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Topic: Cork, Burlap Bag, and Irregular Bottle (Read 8741 times) |
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william wu
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Cork, Burlap Bag, and Irregular Bottle
« on: Dec 13th, 2003, 8:35pm » |
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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.
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| « Last Edit: Dec 13th, 2003, 8:36pm by william wu » |
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James Fingas
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #1 on: Dec 15th, 2003, 6:11am » |
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Here's an interesting idea:
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
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Margit Schubert-While
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #2 on: Dec 15th, 2003, 7:13am » |
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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.
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James Fingas
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #3 on: Dec 15th, 2003, 8:09am » |
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on Dec 15th, 2003, 7:13am, 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 ? |
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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...
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| « Last Edit: Dec 15th, 2003, 8:10am by James Fingas » |
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Margit Schubert-While
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #4 on: Dec 15th, 2003, 8:57am » |
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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.
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unkwoop
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #5 on: Dec 15th, 2003, 4:26pm » |
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I agree that some clarification on the properties of burlap bags would be helpful. Another idea,
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.
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SWF
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #6 on: Dec 15th, 2003, 5:08pm » |
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This looks like a joke question and a solution would be: 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.
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william wu
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #7 on: Dec 15th, 2003, 7:15pm » |
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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.
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TenaliRaman
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #8 on: Dec 16th, 2003, 1:32am » |
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An idea,
push the burlap bag inside the bottle!
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Margit Schubert-While
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #9 on: Dec 16th, 2003, 4:13am » |
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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.
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James Fingas
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #10 on: Dec 16th, 2003, 7:01am » |
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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.
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| « Last Edit: Dec 16th, 2003, 7:03am by James Fingas » |
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SWF
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #11 on: Dec 16th, 2003, 7:37pm » |
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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.
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Margit Schubert-While
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #12 on: Dec 17th, 2003, 7:42am » |
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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.
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James Fingas
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #13 on: Dec 17th, 2003, 10:07am » |
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on Dec 16th, 2003, 7:37pm, 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). |
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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)
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Margit
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #14 on: Jan 4th, 2004, 1:57am » |
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William, have you got further info about this ?
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Sklarface
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #16 on: Jan 5th, 2004, 5:00pm » |
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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.
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aero_guy
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #17 on: Jan 7th, 2004, 11:56am » |
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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.
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rmsgrey
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #18 on: Jan 8th, 2004, 7:17am » |
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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...
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Sklarface
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #19 on: Jan 8th, 2004, 12:52pm » |
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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.
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Margit
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #20 on: Jan 9th, 2004, 1:45pm » |
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Have you read reply #12 ? We need constraints on the bottle.
Interesting is that the prob came from a CHEMISTRY teacher.
Hmm.
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Sklarface
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #21 on: Jan 9th, 2004, 7:59pm » |
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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
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aero_guy
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #22 on: Jan 11th, 2004, 4:46pm » |
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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.
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CMR
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #23 on: Jan 12th, 2004, 11:16am » |
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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?
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TenaliRaman
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #24 on: Jan 12th, 2004, 11:34am » |
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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!!
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| « Last Edit: Jan 12th, 2004, 11:35pm by TenaliRaman » |
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