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        riddles >> hard >> Cork, Burlap Bag, and Irregular Bottle
        
(Message started by: william wu on Dec 13^th, 2003, 8:35pm)

Title: Cork, Burlap Bag, and Irregular Bottle
Post by william wu on Dec 13^th, 2003, 8:35pm

You are locked in a room. In front of you are an irregulalry shaped bottle that is full of water, a cork that fits in the said bottle, and a burlap bag. Your captor says he will release you if you dump out exactly half the water and cork the bottle. What do you do? You don't have any other materials aside from the aforementioned ones above.

Source: This one comes via e-mail from Emerson Sklar, a high school student relaying a puzzle given by his computer science teacher Clint Nesler, in West Virginia. I don't how to solve it, and I couldn't get any hints. If it's really solvable, I think the design is elegant enough to make the puzzle worthy of becoming a classic.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by James Fingas on Dec 15^th, 2003, 6:11am

Here's an interesting idea:

[hide]Tear the burlap bag in half, then soak the whole thing evenly. Stuff one half of the bag back into the bottle, then cork it. QED[/hide]

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Margit Schubert-While on Dec 15^th, 2003, 7:13am

Well James, I don't think so. Over on this side of the pond, burlap bags are made from jute, flax whatever, which is treated to make it water resistant. However they cannot hold water. Also, ever tried tearing one of these ?
Maybe we need a better definition of the burlap bag.
So what to do with this bag. Put the bottle and/or cork in it and then ? Whirling it around your head doesn't seem to bring much.
I would also like to know the definition of "irregularly shaped".
Will this work with a bottle that has a hollow handle on the side that is part of the bottle ? Will it work with a Klein bottle?
William, maybe you can get these Q's ansered.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by James Fingas on Dec 15^th, 2003, 8:09am

on 12/15/03 at 07:13:50, Margit Schubert-While wrote:

Over on this side of the pond, burlap bags are made from jute, flax whatever, which is treated to make it water resistant. However they cannot hold water. Also, ever tried tearing one of these ?

Do you mean that you can't even get one wet? If so, that is the most remarkable water-resistant treatment I've ever heard of. Your point about such a bag being difficult to tear is a good one, however...

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Margit Schubert-While on Dec 15^th, 2003, 8:57am

Well, perhaps water-repellant is more accurate. If you had enough water (which we don't) and enough time, I suppose a total immersion for a day or so (guessing) might be enough to saturate the cloth but then very unevenly.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by unkwoop on Dec 15^th, 2003, 4:26pm

I agree that some clarification on the properties of burlap bags would be helpful. Another idea,

[hide]Assuming the burlap bag is water impermeable, roll the lip of the burlap bag down until the the volume of the bag is roughly that of the bottle. Empty the water into the bag, adjusting how much bag is rolled off as you empty the water such that when the bottle is empty the bag's volume exactly contains the water, except that now we have a vessel that is both symmetric and deformable. Squeeze half of the bag flat allowing the overflow to run back into the bottle.[/hide]

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by SWF on Dec 15^th, 2003, 5:08pm

This looks like a joke question and a solution would be: [hide]Dump out the entire bottle. At some point it is exactly half empty, which meets the first requirement. Put a cork in the bottle, which satisfies the second requirement[/hide].

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by william wu on Dec 15^th, 2003, 7:15pm

Some more information: The teacher says that there is a quote unquote "elegant" answer, and it is not a joke question (we've also offered SWF's joke solution and it was denied; I believe the "exactly half" specification precludes this solution). Futhermore, the bag is known to be water-absorbent.

James's idea is interesting, but it begs the question of how to rip the bag exactly in half without a knife.

I'll keep you guys posted as I find out more.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by TenaliRaman on Dec 16^th, 2003, 1:32am

An idea,
push the burlap bag inside the bottle!

