Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 136

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DmitriyN:
Find 100k and buy a ready-made solution. This is a problem in which it is not the process but the result of the solution that is interesting.
 
TheXpert:
Then that one rotates. Spit it out.

I wish. I thought the solution was simple, but it turns out to be more complicated. The moderator blew me off. Anyway, let's assume that both pucks move in a straight line. But the rotating one takes a longer "path" than the non-rotating one (even if the trajectories coincide). The points are moving in curves at the spun one.

Everything is solved with integrals, but I wish I could do without them...

P.S. By the way, the trolley problem was solved in the same way, by equations of motion. Asked for a clarifying question - and almost immediately accepted.

P.P.S. And more news: my variant at 60-epsilon meters in the chase was found correct. But we need to look further, as it's not the maximum.

Have you got an idea how to do it? I think you got to 50.

Here's what I think (spoiler): Allow the occupant to run into the forbidden (previously checked) corridor.

 
Mathemat:

If only. I thought the solution was simple, but it turns out to be more complicated. The moderator blew me off. In short, consider that both pucks move in a straight line. But the rotating one takes a longer "path" than the non-rotating one (even if the trajectories coincide). The points are moving in curves at the spinning one.

Without going into too much detail -- some of the spin is spent on overcoming friction. And only on one side. If to go into details, then... I don't know :) that's why I didn't answer.

Purely logically -- how can a puck with less energy travel a shorter distance? Although okay, maybe I found a counter-example. But that's not the case.

Have you got an idea how to do it? I think you've made it to 50.

Here's what I'm thinking (spoiler): Allow the occupant to run into the forbidden (previously checked) corridor.

I don't know about 60 either. I tried the spoiler, it didn't work.
 
TheXpert: Purely logically -- how can a puck with less energy travel a shorter distance? Okay, maybe I found a counterexample, though. But that's not the case.
Just screw the puck hard enough so that it stays in place. The energy is high and the distance will be small.
 
ilunga: 20 metres more.
I have even more coming out. But so far I've sent a solution to what you wrote earlier.
 

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.

 
Mathemat:

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.

Interesting. It seems to me that a compressive mapping should be constructed here, by Banach's theorem it should have a fixed point. Thus, if such a mapping exists, the problem is solved automatically.
 
DmitriyN:

Task: Find the lowest: power (kW), capacity (l/min) and generated pressure (kg/cm^2) of the pump that provides this hanging in the air.
The weight of the hose, the friction losses of the water in the hose, the efficiency of the pump - do not take into account. Let the mass of a man with his equipment on him be 100 kg.

F=G*v, -the force created by the water jet, where G-flow rate, v-velocity of ejection.

Thus:

(kg/s)*(m/s)=(m/(s*s))*kg - units,

G*v=9.81*100

Which parameter is fixed in the task? Flow rate or speed?

 
joo:

Which indicator is fixed in the task? Consumption or speed?

Let it be flow rate. F=G*v is a strange formula :(.
 
DmitriyN:
Let there be a flow rate. F=G*v - that's a weird formula :(.

What does 'Let there be a flow rate' mean? And what is it, the flow rate? :)

Let there be a flow rate of 10 g/s, then:

0,010*v=9,81*100

v=9,81*100/0,010;

v=9.81*100/0.010=98100 m/s.

How it is! It is 353160 km/h.

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