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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Nevermind. Problem 8.
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OrgoneConclusion
Blue Fish Group



Registered: 04/01/07
Posts: 45,414
Loc: Under the C
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How many chucks could a woodchuck chuck?
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once in a lifetime
sun child



Registered: 02/12/15
Posts: 1,807
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2 planes go out, half way through; one plane gives to the other its half reserve,
that remaining plane then has enough to get 3/4 of the whole way;
to get a half-fuel out to that plane would then require. .
Instead of doing the math on that part, one plane could fly out to meet it going the other direction, as I notice you didn't say one can't fly in the other direction - which won't affect the 1 plane flying around the original direction. So if that's allowed, which still maintains the integrity of the first plane's trajectory - it looks like only 3 planes are required.
-------------------- Innocent, Oldfield & Hegerland Julia Delaney, Bothy Band Rasta Girl, Sister Carol Genesis, Jorma K I Wish You Peace, Lawrence Laughing Do Your Thing, Moondog large . . music garden . . veryall peace them hiStarhouse - main Time Traveler's Guide
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deff
just love everyone



Registered: 05/01/04
Posts: 9,406
Loc: clarity
Last seen: 20 minutes, 37 seconds
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but the planes have to still each fly back to the base and land, no?
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once in a lifetime
sun child



Registered: 02/12/15
Posts: 1,807
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Re: mathematical brain teaser thread [Re: deff]
#21869345 - 06/28/15 04:42 PM (8 years, 7 months ago) |
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Oh, yes. Back to work hehe
-------------------- Innocent, Oldfield & Hegerland Julia Delaney, Bothy Band Rasta Girl, Sister Carol Genesis, Jorma K I Wish You Peace, Lawrence Laughing Do Your Thing, Moondog large . . music garden . . veryall peace them hiStarhouse - main Time Traveler's Guide
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Quote:
once in a lifetime said: 2 planes go out, half way through; one plane gives to the other its half reserve,
that remaining plane then has enough to get 3/4 of the whole way;
to get a half-fuel out to that plane would the require. .
Instead of doing the math on that part, one plane could fly out to meet it going the other direction, as I notice you didn't say one can't fly in the other direction - which won't affect the 1 plane flying around the original direction. So if that's allowed, which still maintains the integrity of the first plane's trajectory - it looks like only 3 planes are required.
Actually, that is the correct answer.
Here is the official answer:
Three airplanes will do the trick. One of many solutions, and perhaps the most efficient, requiring only five tanks of fuel:
Planes A, B, and C take off together. After going 1/8 of the distance, C transfers 1/4 tank to A and 1/4 to B. This leaves C with 1/4 tank: just enough to get back home.
Planes A and B continue another 1/8 of the way, then B transfers 1/4 tank to A. B now has 1/2 tank left -- sufficient to get back to base, where it arrives with an empty tank.
Plane A, with a full tank, continues until it runs out of fuel 1/4 of the way from the base. A is met by C, which has been refueled at the base. C transfers 1/4 tank to A, and both planes head for home.
The two planes run out of fuel 1/8 of the way from base; they are met by refueled plane B. Plane B transfers 1/4 tank to each of the other two planes. The three planes now have just enough fuel to reach the base with empty tanks.
-------------------- Vi Veri Universum Vivus Vici
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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PROBLEM 9
Quote:
An airplane, traveling with a constant engine speed, makes a large and perfect circle parallel to the ground. There is no wind. Will it complete the same circle in greater, less, or the same time if there is a wind of constant speed and direction, assuming that the plane travels with the same constant engine speed that it had before?
-------------------- Vi Veri Universum Vivus Vici
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OrgoneConclusion
Blue Fish Group



Registered: 04/01/07
Posts: 45,414
Loc: Under the C
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Re: mathematical brain teaser thread [Re: deff]
#21869385 - 06/28/15 04:49 PM (8 years, 7 months ago) |
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Quote:
deff said: but the planes have to still each fly back to the base and land, no?
No, the refueling plane's pilots willingly sacrifice their lives for the sake of the riddle.
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OrgoneConclusion
Blue Fish Group



Registered: 04/01/07
Posts: 45,414
Loc: Under the C
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Quote:
DividedQuantum said: PROBLEM 9
Quote:
An airplane, traveling with a constant engine speed, makes a large and perfect circle parallel to the ground. There is no wind. Will it complete the same circle in greater, less, or the same time if there is a wind of constant speed and direction, assuming that the plane travels with the same constant engine speed that it had before?
Even without wind, it could not make a perfect parallel circle as the ground is uneven and the earth is rotating. You would need a perfect non-rotating and stationary sphere to even meet the first part of the riddle.
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once in a lifetime
sun child