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Margit Schubert-While on Dec 16^th, 2003, 4:13am

Ah, an absorbent bag. Remind me, next time I come over the pond, not to go shopping when it's raining ;)
I still think we need some restriction on the bottle size.
One of the (normal) smallest bottles is the miniature (100 ml).
One of the (normal) largest is the Nebucandnezzar (10 l, I think)
If absorbtion is part of the solution, I can't see how this would work. I'm assuming also a roughly 1 and a half foot square bag. Reasonable ?
William, I still think we are missing some constarints.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by James Fingas on Dec 16^th, 2003, 7:01am

It's probably an old and worn burlap sack, which would make it easier to soak and easier to tear. Here's an idea of how to tear it relatively accurately in half:

i) Pick a point on the edge of the bag. Hold it up by that point.
ii) Note which direction is straight down. Make a small tear in that direction.
iii) Now hold up the bag right at the end of the small tear.
iv) Repeat ii - iii until the bag is severed in half.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by SWF on Dec 16^th, 2003, 7:37pm

The words "exactly half" are what made me suggest the joke answer. You can get very close to half: pour out almost half. Mark the perimeter of the water level using the burlap (maybe by pulling a fiber from it and tying it around the bottle it where the water level is). Flip over the bottle to switch the previously water filled and air filled halves. If the new water level corresponds to that marked before inverting the bottle, then it is exactly half full. You need to hold the bottle precisely 180 degrees flipped over from before, but that is not hard because the water surface indicates level. If not, add (by squeezing from the absorbant burlap) or remove some water and repeat. This will not work with very irregular bottles.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Margit Schubert-While on Dec 17^th, 2003, 7:42am

Well SWF, you are assuming the bottle is not opaque.
As I said, William needs to calrify the constraints on the bottle.
If the bottle is opaque AND irregular (examples Y-shaped or Klein), then there is no conceivable way to determine a half without taking the water out of the bottle (I think - except of course by weighing)
This occurs to me :
This also depends on a bottle constraint - It cannot contain too much water :
Bags are normally constructed of two roughly square pieces of cloth stitched together on three sides.
We need five hands for this - Hold the bag at the four corners under tension and horizontally above the floor. The 2 sides of the bag should be in contact.
Now, carefully dribble water onto the exact center of the bag such that no drops occur from the underside. The water will be absorbed by both sides of the bag in a circular fashion.
You will neeed a lot of patience !
Now, theoretically, we have half the water in/on one side of the bag.
Now to find a (realistic) way of unstitching/tearing the bag along it's edges.
Even then, how to get ALL the water from one side back into the bottle.
If the bottle has a wide enough neck, I suppose we could get this half bag into the bottle.
Ho-Hum, I'm still convinced we need a mor rigid defintion.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by James Fingas on Dec 17^th, 2003, 10:07am

on 12/16/03 at 19:37:06, SWF wrote:

Mark the perimeter of the water level using the burlap (maybe by pulling a fiber from it and tying it around the bottle it where the water level is).

Another way to mark the water level in the bottle could be to rub the burlap bag against itself to produce a quantity of short fibers. Dump out about half of the liquid in the bottle, then add the fibers to the remaining liquid. Insert the cork and shake vigorously. Then wait.

Hopefully a significant quantity of the fibers float and will tend to produce a ring around the bottle. Invert the bottle (disturbing the ring as little as possible) to see if you have more than half or less than half, then adjust the water level accordingly. This should work on any bottle (barring VERY pathological cases)

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Margit on Jan 4^th, 2004, 1:57am

William, have you got further info about this ?

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by william wu on Jan 4^th, 2004, 9:46am

Nope, still awaiting further information. Don't worry I'll let you guys know when I do :)

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Sklarface on Jan 5^th, 2004, 5:00pm

Hey, I (rather, my teacher) is the originator of this problem. He says he got it from his chem teacher way back when, and in the 37 years of teaching his teacher told thi sproblem to everyone he met, and my teacher and one other person were the only people to figure it out (possibly a fictionalized boast, but...). Ive been bugign him with this problem nonstop for a good while, posing tons of answers, and havent come to a correct one.

Hmm..
Well... tomorrow i will pose the one about Keeping the 2 bags touching, and pouring it so they absorb the same amt, then ?

Rip the bag in half along the seam? and stuff that half in the bottle? It says you have to have half the water int the bottle, nothin about some burlap too...

The cork, tho.. I seem to think it may play some factor (then again, ti may just be something in there to add an annoying extranneous factor)..
I'll keep everyone posted.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by aero_guy on Jan 7^th, 2004, 11:56am

How about this:

You rip a long thin strip off the burlap bag and place one end in the bottle with the other hanging out. Now hold it in place with the cork. Eventually enough water will leave the bottle through capillary action along the piece of bag and evaporation that there will half left, and the bottle will already be corked.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by rmsgrey on Jan 8^th, 2004, 7:17am

Maybe it's a trick question?

