Brain Teaser No 3

quote:

Originally posted by munch:
Three .munch

Nope, not 3 ;-)

Remember "that all aeroplanes return safely to their island base"

Two?

Imagine a clock as the circle to get around...only one plane needs to get all the way around but all planes must safely return to the island...

By half way around there has to be suffient planes to donate fuel to the one plane that will go all the way but all those planes also need to be able to fly back...

And there is no reason why some planes cannot set out in the other direction to give fuel for the second half of the trip....

One

If one plane can get halfway around the world - and then run out of gas - then one plane can get one quarter of the way around the world safely and return to the island.

If one of the planes can be fully refueled at any point at, or past, the quarter-way mark; then that plane can get to the point where a plane flying from the island base in the opposite direction will be able to meet it (assuming there is radio communication between the planes which seems a safe assumption).

If only one plane is to make the great circle in one trip, and the groundspeed is constant for all of the planes; then any plane that is to refuel the nominated circumnavigator MUST leave with that plane - or it will never catch up.

That's as far as I've gotten...

It does not say the planes fuel tank is full, only that it holds enough fuel to get halfway around the world. Fill it with the fuel present on the island and hey presto, round the world using just one plane.

If a plane is to contribute to the journey then it must donate some fuel before it gets a quarter of the way around...remember they only hold enough fuel to go halfway, so for a plane to return it only has enough fuel to go a quarter way...but going that far means it has none spare to donate...otherwise it can't make it back..

So you are looking at a relay of planes in both directions to get just one all the way around.

OK it is 3 but I have issues with the logic behind the answer...although there is nothing to say that the same plane cannot return to base, refuel and then go out in the opposite direction....Argh..!! I am just not bright enough it would seem.

quote:

Originally posted by Steve O:
It does not say the planes fuel tank is full, only that it holds enough fuel to get halfway around the world. Fill it with the fuel present on the island and hey presto, round the world using just one plane.

Assuming there is no trickery with the question such as the world not being spherical (not stated either):

Three.

Given a constant groundspeed, three planes must leave together. One peels back after transferring to the other two. This gets one of the "donor" planes further than 1/4 of the way. The one that peels back can refuel and help the other "donor" plane get back to the island after it has first returned and refueled. This gets the circumnavigator far enough for the two donors to fly the same exercise - but flying in the opposite direction to meet up with the circumnavigator.

Haven't worked out the detail fully, but, three planes.

Three aeroplanes are sufficient to ensure the flight of one of them around the world. There are many ways in which this may be done, but the following seems to be the most efficient.

Planes A and B and C take off together. After going one-eighth of the way, C transfers ¼ tank to A and ¼ tank to B. This gives A and B full tanks and leaves C with a ¼ tank sufficient just to get back to base.

Planes A and B continue a further one-eighth of the way when B transfers ¼ tank to A. B now has ½ tank left, sufficient just to get back to base.

Plane A meanwhile, with a full tank continues until he runs out of fuel ¼ way from base (¾ way round the world). Here A is met by C which has been refuelled at base. C transfers ¼ tank to A and both planes head for home.

A and C run out of fuel one-eighth way from base where they are met by refuelled plane B. B transfers ¼ tank to A and ¼ tank to C and the three planes then have just enough fuel to reach base with empty tanks.

It's morning in the UK, Macker. I'd have thought those kipper breakfasts would have invigorated the English mind enough to solve this problem first...

Wouldn't you say?

3

Aircraft 1,2 & 3 start together
At 1/8 point, Aircraft 3 refuels Aircraft 2 to a full tank
At 1/4 point Aircraft 2 refuels Aircraft 1 to give him a full tank, leaving Aircraft 2 with 1/4 of a tank and then heads for home.
Aircraft 3 refuels aircraft 2 at 1/8 point and both aircraft 2 and 3 return to base.
Aircraft 2 and 3 take off in reverse direction when Aircraft 1 reaches half way point
Aircraft 3 refuels Aircraft 2 at 7/8 point and returns home
Aircraft 2 meets aircraft 1 at 3/4 point and refuels Aircraft 1 to give him a full tank for the rest of the journey home leaving himself quarter of a tank.
Aircraft 3 refuels Aircraft 2 and Aircraft 1, 2 and 3 return safely to base.

quote:

It's morning in the UK, Macker. I'd have thought those kipper breakfasts would have invigorated the English mind enough to solve this problem first...

Unless I'm very much mistaken, Munch solved it 10 mins after the original post was made. Come on Kiwi's, keep up [BTW Nice explanation of Munch's logic Macker!]

