I know where this is going, and I too was amazed by the answer until someone pointed out to me the fallacy in the maths.Quote:
Originally Posted by prendrelemick
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I know where this is going, and I too was amazed by the answer until someone pointed out to me the fallacy in the maths.Quote:
Originally Posted by prendrelemick
I know of no maths fallacies in need of explanation. Is the answer a proportionately inverse square root of someone's ego/party pooping potentiality?
I'm am gonna be reckless and not check this very basic equation (which I never use) just to get a seat-of-my-pants atmosphere going.
Circumference=2πr
(π is the symbol for pi, not the letter 'n')
So, next:
Circumference + 6 feet=2πx (We want to know x, ie. the new radius, in terms of r.)
2πr+6 = 2πx (then, divide both sides by 2)
πr+3 = πx (then divide by π)
r+3/π = x
3/π = 0.95, approximately
This makes me think that the rope would float a little less than a foot above the surface of the Earth.
However, Mark's post makes me think that this straight-forward approach might be a natural, but erroneous one. If that's the case, I will gladly be the sacrificial lamb we require for the demonstration of such, especially considering the absence of responsibility (for the next puzzle) that comes along with it.
That is the answer I was looking for, but Mark has scuppered my confidence in it.
I reckon the answer is the same no matter what the circumference of the orb.
The next question could be, What's the mathematical fallacy involved here.?
To be honest, I'm on shaky ground here. The first time I saw this problem I came up with the same answer as Bill, using the same method. Some time later I mentioned it to a guy who I consider better than me at maths, and he took it to bits and pointed out a fallacy - though I can't now remember what the hell it was.
However, I've looked online to find the debunking maths - and I can't. On the other hand there are plenty of sites that present the solution that mick was looking for... Here's one (though it frames the problem by starting with the difference between the radii - three feet - and asking for the difference in the circumferences).
Looks pretty authoritative and convincing, doesn't it?
So maybe I just have to get past the following counterintuitive image:
I am standing on a plain in Kenya. I am holding two six-foot lengths or rope. At my feet there's a rope tight to the ground, stretching west and east to the horizon. There's also a tennis ball with a short piece of rope wrapped around it.
I cut the rope around the tennis ball and magically splice in one of my six foot lengths. I make the new rope into a circle on the ground and put the tennis ball in the middle.
I then cut the rope that's stretching both ways to the horizon, and splice in the other six foot length. Suddenly the rope along the ground floats - all the way to the horizon - in fact, all the way round the world. My six feet of rope has introduced slack along its 40000 miles. How much slack? Well, the rope floats at a height precisely equal to the distance from the tennis ball to the rope that surrounds it.
Put like that, it does seem unlikely, doesn't it? But, actually, that doesn't mean it's wrong. As I say, it might simply be counterintuitive. Me, I'm a great believer in the unarguable authority of maths so - despite the fact that this friend of mine once showed me what he considered to be flaw in it - I'm going to have to go with bill's calculation until someone shows me why it's wrong. It's the best explanation we have until we have a better one.
And that, as we so often say in a different context on this forum, is what science is.
The ropey floaty rope? As a physical impossibility and physics being a branch of maths, we could discount that one
Tides? Deep sea waves? Moon's gravitational pull?
Mountains? And snow and ice to change the tension of our fallacious measuring instrument?
Equator and Poles? get a lot of crackle and sputter there
Forgive me - maths isn't my strong point - in fact it's my weakest. I think we're all going to be gobsmacked when its revealed, hopefully. I love it when axioms and stuff get shattered
To be fair it only works with an imaginary earth and imaginary rope.
I have a feeling that the whole thing might've been more daunting if we had been provided the circumference of the Earth as measured in feet, and been therefore tempted to figure it out that way. With calculators, it would've been easy, I guess, but after all of those big numbers, the result might've been surprising. But I think Mark is right about the surprise really being about how the radius doesn't matter. I checked a site last night (soon after my post...) and saw a less succinct description than the one in the site Mark linked to, but it had a section with a bolded heading mentioning this fact.