Maybe the answer is to put the bag over your captor's head, break the bottle, and threaten him with a sharp fragment of glass until he releases you...

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Sklarface on Jan 8^th, 2004, 12:52pm

I told my teacher the capillary action one (see 2 posts above), he said it would work, but he didnt think capillary action would stop at exactly half (the air is dry (or drier than the bottle would hypothetically be), and more htan half would leak out).
Hmm.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Margit on Jan 9^th, 2004, 1:45pm

Have you read reply #12 ? We need constraints on the bottle.
Interesting is that the prob came from a CHEMISTRY teacher.
Hmm.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Sklarface on Jan 9^th, 2004, 7:59pm

Hey, herees a link to another forum (this one about a stephen king trilogy), but i posted the riddle there,a nd people are tryin to work on it. None of the answers are right so far.. but may point you in the right direction (havent checked the last real answer yet, so..)

http://thedarktower.net/forums/index.php?showtopic=2926&st=0

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by aero_guy on Jan 11^th, 2004, 4:46pm

My reply about evaporation would not tell you when you had exactly half of the water in a corked bottle, but its benefit would be that at SOME POINT there would be exactly half corked. The point is that the other methods require you to cork the bottle when you think you have it, this way you are guaranteed to have the solution at some point, though you will not know when.

The bag ripping idea so far seems most likely, here is a variation. First rip the bag in half. You can then pull off individual threads from parts of it until you have two nearly identical pieces. Hold them flat against each other and soak. Let then water saturate them as it will (you will probably have to turn it upside down a couple times to make sure it doesn't drip), and then stuff one of them in the bag.

I just had another really good idea, I have to go home now, but I will work on it and get back to you guys later.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by CMR on Jan 12^th, 2004, 11:16am

How about this. We know that with any bottle, regular or irregular shaped, if the bottle is exactly half full, the water line will be at the same place on the bottle if you flip the bottle exactly 180 degrees. It will be at the level of the geometric centroid. For example, if we have a cylinder, the water line will be exactly halfway up the cylinder if we put it upright or upside down. On a container shaped like a cone it would be at ¼ h.

It follows that all we need to do is determine the location of the centroid on our container. If we pull threads of burlap from the bag, we can pour some water out, place the container on the ground, hold a thread around the container at the water level, flip the container 180 degrees, and if the new water level is above our thread, we need to pour out more water. Repeat this process until both water levels line up with the tread. Obviously being careful not to move the thread while flipping and not taking too much water out at once.

Any thoughts?

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by TenaliRaman on Jan 12^th, 2004, 11:34am

Assuming that the cork fits the bottle perfectly, CMR i think your solution stands good!!! However one problem i think is locating the centroid of a irregular bottle would be a bit hard.

However i think your solution can be modified a bit avoiding the need of locating the centroid.The solution lied in your statement itself "We know that with any bottle, regular or irregular shaped, if the bottle is exactly half full, the water line will be at the same place on the bottle if you flip the bottle exactly 180 degrees".

Lets simply use this fact.Mark the water level using thread and flip, if water level not same remove some water and continue with this iteration process.

Thanks towr!! (must have been sleepy then!)
Sorry SWF!!

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by towr on Jan 12^th, 2004, 12:33pm

TenaliRaman, I don't really see what your reply adds to CMR post, since he says the same thing in his second paragraph..

In any case SWF allready suggested the same thing earlier..
And with very irregular shapes it simply won't work.. The water has to be able to flow freely. If for instance you have something like an upside down glass trapped inside the bottle then when you turn it upside down, there won't necessarily be just one water level, but one for the glass and one for the rest of the bottle.
And you can easily further complicate the shape of the bottle..

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by SWF on Jan 12^th, 2004, 5:10pm

Thank you for noticing, towr. Also, the following comment about the centroid is false:

on 01/12/04 at 11:16:28, CMR wrote:

...the water line will be at the same place on the bottle if you flip the bottle exactly 180 degrees. It will be at the level of the geometric centroid.

Even for a simple shape like a cone with its axis oriented vertically, if half filled, the water line does not pass through the centroid.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Sklarface on Jan 14^th, 2004, 11:02am

Hey, the answer has been found!
lol
What you do is:
Rip a string from the burlap. Take a bit of tyh water in your mouth and cork the bottle. Look at the water line, tie the string so it wraps around at that point, and then flip the bottle. Use that to estimate if there is too much or too little water in it (if at middle, water level will be the same as before flipped). If too much, sip a bit more; if too little, spit some back.

