Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 40

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ilunga:
In the first approximation, the capacity of the tank should be at least as large as to cover the maximum distance between the drums
In the last approximation, too. And if this condition is fulfilled, the route is possible in any direction. (Only you may have to start from different barrels).
 
MetaDriver:
In the last one too. And if this condition is fulfilled, it is possible to run the route in any direction. (Only you may have to start from different barrels).

No. That's not good enough! I can give you an example....

You need a minimum distance too !

 
... and as the maximum section without barrels can be made as close as possible to the length of the circle, the tank must hold exactly 100 litres, no more, no less, to guarantee passage through it.
 
Manov:

No. That's not good enough! I can give you an example....

Come on.


You also need a minimum distance !

Give me an example first, then we'll see.
 
alsu:

... And since the maximum section without barrels can be made as close as possible to the length of the circle, the tank must hold exactly 100 litres, no more, no less, to guarantee passage through it.

For a guaranteed "in all cases", yes.

It's interesting to check Manov's claim that there could be an arrangement where passage is only possible in one direction. (With a limitation on tank size < 100)

 
MetaDriver:
Come on.


Give us an example first, then we'll see.

Tank capacity =30 litres. You can do 31, 32.

 
Manov:

Tank capacity =30 litres. You could do 31, 32.

Yep, convinced. Capacity must be at least Max+Min.

However, this example is symmetrical. If the condition (Max+Min) is met, passage is possible in both directions.

What about the "one-pass" example?

 
Manov:

Tank capacity =30 litres. Can also be 31, 32

Start at point 25. Reach the next 25, fill up (tank capacity 40). Pass 15 km, fill up 10 (tank 35). Pass 30, fill up 30 (35 in the tank). Pass 30, fill up 10 (in the tank 15).Pass the remaining 15 km. Reverse direction in the same way.
 
Mathemat:

I wanted to do the same at first, but then I got carried away))
 
Mathemat:

I haven't considered the other options that have now come out, but I'll post my decision nonetheless:

A: It is possible, in any direction.

.............................

The new MegaFunction will immediately start with a big jump at zero (30L) and will obviously be no lower than zero everywhere.

Please note that the driving direction hasn't changed, and it doesn't have to. It is sufficient to choose the starting point of the graph correctly and drive from it.


Yep, beautiful.

Obviously a cyclist can start in both directions with a similar result (finding the right start). Although the starting point might be different.

The question arises: Is it possible for the minimum to be different in magnitude, moving in different directions?

The answer would shed light on the possibility that a "nipple" exists, in the form of a tank size constraint (Min1 < V tank < Min2).

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