35 replies to this topic

[rookie1ja]

no probs, there are many such posts on my forum that made me laugh

[soldier3001]

Rookie, it seems that the only way your plan would work is for the planes to be able to land over the 2/3 mark and wait for an airplane to come fuel it up. Are the planes able to land? Or can they hover without burning fuel?

[Smithsps]

Lets see if i can solve this.

A1 = 1st Plane
A2 = 2nd Plane
A3 = 3rd Plane

They fly counter-clockwise. (NP-1-2-3-SP-4-5-6-NP)
North Pole
(Point 1) (Point 4)
(Point 2) (Point 5)
(Point 3) (Point 6)
South Pole


A1 starts
A2 starts
A1 gets to 75% fuel (Point 1)
A2 gets to 75% fuel (Point 1)
A1 gives 25% of fuel to A1
A1 has 100% fuel
A2 returns and refuels
A1 get to 75% fuel (Point 2)
A2 flies to (Point 2)
A2 gives 25% to A1
A1 has 100% fuel
A3 flies to (Point 1)
A2 flies to (Point 1)
A3 gives 25% fuel to A2
A2 has 25 % fuel
A3 returns and refuels
A2 returns and refuels
A1 flies to the South Pole
A2 flies to (Point 5)
A1 flies to (Point 5)
A2 gives 25% fuel to A1
A1 has 25% fuel
A2 has 25% fuel
A1 flies to (Point 6)
A2 flies to (Point 6)
A3 flies to (Point 6)
A3 gives 25% fuel to A1
A3 gives 25% fuel to A2
A1 has 25 % fuel
A2 has 25 % fuel
A3 has 25 % fuel
A1 flies to the North Pole
A2 flies to the North Pole
A3 flies to the North Pole

*CONGRATS* If you have got to this point you have nothing more to read.
This shows it can be done!

Like the solution?

[coffee.lady]

I was also stuck on the concept of hovering.

[Kend0g187]

No planes have to hover. The puzzle does not specify the speed that the planes have to fly at. Instead of flying at the same speed as the refuling planes and then waiting for them to catch up, the main plain can simply fly slower.

[Davey]

My initial thought on this was that it could simply be done with 2 planes. Remove gas tank of plane #2 and retrofit to plane #1.

[ALFRED]

This puzzle is very similar to the army trucks crossing the dessert puzzle but I like that added twist of it circumnavigating a planet so that planes can meet up with the original plane from the other side of the destination as well. Good puzzle rookie1. Maybe add the stipulation that planes can land wherever they need to refuel but there is no other plane fuel anywhere else on the planet. That way there's no confusion about whether or not the planes need to hover or burn fuel while waiting for refueling.

Nice job PAUL in explaining the solution with a detailed diagram.

[tink]

that i kinda weird

[atulchaudhary]

I believe this is a solution (that doesn't require planes to hover):

Let the fraction of fuel-tank-filled for planes A, B, and C (respectively) be represented as:
[1, 1, 1]

<!-- ia0 -->airplane_puzzle.gif<!-- ia0 -->[/attachment:6a5ea]

1. All 3 planes go 1/4 the way toward the south pole. [3/4, 3/4, 3/4]
2. At that point plane C gives 1/4 tank to EACH of the other planes, leaving them full, and plane C with 1/4 tank to return to the north pole. [1, 1, 1/4]
3. At the equator, plane B gives plane A (the "full-circle plane") 1/4 tank, thus filling plane A; plane B has 1/2 tank left to return to the north pole. (Plane C arrives at airport) [1, 1/2, 1]
(Plane A now has enough fuel to pass the south pole and reach the equator on the other side.)
4. When plane B arrives at the airport, both B and C must instantly refuel and leave going the other direction. [1/2, 1, 1]
5. At 1/4 the way from the north pole, plane C gives plane B 1/4 tank, filling it up, while leaving itself with 1/2 tank to get back with (plenty). [1/4, 1, 1/2]
6. Plane B meets plane A at the equator as plane A is running out of fuel. Plane B, which has 3/4 tank left, gives half its fuel to plane A, leaving 3/8 tank in each plane. Plane C reaches the airport at this same time. [3/8, 3/8, 1]
7. Plane C instantly refuels and goes back to meet planes A and B at 1/4 the way from the north pole, with plenty of fuel for all three to return safely. [1/8, 1/8, 3/4] --> [1/3, 1/3, 1/3]

It sounds a bit messy, and I assume things happen instantly, but it works, doesn't it??

good explanation. i 2 solved the puzzle this way.

[skirider]

Couldnt you just fly all 3 to the south pole then have a C47 with enough fuel to fully resupply the planes at the s pole, leave the C47 at the s pole then fly the 3 that HAVE to make it around back up to the N pole. Easy, assuming the army doesnt care about C47s.