Nice job workin on the problem.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by william wu on Jan 14^th, 2004, 7:18pm

on 01/14/04 at 11:02:51, Sklarface wrote:

Hey, the answer has been found!
lol
What you do is:
Rip a string from the burlap. Take a bit of the water in your mouth and cork the bottle. Look at the water line, tie the string so it wraps around at that point, and then flip the bottle. Use that to estimate if there is too much or too little water in it (if at middle, water level will be the same as before flipped). If too much, sip a bit more; if too little, spit some back.

Nice job workin on the problem.

Part of me thinks it's kind of clever, but another part of me says :P Some aspects of the solution I dislike include 1) Inaccuracies induced by saliva backwash, and importantly, 2) you need a level surface to rest the bottle on such that the water level can be properly "roped" by the burlap string. However, no such surface or table is stipulated in the problem. If the floor is flat, that would work; but for all we know you could be standing on a grassy hill.

Furthermore, even if assume we have such a surface, and we ignore bottles for which the water level is not the same when the bottle is half full inverted, we still need the bottle's centroid to be such that the bottle doesn't tip over when stood on either its bottom or its corked top. Maybe you could get away with using your hands to hold the unstable bottle against the level surface, but that leaves you with the problem of simultaneously roping the thread to mark the water level AND keeping the bottle from tipping over. Quite difficult -- you'd probably have to get your feet involved, or other parts of the body in some contorted position.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Sklarface on Jan 15^th, 2004, 2:21pm

Well, william, thats true, it would be hard if it doesnt have a flat surface. And saliva would play a part (though you could just sit there till you almost died from dehydration...). The part about "and we ignore bottles for which the water level is not the same when the bottle is half full inverted," wouldnt matter, I thought it would, but.. it doesnt. lol. If you have half the bottle full, and you tip it over, the water level will remain the same. Ill draw a drawing, lol. See attatched.
Anyway, thanks everyone for working on the problem. Interesting one (is it bein added to any of the riddle pages?).

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by towr on Jan 15^th, 2004, 2:30pm

try it with this bottle..

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Sklarface on Jan 15^th, 2004, 5:18pm

lol, it wouldnt matter how F^d up the bottle is, to the line will be the bottom 50% of the volume, flip it, still 50% of the bottle.

Doesnt make sense, but...
Try it! I tried it (lol, quite a sight to see, had water everywhere), but it does work. And, if you think you have some irregularly shaped bottles, wait till you come over here to WV... lol

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by towr on Jan 16^th, 2004, 12:47am

When my bottle is filled, and you turn it upside down to let some water out, there won't be one water surface left, but multiple.
Moreso, when you turn it back right side up, there will again not be just one water-surface, and different ones than the time before..

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by towr on Jan 16^th, 2004, 1:27am

I could probably design bottle that are a lot more evil than this.. But I hope this attachment will show why this one is bad enough as it is..

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Margit on Jan 16^th, 2004, 1:44am

Well, I must say that if this is indeed the "solution", then I am very disappointed not to say disgusted.
My comments :
You must have very different burlap bags over your side of the pond. I cannot get any sort of regular piece of material from the bag, let alone a string. Using both hands and feet, I can succeed in tearing it into useless irregular pieces.

I said we needed constraints on the bottle. You need to be able to see into it. I have many bottles where this is not the case including whiskey, cognac, wine bottles not to mention kitchen items such as oil and vinegar bottles.

I'd like to see somebody try it with one of these :
http://www.kleinbottle.com/

And, of course, the larger the bottle, the greater the error margin. The problem states "exactly half". Try it with a
Nebucandnezzar champagne bottle.
Just not very satisfying at all.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by towr on Jan 16^th, 2004, 2:27am

on 01/16/04 at 01:44:18, Margit wrote:

I'd like to see somebody try it with one of these :
http://www.kleinbottle.com/

If we go by their claim, than a klein bottle has no volume, so a full one is an empty one is a half full one, so you're done before you start..
(Of course despite their zero-volume claim it can conatin something, which means it doesn't have zero volume)

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by CMR on Jan 16^th, 2004, 11:55am

on 01/12/04 at 17:10:36, SWF wrote:

Thank you for noticing, towr. Also, the following comment about the centroid is false:

Even for a simple shape like a cone with its axis oriented vertically, if half filled, the water line does not pass through the centroid.