I guess another example would be one's belt. If someone's waist were 36 inches around (mine is significantly less, but close enough to do the thought experiment, ahem), then tripling the length of the belt would lead to the same 1 foot of hovering space.
And, actually, this puzzle has just now given me second thoughts about how significant a few extra inches around the waist might be--easing into this only 'slightly' larger size might be a surprisingly more roomy endeavor than I had imagined. Or have I noticed that before?
Anyhow, I'll provide another puzzle, something probably less stunning, I'm afraid.
============ ============ =========== ============ ============ ===========
A man has a large, empty, clear, unmarked punch bowl that can hold exactly 8 liters of water. He has two filled bottles of water that can hold exactly 500 ml each. He also has another much larger container that can hold up to 20 liters, but markings on the side of this container indicate that it has exactly four liters of water inside of it. He also has a grease pencil which can write on glass.
The man would like to make markings on the side of the punch bowl to indicate the levels at which it would contain 500 ml, 1000 ml, 1500 ml, 2000 ml, 2500 ml, etc. Using only what is described above, how many such markings can the man make?
Having given this quite some considerable thought over the past few seconds - ten?
Thanks for kicking the speculation off for us! Sorry, though, more marks can be made.
(Also, since this is a puzzle that I made up real quick, I have to admit that there could be more than one correct answer, depending on some information that I hadn't thought to provide.)
Aah - he may also be able to submerge the two (empty) 500ml bottles to increase the range by ah two, is it?
Therefore 12?
(though the accuracy of these may depend on the size and shape of his fingertips)
Maybe! Well, yes, actually that is absolutely correct IF you are referring to the following markings:
500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000
UNLESS something....
Your answer is the one that I had in mind when I typed up this puzzle, but I have since come up with another possible answer. Since these puzzles are sometimes difficult to find or make up (in my opinion) why don't we let the speculation on this one continue.
Can anyone think of a way in which this scenario might permit a marking or markings beyond the 6000 ml level?
A clenched fist comes to mind.
Were he to remove 500ml and insert his hand until it displaced 500ml, make a mark on his wrist or forearm, remove, repeat process with other hand, reinsert 500ml and two empty bottles and one hand, then the other, making final marking on the container with pen in his mouth taking it up to fourteen
(yes, it would all require a little dexterity, but where there's a will...)
I think that is a great idea, and what you describe would get you two more markings, thus reaching 7000. I suppose 7500 could be reached by using a foot, provided the shape of the foot and the bowl allow for the foot to be conveniently marked, and the bowl could fit the bottles, hands, and foot.Quote:
Originally Posted by MystyrMystyry
ANYHOW, I had also realized that the "much larger" container that I introduced (because I didn't want it to be something that could be submerged) ended up as something that the bowl might be submerged in. That is, if all of the water is put into the larger container, then the punch bowl could be submerged, marking off the gradations as it is lowered inside the larger container (which the puzzle mentions is already marked). There are problems with this, though. The material of the bowl would likely displace more than the plastic of a typical 500 ml bottle, which would throw things off. Also, the bowl might not fit in a narrow "much larger" container, or the "much larger" container might be VERY wide and be shorter than the bowl.
SO, on more than one account, your "clenched fists" get us 6500 ml and 7000 ml, and probably to the extra 7500 ml measurement, thus beating the original answer I had formulated (12) AND ALSO achieving a greater plausibility than the "perhaps allowable, but heavily-hypothetical" solution I later conceived.
That means you win, you are correct!, Mystyr, and are therefore tasked with the responsibility of presenting us with the next puzzle.
Hey, cool, I did something inadvertantly smart - haven't been there in a long time...
As I was going to St Ives
I met a man with seven wives
The seven wives had seven sacks
The seven sacks had seven cats
The seven cats had seven kits
How many were going to St Ives?