Unless I'm very much mistaken, Munch is not English.

Ha! (wiping egg off face) Don't tell me he's a Kiwi too....?

quote:

Originally posted by Stubby:
[BTW Nice explanation of Munch's logic Macker!]

I cheated and found the answer on the net...that's why i said I wasn't bright enough...

PS: I own the personalised number plate "STUBY2" - how weird is that...it means nothing to me but i have owned it for about 15 years, it cost me $22 and I got it from a church minister from a car that he purchased from a Pub owner - presume it means a stubby of beer (a down under term)...

quote:

Originally posted by Stubby:
Ha! (wiping egg off face) Don't tell me he's a Kiwi too....?

Hell, it's me that might have the egg facial here! I seem to recall that Munch has been around the forum longer than his registration date says - and that he (?) is German.

Sorry for discussing you like this Munch.

quote:

Assuming there is no trickery with the question such as the world not being spherical (not stated either):

Deane,

Apologies for the ambiguity. I know how irritating it is to find a "puzzle" that turns out to me no more than a play on words or some sort of trickery. If I had spotted your concern - and it is a valid concern, I would have reasured you sooner that there was no trickery and that the world should be considered spherical for the question.

From a general perspective, please rest assured that all of my "Brain Teaser" puzzles are straight-forward (even if a little "impractical") and do not depend on trickery (*). I try to ensure the wording is unambiguous and will always clarify a point where my wording is found wanting. I also have carefully worked through all the answers. If I don't know the answer, I will state this when posting the question. If you look up the Brain Teaser No 1 thread (over a hundred pages I'm afraid !!), you will see what I mean. I think I only posted one question to which I didn't know the answer......although lots of other people posted brain teasers that left me struggling (but not Ken C!!)

(*) Perceiving that the world is round is typical of several Brain Teasers and not considered trickery - see the very first post in Brain Teaser No 1.

I hope you (and others) will be re-assured by what I have said, but if anything ever seems ambiguous, just ask.

Of course, half the fun of a brain teaser involves looking at things from a different perspective, and a bit of "lateral" thinking is often required - but hopefully not trickery.

Cheers

Don

quote:

Originally posted by munch:

quote:

Originally posted by Deane F:
Unless I'm very much mistaken, Munch is not English.

I am English .regards munch

Ahem. Apologies.

>Commanding officer leaves Deane F in tent alone with revolver loaded with one bullet<

OK you guys did really well, flying around the world. How are you all at....

Crossing a Desert

An unlimited supply of fuel is available at the edge of the Empty Quarter (the 800 mile wide desert adjoining Oman, UAE and Saudi) but there is no source in the desert itself (plenty of crude in the ground….but nothing to fuel your truck).

Your truck can carry enough fuel to travel 500 miles. The truck does 10 miles to the gallon and can carry 50 gallons of fuel. Lets refer to this as one "load" of fuel. You can build up refuelling caches at any spot along the way. These caches can be any size and we will assume no losses due to evaporation, theft etc etc.

What is the minimum amount (in loads) of fuel this truck will need in order to cross the 800 mile desert?

Is there a limit to the width of desert the truck can cross?

Cheers

Don

quote:

Originally posted by Deane F:

quote:

Originally posted by munch:

quote:

Originally posted by Deane F:
Unless I'm very much mistaken, Munch is not English.

I am English .regards munch

Ahem. Apologies.
>Commanding officer leaves Deane F in tent alone with revolver loaded with one bullet<

Munch non-smiley

Adam non-smiley

I thought Munch was Norwegian?

Any how, I'm glad Deane obviously missed with his Captain's revolver and is still with us.

cheers

Don

quote:

Crossing a Desert

An unlimited supply of fuel is available at the edge of the Empty Quarter (the 800 mile wide desert adjoining Oman, UAE and Saudi) but there is no source in the desert itself (plenty of crude in the ground….but nothing to fuel your truck).

Your truck can carry enough fuel to travel 500 miles. The truck does 10 miles to the gallon and can carry 50 gallons of fuel. Lets refer to this as one "load" of fuel. You can build up refuelling caches at any spot along the way. These caches can be any size and we will assume no losses due to evaporation, theft etc etc.

What is the minimum amount (in loads) of fuel this truck will need in order to cross the 800 mile desert?

Is there a limit to the width of desert the truck can cross?

There isn't a squadron of UH-64 Apache attack helicopters lurking perchance?

quote:

ONE . Regards English .Born in the same Hospital as Mick from the Stones.init

Munch, If the "ONE" is your answer, you are going to have to explain it, because its not the answer that I have in mind.

Cheers

Don