SWF:

Maybe I am wrong, but if the water line does not pass through the centroid, where does it pass through? I thought the definition of the geometric centroid was the centre of mass (or volume) of a 3 dimensional object.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by John_Gaughan on Jan 16^th, 2004, 4:21pm

If you have an irregular bottle like in towr's diagram, you do not have a single water line. Sure, maybe one does pass through the centroid, but which one? If so, it would be a coincidence, and it would not necessarily mean you have half of the bottle left.

I still think the idea of a burlap bag absorbing water is ludicrous. One of the characteristics of burlap material is that it is extremely pourous and while the individual strands may not be water-repellant, they aren't exactly sponges, either.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by SWF on Jan 16^th, 2004, 6:24pm

on 01/16/04 at 11:55:41, CMR wrote:

Maybe I am wrong, but if the water line does not pass through the centroid, where does it pass through? I thought the definition of the geometric centroid was the centre of mass (or volume) of a 3 dimensional object.

For a general shape, there is not a point that a plane dividing the volume in half always passes through. It will pass through the centroid in certain circumstances such as when it is a plane of symmetry.

Centroid is a 'balance' point, but that does not mean half of the volume is on each side of it. Whether something balances also depends on how far things are from the balance point. For example, an adult on a seesaw can balance with a small child if the adult sits close to the pivot point. When they balance, the pivot point is below the centroid, but more than half the weight is on the adult's side.

CMR, the way you quoted me makes it look like I am claiming my own statement is false. :o I know it is unintentional- the board leaves out previous quotes inside of quotes.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Margit on Jan 17^th, 2004, 4:04am

Well, I would suggest that we lock Sklarface's teacher and the chem teacher into a room where there is :
a) An unlimited supply of water
b) An opaque regular bottle
c) A Klein bottle (either opaque or not)
d) Corks to fit the afore mentioned bottles
e) Two burlap bags (USA/Europe)
and let them out when they think they can produce a corked bottle that is "exactly half full".

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Icarus on Jan 18^th, 2004, 12:12pm

That would be interesting for the Klein bottle alone. A true klein bottle does not exist in 3-dimensional space, so what we are left with showing is nothing but a self-intersecting fraud.

If we lock them in with a real Klein bottle, can I go along? I'd love to see one! (And yes, a real Klein bottle has 0 volume because it isn't really a bottle: it has no interior.)

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by rmsgrey on Jan 20^th, 2004, 9:33am

If you want to be picky, an opened ordinary bottle has no well defined volume - the boundary between "interior" and "exterior" is a matter of opinion. If you define volume along some scheme such as the maximum volume of fluid that can be carried by the bottle under standard conditions, then a Klein bottle has a non-zero volume.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by Icarus on Jan 20^th, 2004, 4:45pm

Nay - that is once again the case for our pseudoklein bottle only. A real klein bottle, such as exists only in 4 or more dimensional space, is incapable of enclosing a volume. Indeed the very concept of it's volume is hard to define. As an example, consider a circle in the plane. Its area is easily defined, and since the formula is well-known, easily calculated. Now bend half of the circle up at a right angle to the plane. What is the area of the bent circle? The concept lacks a good definition.

The same thing is true of the klein bottle, which requires such a bend out of 3D to even exist.

Title: Re: Cork, Burlap Bag, and Irregular Bottle
Post by rmsgrey on Jan 22^nd, 2004, 8:10am

But you can surely still hold 2D "water" in such a folded circle, or in a Mobius Strip. Any situation in which a Klein Bottle can exist runs into the problem of what prevents the water from leaking out of the "sides" of the ordinary bottle anyway, so I suspect that any attempt to define capacity in such a way that an ordinary 3D bottle has a non-zero capacity while a Klein Bottle doesn't, while still being applicable to the riddle, will either fail, or simply not apply to the klein bottle, in which case, I suspect, a reasonable extension will. Of course, this is such a sweeping statement, I'm at least half expecting it to be disproved, but lacking a Klein Bottle (and, for that matter not having a tap handy at the moment) I'm not in a position to determine experimentally whether or not it wil hold water.