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InvisibleDividedQuantumM
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Re: mathematical brain teaser thread [Re: OrgoneConclusion]
    #21869293 - 06/28/15 04:30 PM (8 years, 7 months ago)

Nevermind.  Problem 8.


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InvisibleOrgoneConclusion
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869300 - 06/28/15 04:33 PM (8 years, 7 months ago)

How many chucks could a woodchuck chuck?


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Invisibleonce in a lifetime
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869306 - 06/28/15 04:35 PM (8 years, 7 months ago)

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.


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Offlinedeff
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Re: mathematical brain teaser thread [Re: once in a lifetime]
    #21869335 - 06/28/15 04:40 PM (8 years, 7 months ago)

but the planes have to still each fly back to the base and land, no?


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Invisibleonce in a lifetime
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Re: mathematical brain teaser thread [Re: deff]
    #21869345 - 06/28/15 04:42 PM (8 years, 7 months ago)

Oh, yes.  Back to work :smile: hehe


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InvisibleDividedQuantumM
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Re: mathematical brain teaser thread [Re: once in a lifetime]
    #21869354 - 06/28/15 04:43 PM (8 years, 7 months ago)

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.


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InvisibleDividedQuantumM
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869377 - 06/28/15 04:47 PM (8 years, 7 months ago)

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?




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InvisibleOrgoneConclusion
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Re: mathematical brain teaser thread [Re: deff]
    #21869385 - 06/28/15 04:49 PM (8 years, 7 months ago)

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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InvisibleOrgoneConclusion
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869394 - 06/28/15 04:53 PM (8 years, 7 months ago)

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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Invisibleonce in a lifetime
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869397 - 06/28/15 04:53 PM (8 years, 7 months ago)

Oh, cool.  Dumb luck, triumphs again :smile: 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 . .  very
all peace                    them hi
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Invisibleonce in a lifetime
sun child
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Re: mathematical brain teaser thread [Re: once in a lifetime]
    #21869413 - 06/28/15 04:55 PM (8 years, 7 months ago)

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.


--------------------
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I Wish You Peace, Lawrence Laughing                                                                                                                    Do Your Thing, Moondog                     
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InvisibleKurt
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Re: mathematical brain teaser thread [Re: DividedQuantum] * 1
    #21869424 - 06/28/15 04:57 PM (8 years, 7 months ago)

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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InvisibleOrgoneConclusion
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Re: mathematical brain teaser thread [Re: once in a lifetime]
    #21869441 - 06/28/15 05:00 PM (8 years, 7 months ago)

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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InvisibleDividedQuantumM
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Re: mathematical brain teaser thread [Re: Kurt]
    #21869455 - 06/28/15 05:02 PM (8 years, 7 months ago)

@Kurt:  No worries!

@OC:  They're just math problems!  They do not need to be logically ironclad to convey the problem.

@once:  Try again!


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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869475 - 06/28/15 05:05 PM (8 years, 7 months ago)

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 . .  very
all peace                    them hi
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InvisibleDividedQuantumM
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Re: mathematical brain teaser thread [Re: once in a lifetime]
    #21869482 - 06/28/15 05:06 PM (8 years, 7 months ago)

Right answer, wrong reasoning.  Try to think about the timing, as OC suggested.


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InvisibleOrgoneConclusion
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869513 - 06/28/15 05:12 PM (8 years, 7 months ago)

Here is a real mind-crippler: How much more life would one have if they never visited The Shroomery?


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Invisibleonce in a lifetime
sun child
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Re: mathematical brain teaser thread [Re: OrgoneConclusion]
    #21869524 - 06/28/15 05:15 PM (8 years, 7 months ago)

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 :smile:


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I Wish You Peace, Lawrence Laughing                                                                                                                    Do Your Thing, Moondog                     
large  . . music garden . .  very
all peace                    them hi
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Invisibleonce in a lifetime
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Re: mathematical brain teaser thread [Re: once in a lifetime]
    #21869526 - 06/28/15 05:15 PM (8 years, 7 months ago)

there's no lack of friendship or play by doing so :smile: true story.


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I Wish You Peace, Lawrence Laughing                                                                                                                    Do Your Thing, Moondog                     
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InvisibleSun King
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869539 - 06/28/15 05:18 PM (8 years, 7 months ago)

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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