Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 218
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Well, it's only a 12-gon. We need a solution for arbitrary N.
Inaccurate. And I asked for 5 significant digits, not 3.
P.S. I first published an answer giving exactly that figure. It was not accepted. Thought a little more, specified physics of process and wrote correct solution.
Well, it's only a 12-gon. We need a solution for arbitrary N.
It is not exact. And I asked for 5 significant digits, not 3.
P.S. I first posted an answer giving exactly that figure. It was not accepted. I thought a little more, refined the physics of the process and wrote a correct solution.
I've looked over everything, considered various possible theories regarding the process, and this time the answer is 0.00400000 m/s.
Alas, that's not accurate either. And the unit of measure is more like cm/s.
If you want - write to me in a private message about the main assumptions.
The process itself is very simple: the total momentum of the system is zero. But it is what you will do with the crab that I am most interested in.
Mathemat:
A regular N-gon is inscribed into a circle of unit radius. Find the product of the lengths of all its diagonals drawn from one vertex (counting the adjacent sides).
Here we have the following formula: (2R)^(N-1) * sin(180/N) * P(sin(M *180/N)), m from 1 to N-2, and P is the product of range of values.
the formula comes out like this: (2R)^(N-1) * sin(180/N) * P(sin(M *180/N)), m from 1 to N-2, and P is the product of the range of values.
The final expression is extremely simple and does not contain any P symbols. Try to simplify the formula.
By the way, the radius of the circle is known, it is 1.
A monorail tram runs between points A and B on a single paved track at a constant speed. The tram can pick up or drop off a passenger at any point on the route as desired, without wasting time or losing speed. At some arbitrary moment of time a passenger approaches an arbitrary point on the rail, wishing to go to another arbitrary point on the tram route. Prove that on the first passing by the passenger the tram is likely to go in a different direction than the passenger wants to go. Find the exact value of the probability of this event.
The weight is 4, the problem is here.
FAQ (moderator's quote):
Как и во всех других задачах на вероятности, вопрос в этой задаче можно переформулировать через клонирование миров:
Представьте, что вы создали много-много идентичных миров. В каждом мире вы как создатель случайным образом выбираете конкретную ситуацию из множества, описанного в задаче. Сначала с помощью генератора случайных чисел (есть на предусмотрительно купленном вами в магазине калькуляторе) вы выбираете время, когда придет пассажир. Затем, еще раз запуская генератор, выбираете положение пассажира на маршруте. Затем точно так же выбираете точку на маршруте, в которую хочет попасть ваш пассажир. И.... ждете первой встречи пассажира с трамваем.
Вопрос в том, в каком проценте миров пассажир испытает разочарование при первой встрече с трамваем, если число созданных миров устремить к бесконечности.
Megabrain is imprisoned and told that he can only get out of here if he can open the doors. The doors are opened with the following device: there is a "cube" in front of the entrance, with holes made on each side on four sides. There is a lever in each hole. The levers do not stick out of the holes but are hidden in recesses, i.e. the position of the levers is not visible. The levers can go up and down. The doors open when all four levers are either raised up or lowered down. Megamind can put his hand or both hands into the recesses and then manipulate the levers (raise, lower, do not change position). Then he has to take his hands out of the recesses. As soon as the hands are taken out, the parallelepiped automatically untwists, and once it stops, it is impossible to tell where the hands were put in. Water is poured into the prison, it will flood the cell in 10 minutes, the parallelepiped twists for exactly one minute. How does Megamind escape?
Weight is 4. The task here.
FAQ:
- The parallelepiped can be replaced by an ordinary drum. Megamozg looks at this drum, in which there are 4 holes, in which the levers are hidden (he can't see their positions until he sticks his hands in them)
- hands can only be inserted at one time and only into two holes. It is forbidden to change the holes during one manipulation.
Megabrain is imprisoned and told that he can only get out of here if he can open the doors. The doors are opened with the following device: there is a "cube" in front of the entrance, with holes made on each side on four sides. There is a lever in each hole. The levers do not stick out of the holes but are hidden in recesses, i.e. the position of the levers is not visible. The levers can go up and down. The doors open when all four levers are either raised up or lowered down. Megamind can put his hand or both hands into the recesses and then manipulate the levers (raise, lower, do not change position). Then he has to take his hands out of the recesses. As soon as the hands are taken out, the parallelepiped automatically untwists, and once it stops, it is impossible to tell where the hands were put in. Water is poured into the prison, it will flood the cell in 10 minutes, the parallelepiped twists for exactly one minute. How does Megamind escape?
Weight is 4. The task here.
FAQ:
- The parallelepiped can be replaced by an ordinary drum. Megamozg looks at this drum, which has 4 holes in which the levers are hidden (he can't see their positions until he sticks his hands in them)
- Hands can only be inserted into two holes at the same time. It is forbidden to change holes during one manipulation.
1. Insert your hands into the two opposite holes.
2. levers put in the same position say down, if the other two levers are also down then the door opens.
3. After scrolling we go to point 1.
judging by the history of posts in this thread Megamog brains lucky man and got out of various trouble, I think he will be lucky here with a probability 0.9 )
S.O.S.: although I may not have counted correctly
1. put your hands in the two opposite holes
2. levers put in the same position, say down, if the other two levers are also down then the door opens.
3. After scrolling, we go to point 1.
Judging by the history of posts in this branch of megamogz fartitelny man and got out of various trouble, I think here he will be lucky with a probability 0.9 )
ZS: although the probability I have not counted correctly.
There are no probabilities here.
You need a logical sequence that, in no more than 10 steps , is guaranteed to lead the megamosk to open the doors. No special knowledge required, and the task is completely honest, with no pitfalls.
Of course, he is a lucky guy, but his luck is 100 percent due to his brain and not to his luck.
A monorail tram runs between points A and B on a single paved track at a constant speed. The tram can pick up or drop off a passenger at any point on the route as desired, without spending any time or losing speed. At some arbitrary moment of time a passenger approaches an arbitrary point on the rail, wishing to go to another arbitrary point on the tram route. Prove that on the first passing by the passenger the tram is likely to go in a different direction than the passenger wants to go. Find the exact value of the probability of this event.
Weight is 4, the problem is here.