Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 39

 

I have this solution.

Let us fix the direction of traversal and consider the following operation.

1.Choose a barrel A, which has more gasoline than the amount needed to get to the next barrel. If there is no such barrel, the route is trivial - the algorithm is complete. We mentally move the next barrel B in the route direction by such a distance that there is exactly enough gasoline in barrel A to reach barrel B. Obviously, the route properties (its passability) do not change, but only one thing changes - the number of possible choices of barrel A decreases by 1 (or does not change).

2. Repeat operation 1 as long as it is possible. We obtain an equivalent route in which there is exactly enough gasoline in each barrel to cover the distance to the next one. Consequently, the original route is also passable.

 
alsu:

I have this solution.

Let us fix the direction of the detour and consider the following operation.

1.Choose a barrel A, which has more gasoline than the amount needed to get to the next barrel. If there is no such barrel, the route is trivial - the algorithm is complete. Let us mentally move the next barrel B in the direction of the route at such a distance that there is exactly enough gasoline in barrel A to reach barrel B. Obviously, the route properties (its passability) do not change, but only one thing changes - the number of possible choices of barrel A decreased by 1.

2. Repeat operation 1 as long as it is possible. We obtain an equivalent route in which there is exactly enough gasoline in each barrel to cover the distance to the next one. Consequently, the original route is also passable.

Yeah, that's an option, too. Score.
 
Mathemat:

There is a 100 km long ring road on which a finite number of fuel barrels are randomly scattered. The total amount of fuel in the barrels is 100 litres, but the distribution of fuel across the barrels is arbitrary. A car has a fuel consumption of 1 litre/km and an empty tank with a capacity of more than 100 litres. Is it possible to bypass the entire road in any direction?

Note: the car is from the occupiers, like "Fuck fuel economy!

Look for an elegant solution. Elegant has no physical limitations, but there's an invariant suitable for any, including physical.

More interesting variant, if tank capacity (per car) is about 50l. (or 75l.) Of course, tonnage of tanks is less than tank's capacity.

Intuition says that one can drive in one direction only, but the proof does not work out....

It's possible and unresolvable.....

 
Manov:

More interesting if the tank capacity (per vehicle) is around 50l. (or 75l.) Of course, the capacity of the drums is less than the capacity of the tank.

Intuition says that it is possible to drive all the way around in one direction only, but the proof does not work out....

It's possible and unresolvable.....

Then it may be impossible to pass at all.

A trivial example - three 30-litre barrels very, very close together (say, on 1/10th of a circle).

 
ilunga:

Then it can happen that it is not possible to drive at all

A trivial example is one barrel with all 100 litres

Manov:

.................................. Of course, the capacity of the drums is smaller than the capacity of the tank.

.....................
ilunga, be careful!
 
MetaDriver:
ilunga, pay attention!
already corrected, what speed you gentlemen have =)
 
ilunga:

Then it may not be possible to drive at all

A trivial example - 3 barrels of 30 litres very, very close together (let's say 1/10th of the circumference)

Where do you put another 10 litres?

.....Racea..... steal......

 
MetaDriver:

Where did you put the 10 litres?

.....Racia..... steal......

All right, all right, 34. Refund with interest =)

there's still no way around the whole circumference.

 
ilunga:

Then it may happen that it is not possible to pass at all

Trivial example - 3 barrels of 30 litres very, very close together (let's say on 1/10th of a circle)

Yes, roughly....

How do you prove how much the minimum tank capacity will be?

It is clear that if minimum distance = 1/10 -> 90l. If 1/5 -> 80l. ...

But the proof doesn't work.... :(

 
Manov:

Yes, roughly....

How do you prove how much the minimum tank capacity will be?

Clearly, if minimum distance = 1/10 -> 90l. If 1/5 -> 80l. ...

But the proof doesn't work.... :(

As a first approximation, the capacity of the tank should be at least as large as to cover the maximum distance between the drums