances (3 for, 2 against), or he will be excluded altogether.

The latter is in favour of any profit greater than zero, because if there are two of them, the main one will take all the profits

 
lazarev-d-m:

Another option would be to

1) in order to stay "in power", the main brain has to persuade 2 more people to vote in favour.

2) Better conditions have to be proposed than if the five had to divide it in the same way

Your reasoning is logical, and your option is close to the exact result.

The answer is the only one, there are no other options at all. Suggest the exact scheme without ambiguities at all: a1, a2, a3, a4, a5, a6.

 
MetaDriver:

This is the text of a C program. Find three ways to change one character in it so that the program prints 20 asterisks. To change means not to add, remove, or rearrange, but to change it.

main() { int i, N=20; for (i = 0 ; i < N ; i--) { printf("*"); } }


--

I found one way. :) I need two more.

main() { int i, N=20; for (i = 0 ; i < N ; N--) { printf("*"); } }
main() { int i, N=20; for (i = 0 ;-i < N ; i--) { printf("*"); } }
main() { int i, N=20; for (i = 0 ; i + N ; i--) { printf("*"); } }
 
Contender:

Yes, the third way is the most unobvious - if one does not know that an expression in C always has a meaning, including logical. But this is the one that I immediately thought of.
 
DmitriyN:

Near our planet there is (hypothetically) some planet shown in the figure below. We know the diameter of this planet, let it be D. We need to find the distance L from the surface of the Earth to the surface of this planet using the figure.
Assume that the picture was taken with this camera.

The data are insufficient. And it's not clear what kind of data we need here. The magnification of the machine, for example. I personally have no desire to get into the maze of very specific optics made by Canon to figure it out. But someone might like it.

If there were the moon next to it in the picture, the answer would be very simple.

Given oxygen cylinder

Do the math yourself, Dima. It's not a pure physics problem. Can you calculate the speed of the oxygen jet and the flow of oxygen from the hole?

 
DmitriyN:

We'll assume the photo was taken with this XXX camera.

You're playing with fire, Dima. Advertising is strictly prohibited on this site, violators can get an eternal ban. And we're so used to your nickname... Better not.
 
DmitriyN:

A physics, mathematics and astronomy problem.

There is a planet near our planet (hypothetically) shown in the figure below. We know the diameter of this planet, let it be D. We have to find the distance L from the Earth's surface to the surface of the planet using the picture.
Assume that the picture was taken with the XXX camera.

All objects on the "photo" (except for the sought planet) have fractal structure, so it is impossible to detect (calculate) their absolute sizes. The conclusion is simple: the problem is unsolvable, because there are no objects comparing the size of the planet with which the distance could be calculated. Knowledge of the camera model will not help, can only do harm (see post above).
Reason: