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You have a jug of milk and a jug of water. You must empty both jugs into a nine gallon barrel.

You must be able to:

  1. Differentiate between the milk and the water
  2. Separate the milk from the water

You cannot:

  • Add any sort of divider into the barrel
  • Change the molecular make up of either substance
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    $\begingroup$ Looking at the various answers here, it occurs to me that puzzles are like wishes in at least one important respect; one tends to get what one actually asked for, rather than what one intended to ask for. $\endgroup$ – Trevor Powell Feb 11 '18 at 11:54

15 Answers 15

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You could

pour the water in, freeze it, then add the milk.

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    $\begingroup$ One could argue that freezing the water (creation of hydrogen bonds between the molecules) changes the "molecular make up" of the water, depending on what one defines as "make up". $\endgroup$ – oerkelens Feb 7 '18 at 9:33
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    $\begingroup$ Freezing just the water and then pouring milk on it (or vice versa) won't work because you can't separate the two perfectly afterwards - pouring room temperature water on frozen milk will necessarily unfreeze some of the milk. You have to go with @PaulParker's original intended answer to be able to really separate the two afterwards. $\endgroup$ – Tacroy Feb 7 '18 at 16:03
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    $\begingroup$ @oerkelens As a chemist I assure you that freezing is not considered to be a chemical change (changing the molecular make up). It's pretty much a purely physical change as it's nearly completely reversible with a change in temperature and/or pressure. Hydrogen bonds are not anything like molecular bonds, they are simply inter-molecular forces. $\endgroup$ – ColGraff Feb 8 '18 at 23:10
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    $\begingroup$ @PaulParker, cutting the jugs open is not a reasonable interpretation of emptying them into the barrel. IMO if that's the intended answer then the question should be tagged lateral-thinking and a number of Rubio's comments should be flagged as outdated. $\endgroup$ – Peter Taylor Feb 9 '18 at 11:38
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    $\begingroup$ physically this is not a valid answer. If you freeze the water and pour milk on it, there will be physical reaction between water and milk since their temperature will not be the same: it will freeze some water in the milk or melt some water, depending on the temperatures and densities of two substances.... $\endgroup$ – Oray Feb 9 '18 at 13:49
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Using centripetal force, keep the barrel rotating
enter image description here

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    $\begingroup$ This is a round barrel (the diagram is a bit inaccurate, substituting straight lines for curves - the surfaces of the milk and the water won't be straight either). And the proposed solution will even work with an ellipsoid (american football), as long as it's not not a perfect sphere. $\endgroup$ – Klaws Feb 6 '18 at 10:29
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    $\begingroup$ @PaulParker: This is a side view, not top-down. The milk and water are in the "top" and "bottom" of the barrel. $\endgroup$ – user2357112 Feb 6 '18 at 20:18
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    $\begingroup$ This is awesome but one thing isn't clicking for me... How would you put the milk/water in? I get how you put the first one in, but then the second one cannot just be poured I think. $\endgroup$ – sudo rm -rf slash Feb 6 '18 at 23:51
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    $\begingroup$ or use two plastic pipes to can slowly poor each close - but not exactly at- to the center $\endgroup$ – ntg Feb 7 '18 at 10:47
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    $\begingroup$ Or put them in at opposite ends while they're in a frozen state. Then start spinning. $\endgroup$ – Alex Feb 8 '18 at 15:00
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Cut the barrel in half, and pour the milk into one half, and the water into the other.

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    $\begingroup$ The only remotely practical answer. $\endgroup$ – jpmc26 Feb 7 '18 at 0:12
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    $\begingroup$ The puzzle specifies "a nine gallon barrel", not "two four and a half gallon half-barrels", though. $\endgroup$ – Alexander Feb 28 '18 at 18:18
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Instead of inventing ice cream (which will definitely change the molecular make up of the milk, by the way), you could also venture deeper into the lateral thinking loophole abyss and

Empty the water jug into the barrel. Empty the barrel back into the water jug. Empty the milk into the barrel.

Mission accomplished. Because loopholes.

