Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 217
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
At the end of the game there are three pictures left. Both players are tricky and are guaranteed to have a picture of three pictures: 1202 The second player is guaranteed to be framed. The second player will have no choice - he will have to take the small picture, and the big picture will go to the first one.
If the second one has already scored more than the first one by about 22 points, the first one loses.
The aim of the game is to get the sum not less than the opponent's (and preferably more - but that's as far as the map goes).
The whole game is when no one wants to open a pass to the opponent to the big picture. All the time the big picture is left "for later". And in this situation the second one will always lose.
No, not the whole game. The whole game is the whole line of numbers.
The numbers can be 1.22, 44.63, -1953.6666, 5.001, 3976452378454.4, 10^(9^7), 9^(11^7), etc. Any real numbers.
A regular N-gon is inscribed to the circle of unit radius. Find the product of lengths of all its diagonals drawn from one vertex (counting the adjacent sides).
The task is here. The weight is 5.
The answer is intuitively clear, if you calculate it for the first small values of N. The main thing is the reasoning.
Moderators of the resource claim that there is a school solution, but it is not nice. And there is a non-school solution, short and beautiful (I argue that), and I have already got it.
There is a glass aquarium with 20 litres of water on a perfectly smooth floor. At the bottom of the aquarium, under the water, there is a crab sleeping, with a density of 2 g/cm³ and a volume of 100 cm³. The crab wakes up and crawls towards the wall at a speed of 1 cm/s relative to the aquarium. At what speed will the aquarium move relative to the floor if the mass of the empty aquarium is 5 kg?
There. Weight - 5.
FAQ:
- you can assume that 20 litres of water have been poured into the aquarium and then the crab is lowered in.
- no perturbation of the water by the movement of the crab is relevant.
- there is no rough friction between the aquarium and the floor surface (the aquarium is on wheels).
- The crab crawls in a straight line passing through the centre of gravity of the bottom of the aquarium, so there is no rotational movement.
- here it is enough to give the answer in cm/s to the nearest 5 significant digits for me to know that the solution is correct.
- The weight of the problem is too high, the problem is simple: the correct application of the law of conservation of momentum (LCL) is enough. Well, you will have to do something with the crab :)
There. Weight - 5.
Why is the weight so high?
I don't know. I solved it on the second attempt, and that's because I made a mistake in applying FOA (not too much, less than 0.5%, but it was a qualitative difference).
Weight is calculated as a function of the ratio of people who solved the problem to those who saw it. It does not always correspond to the complexity of the problem. Here in this problem it must be because people prefer mathematics to physics.
I don't have any particular preference, but, say, the card games (pref, bridge, etc.) and chess problems there are not really to my liking.
A regular N-gon is inscribed to a circle of unit radius. Find the product of lengths of all its diagonals drawn from one vertex (counting adjacent sides).
The task is here. The weight is 5.
The answer is intuitively clear, if you calculate it for the first small values of N. The main thing is the justification.
Moderators of the resource state that there is a school solution, but it is not nice. And there is a non-school solution, short and beautiful (I argue that), and I have already got it.
I think the first step is to prove that the angle is 90 degrees:
On a perfectly smooth floor, there is a glass aquarium with 20 litres of water. At the bottom of the aquarium, a crab with a density of 2 g/cm³ and a volume of 100 cm³ sleeps underwater. The crab wakes up and crawls towards the wall at a speed of 1 cm/s relative to the aquarium. At what speed will the aquarium move relative to the floor if the mass of the empty aquarium is 5 kg?
Let it be 398e-5.