new puzzle time

[QED]

After all of the arguing going on in the Monty Hall thread, I thought it'd be time for a new puzzle to argue about.

I came across this one a few days ago and found it a little intriguing.

In 3000 years the surface of the Earth is flooded and covered with water due to global warming. The only point above water is a plateau on Mt. Everest, on which the United States has built an airfield and moved some military aircraft and an unlimited supply of fuel to prior to the great flood.

The commanders would like to send a plane to fly completely around the Earth to survey the damage. However, each plane only holds enough fuel to fly half-way around the world, and since the rest of the Earth is flooded there is no place along the way to refuel or land. Fortunately, though, the military planes can refuel each other in-air from their own supply.

Assuming all of the planes are identical, travel at the same speed, and refueling from plane-to-plane is instantaneous, what is the minimum number of planes you would need to have on hand so that one of them could succesfully circumnavigate the Earth? Further assume that no pilot or plane is sacrificed in the mission.

 

[So]

Bah, we don't need another flamewar.

 

[Matthias99]

We used a problem like this in our discrete mathematics class at one point (trying to drive across a desert in a jeep that could only hold so many extra gas cans at once). I'm not going to give details on the answer yet, but it's an interesting problem.

 

[Gibsons]

Should we assume fuel usage is constant, rather than improving as the fuel supply (and hence weight) decreases? That is, at the halfway point of your trip, you've used up exactly half of your fuel?

 

[So]

Impossible, since some plane would have to fly all the way to the midpoint, but since there would be no fuel left, it couldn't refuel another plane.

 

[broon]

The most important thing missing from this riddle is...is the airfield actually a giant treadmill?

 

[Chryso]

There is no way the water would get anywhere near that high no matter how much ice melted.

 

[Matthias99]

Originally posted by: So
Impossible, since some plane would have to fly all the way to the midpoint, but since there would be no fuel left, it couldn't refuel another plane.

Bzzzt. Try again.

Should we assume fuel usage is constant, rather than improving as the fuel supply (and hence weight) decreases? That is, at the halfway point of your trip, you've used up exactly half of your fuel?

I would assume this. It makes the math a hell of a lot easier.

 

[pontifex]

Originally posted by: So
Impossible, since some plane would have to fly all the way to the midpoint, but since there would be no fuel left, it couldn't refuel another plane.

thats not how midair refueling is done now is it? doesn't the tanker plane have a separate fuel tank for refilling?

 

[SSSnail]

6 planes.

Edit: maybe 5, if you get the tail wind.

Edit 2: Think relay people.

 

[maximus maximus]

can one plane carry another plane with it?

can the planes communicate with each other?

 

[Gibsons]

Originally posted by: So
Impossible, since some plane would have to fly all the way to the midpoint, but since there would be no fuel left, it couldn't refuel another plane.

It's possible, because you can refuel the refuelers.

 

[So]

Originally posted by: pontifex

Originally posted by: So
Impossible, since some plane would have to fly all the way to the midpoint, but since there would be no fuel left, it couldn't refuel another plane.

thats not how midair refueling is done now is it? doesn't the tanker plane have a separate fuel tank for refilling?

Well, the wording of the question implies that's how it works. If not, if each tanker can refuel a plane for an effectively unlimited distance, the the answer is simple: 1, with the plane modded to take the internal tanker supply and fuel its own tanks.

 

[ungsunghero]

n/m

 

[ElFenix]

Originally posted by: So
Impossible, since some plane would have to fly all the way to the midpoint, but since there would be no fuel left, it couldn't refuel another plane.

nah, if a plane tops off a plane 1/4 of the way around the world (and then crashes) the refueled plane could then fly halfway around the world to meet another refueling plane (which then crashes) at the 3/4 point, and the fueled plane flies all the way back. so, 3. really 4 because the fuel transfer isn't instantaneous.



nm can't sacrifice a plane

 

[broon]

It would take two planes. A refueling plane and the scout plane leave at the same time. The scout plane tops off it's tank 1/4 way around the world. The refueler returns. The refueler refills and heads out the opposite direction and meets the scout plane at the scout planes 3/4 way around the world and refuels.