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  • $\begingroup$ lateral-thinking at its best :-) $\endgroup$ – yo' Feb 8 '18 at 14:24
  • $\begingroup$ You poured each jug, not both jugs. There was no time when both jugs were in the barrel. $\endgroup$ – Davo Feb 8 '18 at 18:39
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    $\begingroup$ This isn't a lateral-thinking question, though. Especially where lateral thinking is not welcomed, puzzle posters can't close every loophole… and shouldn't have to. $\endgroup$ – Rubio Feb 8 '18 at 19:24
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    $\begingroup$ @Rubio yes, obviously the tag is not there, but that is the tag's fault: lateral thinking is definitely welcomed when the accepted answer is "freeze the water" and the other top answers are "spin the barrel" and "cut the barrel". (I totally agree that my answer is dependent on a much more stupid loophole than the accepted solution, and that the spinning is an actual solution, not a loophole at all. But since OP intended freezing, this definitely was intended as a lateral thinking problem.) $\endgroup$ – Bass Feb 8 '18 at 20:09
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You can empty the water into the barrel, place the water jug in the barrel, and empty the milk inside the (formerly) water jug while it is in the barrel. This will be easy to separate by simply removing the jug.

Edit:

The currently accepted answer ignores the fact that pouring a liquid onto a solid with similar freezing points will melt the surface of the solid, thus allowing a small amount of mixing of the two substances. However, if the barrel were kept extremely cold and the liquids were supercooled, they could be poured in slowly to create separated milk and a water stalagmites.

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    $\begingroup$ Welcome to Puzzling! (Take the Tour!) Note the puzzle says you cannot add any sort of divider into the barrel; your answer really does exactly that. $\endgroup$ – Rubio Feb 6 '18 at 7:39
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    $\begingroup$ A divider is something that separates a whole into parts... my answer doesn't do exactly that and the accepted answer is not only impractical, but also ignores basic physics. $\endgroup$ – technosaurus Feb 6 '18 at 8:02
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    $\begingroup$ Your answer places a physical barrier, impermeable to either liquid, into the barrel and makes use of it to keep the two liquids divided one from the other. In what way is that not adding a divider into the barrel? $\endgroup$ – Rubio Feb 6 '18 at 8:15
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    $\begingroup$ +1, merely for the edit. The accepted solution is unpractical. $\endgroup$ – Evargalo Feb 6 '18 at 10:01
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    $\begingroup$ But.. it does, right? It divides the barrer into two areas, one inside the jug and one outside of it. If your definition of "divider" is more loose than that, i'd reckon there would be many other cheeky solutions using technically qualifying items to separate the two. $\endgroup$ – votbear Feb 6 '18 at 10:04
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Because there are no time constraints specified:

Empty the water into the barrel, and let it evaporate. Then empty the milk into the barrel. They are separated because there is no water in the barrel anymore. The molecular makeup is the same for both, there are just macroscopic phase changes for the water.

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  • $\begingroup$ Do you think that time has no molecular effect on milk? Maybe in outer space, but out there it would freeze:-) But anyway evaporation is a nice shot:-) $\endgroup$ – Przemyslaw Remin May 17 at 13:24
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Use a barrel that already has a divider in it, so you don't have to add one. ;-)

Loopholes! ^^

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    $\begingroup$ This isn't a lateral-thinking question, though. Especially where lateral thinking is not welcomed, puzzle posters can't close every loophole… and shouldn't have to. $\endgroup$ – Rubio Feb 8 '18 at 19:24
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    $\begingroup$ Dude, I know that, I was just joking around. This is why I never claimed to have used lateral thinking, but openly stated that I was using a loophole. I saw that Bass did it, so I wanted to have some fun, too. $\endgroup$ – Alex Feb 10 '18 at 2:15
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Take all the supplies into a zero-G environment; e.g., a spacecraft that is not under power (could be in orbit; could be coasting through space — arguably, these are the same thing, anyway).  Slowly, gently, empty one of the jugs into the barrel.  The liquid will tend to form a (roughly) spherical glob, held together by surface tension.  It may fluctuate for a while, as a result of any residual kinetic energy from the insertion process.  I believe that these fluctuations will diminish after a few minutes.  Then enter the other liquid into the other end of the barrel.

        two globs of liquid floating in a barrel in zero-G

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    $\begingroup$ ....and then the barrel crashes into mars $\endgroup$ – NL628 Feb 11 '18 at 3:54
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You could

Put your milk in a barrel, shake it till it produces butter, then add your galon of water

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    $\begingroup$ When you churn whole milk, it doesn't completely solidify into butter. It separates into butter and liquid buttermilk which has to be drained off. $\endgroup$ – Jaap Scherphuis Feb 6 '18 at 9:14
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    $\begingroup$ On similar lines, you could pour the water into the barrel then froth the milk and pour it on top. They wouldn't stay separated forever but it seems to me that it would at least be as good a solution as freezing. $\endgroup$ – Hugh Meyers Feb 6 '18 at 12:30
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Using a combination of answers here, taking into account their limitations and the criticisms of those methods:

Pour the water into the barrel and freeze it. Invert the barrel, so the ice is now in the top half of the barrel, and pour the milk into the bottom.