Registered: 02/12/15
Posts: 1,807
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Oh, cool. Dumb luck, triumphs again hehe
These last few have really made me laugh and smile.
-------------------- Innocent, Oldfield & Hegerland Julia Delaney, Bothy Band Rasta Girl, Sister Carol Genesis, Jorma K I Wish You Peace, Lawrence Laughing Do Your Thing, Moondog large . . music garden . . veryall peace them hiStarhouse - main Time Traveler's Guide
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once in a lifetime
sun child



Registered: 02/12/15
Posts: 1,807
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My initial thought is that it will be the same length of time, because the wind will aid it as much as slow it down overall, but I could not give you the physics to prove it.
-------------------- Innocent, Oldfield & Hegerland Julia Delaney, Bothy Band Rasta Girl, Sister Carol Genesis, Jorma K I Wish You Peace, Lawrence Laughing Do Your Thing, Moondog large . . music garden . . veryall peace them hiStarhouse - main Time Traveler's Guide
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Kurt
Thinker, blinker, writer, typer.

Registered: 11/26/14
Posts: 1,688
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Apologies for the digression. I just wanted to say I stand corrected on my aside in question 7. You did say "give or present a sentence which says the exact opposite".
Not necessarily a useless aside to make, overall, but it was strictly incorrect in the given provisions. :-)
"It is necessary to follow what is common. But although the Logos is common, most people live as if they had their own private understanding. (Heraclitus DK 22B2)
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OrgoneConclusion
Blue Fish Group



Registered: 04/01/07
Posts: 45,414
Loc: Under the C
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Here is a clue: your answer would be correct if the flying time was the same against the wind as with the wind.
Now get to it!
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Re: mathematical brain teaser thread [Re: Kurt]
#21869455 - 06/28/15 05:02 PM (8 years, 7 months ago) |
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@Kurt: No worries!
@OC: They're just math problems! They do not need to be logically ironclad to convey the problem.
@once: Try again!
-------------------- Vi Veri Universum Vivus Vici
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once in a lifetime
sun child



Registered: 02/12/15
Posts: 1,807
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Here is my answer: it will be greater, because the wind will blow it off course. Since it's been blown off course, it will necessarily have to fly further to create the same circle, and/or reach the same spot.
-------------------- Innocent, Oldfield & Hegerland Julia Delaney, Bothy Band Rasta Girl, Sister Carol Genesis, Jorma K I Wish You Peace, Lawrence Laughing Do Your Thing, Moondog large . . music garden . . veryall peace them hiStarhouse - main Time Traveler's Guide
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Right answer, wrong reasoning. Try to think about the timing, as OC suggested.
-------------------- Vi Veri Universum Vivus Vici
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OrgoneConclusion
Blue Fish Group



Registered: 04/01/07
Posts: 45,414
Loc: Under the C
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Here is a real mind-crippler: How much more life would one have if they never visited The Shroomery?
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once in a lifetime
sun child



Registered: 02/12/15
Posts: 1,807
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I'm sure we've all been aware of how it affects us when arguments are struck up on the internet. . in fact - avoiding that kind of thing may eventually be an evolutionary affect - but you can see how my replying to you has taken it even further away from the original comment; let's just share our best answers to the questions, I would say
-------------------- Innocent, Oldfield & Hegerland Julia Delaney, Bothy Band Rasta Girl, Sister Carol Genesis, Jorma K I Wish You Peace, Lawrence Laughing Do Your Thing, Moondog large . . music garden . . veryall peace them hiStarhouse - main Time Traveler's Guide
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once in a lifetime
sun child



Registered: 02/12/15
Posts: 1,807
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there's no lack of friendship or play by doing so true story.
-------------------- Innocent, Oldfield & Hegerland Julia Delaney, Bothy Band Rasta Girl, Sister Carol Genesis, Jorma K I Wish You Peace, Lawrence Laughing Do Your Thing, Moondog large . . music garden . . veryall peace them hiStarhouse - main Time Traveler's Guide
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Sun King



Registered: 02/15/14
Posts: 4,069
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When the plane is flying with the wind, it is flying away from the wind and the wind can't catch it.
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