 

[pontifex]

Originally posted by: ElFenix

Originally posted by: So
Impossible, since some plane would have to fly all the way to the midpoint, but since there would be no fuel left, it couldn't refuel another plane.

nah, if a plane tops off a plane 1/4 of the way around the world (and then crashes) the refueled plan could then fly halfway around the world to meet another refueling plane (which then crashes) and the fueled plane flies all the way back. so, 3. really 4 because the fuel transfer isn't instantaneous.

yep, thats how i'm approaching it but i don't have an answer to how many.

 

[Ramma2]

How can you have unlimited fuel on a mountain?

 

[ElFenix]

Originally posted by: broon
It would take two planes. A refueling plane and the scout plane leave at the same time. The scout plane tops off it's tank 1/4 way around the world. The refueler returns. The refueler refills and heads out the opposite direction and meets the scout plane at the scout planes 3/4 way around the world and refuels.

the refueller wouldn't have any fuel left after topping off the scout. it takes half of its fuel to get to the 1/4 point, and uses the other half to fill up the scout.

nm can't sacrifice

 

[So]

Originally posted by: Gibsons

Originally posted by: So
Impossible, since some plane would have to fly all the way to the midpoint, but since there would be no fuel left, it couldn't refuel another plane.

It's possible, because you can refuel the refuelers.

Assuming a single fuel supply, you still have a limit to how far they can go. Two planes fly the fist 1/4th of the trip, the first topping off the second, having 1/2 of it's fuel left to return.

The next plane will have to go a higher fraction of distance, but the distance out cannot exceed the distance to return, so at 1/2 of the way around the world, there would be zero fuel to add to the plane...

wait, okay so it is doable, I think.

 

[Chryso]

Originally posted by: broon
It would take two planes. A refueling plane and the scout plane leave at the same time. The scout plane tops off it's tank 1/4 way around the world. The refueler returns. The refueler refills and heads out the opposite direction and meets the scout plane at the scout planes 3/4 way around the world and refuels.

Excellent except the first plane wont make it back so 3.

 

[davestar]

Originally posted by: broon
It would take two planes. A refueling plane and the scout plane leave at the same time. The scout plane tops off it's tank 1/4 way around the world. The refueler returns. The refueler refills and heads out the opposite direction and meets the scout plane at the scout planes 3/4 way around the world and refuels.

nope

1/4 of the way around the world = 1/2 of a tank left

if the refueling plane fully topped off the main plane at this point, the refueler would be empty

the furthest a refueler can go out without an intermediate refueler is 1/6 of the way around the world

i believe the answer is 4

 

[So]

Originally posted by: Chryso

Originally posted by: broon
It would take two planes. A refueling plane and the scout plane leave at the same time. The scout plane tops off it's tank 1/4 way around the world. The refueler returns. The refueler refills and heads out the opposite direction and meets the scout plane at the scout planes 3/4 way around the world and refuels.

Excellent except the first plane wont make it back so 3.

Yup that's it. I'd call it three planes, counting the one doing the actual flight...

 

[Kirby]

Al Gore was right!! :shocked:

 

[So]

Originally posted by: davestar

Originally posted by: broon
It would take two planes. A refueling plane and the scout plane leave at the same time. The scout plane tops off it's tank 1/4 way around the world. The refueler returns. The refueler refills and heads out the opposite direction and meets the scout plane at the scout planes 3/4 way around the world and refuels.

nope

1/4 of the way around the world = 1/2 of a tank left

if the refueling plane fully topped off the main plane at this point, the refueler would be empty

the furthest a refueler can go out without an intermediate refueler is 1/6 of the way around the world

ooh, point.