Given the ridges in a typical nine gallon barrel, and the fact that water expands when it freezes, the ice is likely to be pretty firmly held in place. *8')

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    $\begingroup$ And the ice comes free of the barrel while you're pouring ... SPLASH!!! $\endgroup$ – Rand al'Thor Feb 9 '18 at 17:47
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    $\begingroup$ Given the ridges in a typical nine gallon barrel and the fact that water expands when it freezes, the ice is likely to be pretty firmly held in place. *8') $\endgroup$ – Mark Booth Feb 9 '18 at 17:52
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Simple.

Pour the water into the barrel. Drink it. Pour the milk into the barrel.

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Remove the bottom of the barrel. Empty the jug of water into the barrel. It will fall thru on the floor. Step out of the pool you just formed and repeat with the milk.

Yeah, lateral thinking.

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Pour the milk into the barrel. Then pour some hydrophobic oil on top of the milk. Lastly, very gently pour the water on top of the oil.

Why could this work?

The density of water is $\rho_{\text{water}} = 1$, whereas the density of milk is $\rho_{\text{milk}} \approx 1.03$. I tried using olive oil — whose density is only approximately $0.93$ — and, unsurprisingly, it did not work: water simply passed through the layer of olive oil and mixed with the milk. However, if one did use a hydrophobic oil whose density is between $\rho_{\text{water}}$ and $\rho_{\text{milk}}$, e.g., heavy fuel oil with a density of $1.01$, then it could perhaps work.

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    $\begingroup$ That kind of sounds like adding a divider. It may not be a solid one, but that's adding a liquid divider, so it breaks one of the rules. $\endgroup$ – Sensoray Mar 31 '18 at 14:27
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This is impossible. Milk contains water, therefore in order to separate the two, you would need to remove all the water from the Milk. This would render the milk no longer milk.. which would be altering its makeup significantly.

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  • $\begingroup$ No, it's not impossible. Checkout Ergwun's answer, it's hilarious. :-) $\endgroup$ – Alex Feb 8 '18 at 15:00
  • $\begingroup$ Ergwun's answer does not address the fundamental reason it's impossible. Milk contains water. Ergo, you cannot separate it. Even before you put it in the barrel, it's not separate. $\endgroup$ – Miles Prower Feb 14 '18 at 18:12
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    $\begingroup$ That's beside the point. The question was that there are two liquids (milk and water) who must stay separate after being put into the barrel. You can too separate them before they're put into the barrel, because they're in different jugs. It doesn't matter that milk contains water. It's about having the two liquids from the jugs stay separate. $\endgroup$ – Alex Feb 15 '18 at 8:04
  • $\begingroup$ Right. That is the incorrect premise. There are not two seperate liquids. It's like saying... 'Keep the water and the also-water seperated'. $\endgroup$ – Miles Prower Feb 15 '18 at 15:05
  • $\begingroup$ I think it's fine to say that. Even if it said "Keep two jugs of water separated" it's a premise I'd have no problem with. $\endgroup$ – Alex Feb 19 '18 at 10:05
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The accepted solution of freezing one of the liquids arguably goes against the rule of 'not changing the molecular make-up of either substance'.

So a comparable solution would be:

1. Pour in the water 2. Pour in the milk. 3. Evaporate the combined liquid, removing all the water content and leaving only the milk proteins. (There are 3 or 4 distinct proteins in the milk of most species, all of which are distinct molecules, so technically this does not alter the substance on a molecular level. If changing the state from liquid to frozen solid is acceptable then changing it to a gas must be too) 4. Collect the distilled water in another container 5. Return half of the distilled water to the milk proteins to leave the original quantities of both milk and water.

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protected by Rand al'Thor Feb 9 '18 at 17:57

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