Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 188

[Aleksey Lebedev]

Mathemat:

6*3^7 = 13122 m/s.

I.e. reacts to seven events - three baby claps (twice for each) and once for the fourth.

How about applause at first, then we start this frantic device and *four more claps? :)

[Sceptic Philozoff]

Swan:
How about applause first, then we launch this frantic device and *four more claps? :)

I see.

The child starts clapping when the Megapuzz is already in the sky.

The bird recognises the clap and instantly speeds up. Then it analyses the incoming sound stream after the clap that accelerated it. And so on.

[Vladimir Gomonov]

Mathemat:

Explain in a human way how you did it. I will make an analysis and check it. I don't believe it, it's like a miracle.

You hinted a couple of pages ago, but in your own style, very briefly. I still don't understand what it is.

......

In short, state exactly what you did there in the left pair of columns.

There you go! I thought you understood it a long time ago, you just weren't interested... The essence of the trick: divide BOTH drinks into small doses, then build a queue from each set of doses and run these queues towards each other. Each dose of tea eventually exchanges temperature with each dose of coffee, and the order of contacts is reciprocal. I was afraid that it would be difficult to program, then I thought about the scheme and it turned out to be elementary - two nested loops completely simulate the scheme of reciprocal exchange.Explanation: it is enough to focus on the interchange sequence of any one dose to notice that the queues do not have to contact in "parallel" mode - it is quite possible to pull all doses of the first queue through contact with the first dose of the second queue, then again all doses of the first queue through contact with the second dose of the second queue .. and so on until the list is exhausted, with all single contacts occurring in exactly the same order as in "counter-parallel" queue movement. Here is the text on the mcl:

   // ***** считаем теплообмен *****
   double sVol = TeaPart.v + CoffeePart.v; // суммарный объём частей (чтоб не считать в цикле)
   for(int i=0;i<n1;i++)
     {
      for(int j=0;j<n2;j++)
        {
         TeaParts[i].t = CoffeeParts[j].t =
           ( TeaParts[i].t * TeaPart.v + CoffeeParts[j].t * CoffeePart.v ) / sVol;
        }
     }

If it is still not clear - ask exactly what, I will explain. It is clear to me, but whether I have explained it clearly I do not know.

Well, now I can probably explain why I got hooked on this problem in the first place - because of this very "chud". I have been amazed by counter heat exchangers based on the same principle, only in continuous mode, of course.The essence of the device is two thin (or not so thin) tubes soldered together, with opposite flows of liquids of different temperatures (in general case the liquids are different), tubes are naturally long enough, for compactness rolled up into a roll or spiral or whatever. The effect is similar - almost complete exchange of temperatures (real devices of course have lower efficiency than the ideal ones).In this problem I saw an opportunity to "feel" (to simulate) the device, what exactly I have done. And, by the way, the variant with different initial volumes of two liquids, in fact easy hand movement is transformed into variant with different heat capacities of liquids (well or it is possible to add one more variable-multiplier to the list of parameters).In short - numerical model is complete enough and I have understood it thoroughly in course of the case, what I wanted. And I will explain some additional considerations. Firstly, the problem can be generalized to mutual exchange of any resources (not only temperature), provided "exchange through averaging" (it is the main idea of the problem, right?). Secondly, I'm seeing all sorts of curious indicators for trading, which can be invented on the basis of similar interaction between data sets. However, in this thread it is an off topic, so I will not continue either.

Mathemat:
The gunpowder isn't great, it's almost damp. Here is a screenshot of how I calculated this formula with e. Took me about three hours to do it, and I got it on about the fifth try...

If you want to have a look at it, I'll be glad if you do - and in case you'll get interested again...

[Sceptic Philozoff]

MetaDriver:

There you go! I thought you understood it a long time ago, you just weren't interested... The essence of the trick: we divide BOTH drinks into small doses, then build a queue from each set of doses and run these queues towards each other...

...

// In case you're interested again after my previous explanations...

You've convinced me, it's very effective.

I'm going to try and get a feel for this particular miracle, but not necessarily today.

It's one thing to write a few dozens of lines of code and run the iron for calculation (computer is iron, won't break), and another thing to do it analytically.

[Vladimir Gomonov]

Mathemat:

I'm convinced, it's very effective.

I'll try to try this particular miracle, but not necessarily today.

One thing is to write a few dozens of lines of code and run the iron to calculate (the computer is iron, it will not break), another thing is to calculate it analytically.

OK !

An additional incentive can be formulated: with accurate analytical formulas, the effectiveness (efficiency) of the exchange of resources can be strictly dosed (in the settings, for example, indicator).

[Sceptic Philozoff]

MetaDriver:

An additional incentive can be formulated: with accurate analytical formulas, the efficiency of resource exchange can be strictly dosed (in the settings of an indicator, for example).

There was already a problem with accurate analytical formulas in the previous case. Well you have seen my screenshot.

Yes, when going to the limit, everything comes out nice and tip-top.

OK, morally preparing for a forgiveness.

[Vladimir Gomonov]

[Sceptic Philozoff]

Another problem:

Is it possible to place three white kings and five black queens on a 5x5 board so that white is not under check?

The weight is 4.

I'll post a couple more in the evening.

[Vladimir Karputov]

Mathemat:

Another problem:

Is it possible to place three white kings and five black queens on a 5x5 board so that white is not under check?

The weight is 4.

I'll post a couple more in the evening.

I'll reply to you in person. Let's wait for the results.

[Sceptic Philozoff]

Another one:

There are 2,000 balls that look the same, half of which are aluminium and half are dural. Balls of the same material weigh the same, balls of different materials weigh differently. What minimum number of weighings on a cup scale will be needed to ensure the formation of two groups of different weight from the same number of balls?

The weight is 4.

FAQ:

- The scales are cup scales, infinitely accurate, there are no weights. Weighing is putting something on both bowls, looking at the balance, remembering the result and removing the contents from the bowls,

- Wiki says that the density of dural is about equal to that of aluminium. For this problem, it's enough to assume that it's just different from the density of aluminium,

- In formed groups of different weights of the same number of balls there can be any number of balls, even one at a time,

- proving the minimum number of weights is necessary - unless, of course, you've managed for the minimum possible number of weights.