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You have a leak-proof drum that can hold 50 litres of water. It has a separable lid, like the one you have on barrels.

On Monday, you fill the drum to the brim, the full 50 litres. Then you leave the room and lock it so that no one can reach to the drum while you're gone.

The next day, you come back and add another four litres of water to the drum without taking any out, and not a drop spills, even though no one removed any water from the drum.

How is this possible?

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    $\begingroup$ This shouldn't be closed as too broad since the OP says "another four litres of water". This precludes filling the drum initially with anything other than water. Admittedly the OP could have been clearer, but it is exact. $\endgroup$
    – Paul Evans
    Apr 20, 2016 at 22:21
  • $\begingroup$ @PaulEvans: I VTCed because of the amount of possible answers, not because the question was unclear. The answers are what's too broad, not the question. $\endgroup$
    – Deusovi ♦
    Apr 20, 2016 at 22:27
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    $\begingroup$ @PaulEvans I took "another four litres of water" as saying "another four litres," as in "add a litre of oil and another four litres of water." $\endgroup$
    – SendersReagent
    Apr 21, 2016 at 0:02
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    $\begingroup$ @SendersReagent Nothing like "oil" was initially specified, so I think "another" grammatically associates with "water". But it could have been worded better. $\endgroup$
    – Paul Evans
    Apr 21, 2016 at 0:35
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    $\begingroup$ You could just as easily have filled the drum with 50 litres of air, (or sulfur hexafluoride if you want something strictly heavier than air so it stays in the barrel), or any other gas, really. Nothing says the original contents were liquid. $\endgroup$
    – Darrel Hoffman
    Apr 21, 2016 at 14:22

16 Answers 16

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Here's a guess:

50 liters of ice about 45.5 liters of liquid water. If the container was originally filled with ice (assuming no space), and that ice melted, you would have room to add 4 liters of water, with about .5 liters left to spare (no spillage).

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    $\begingroup$ @KeyboardWielder I don't see why you couldn't fill the drum to the brim with crushed ice. $\endgroup$
    – f''
    Apr 20, 2016 at 20:52
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    $\begingroup$ it could be crushed to a powder, such that there's virtually no space unoccupied by ice within the drum. $\endgroup$
    – Matt
    Apr 20, 2016 at 20:53
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    $\begingroup$ Or, it could be magic, as the title suggests ;) $\endgroup$
    – Matt
    Apr 20, 2016 at 21:45
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    $\begingroup$ Every definition of water that I can find refers to it as a liquid. The solid form of water isn't called water, it's called ice. Adding "another 4 liters of water" implies that you put water in to begin with, which isn't true in this case. $\endgroup$
    – Nuclear Hoagie
    Apr 21, 2016 at 10:20
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    $\begingroup$ @Matt "add another 4 liters of water" can mean that there is water in the drum now. It doesn't have to mean that you filled water in it $\endgroup$
    – Etoplay
    Apr 21, 2016 at 12:13
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I believe the answer is:

4 or more litres of water had evaporated

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  • $\begingroup$ Yeah, I was going to say either that or the drum had a leak. :) $\endgroup$
    – KeyboardWielder
    Apr 20, 2016 at 20:49
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    $\begingroup$ And it doesn't say you put the lid on, only that you have one $\endgroup$
    – BruceWayne
    Apr 20, 2016 at 22:14
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    $\begingroup$ I was thinking that this would be the obvious solution. $\endgroup$
    – Evan Carslake
    Apr 20, 2016 at 23:19
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    $\begingroup$ @cst1992: The room might be really hot and dry. $\endgroup$
    – sumelic
    Apr 21, 2016 at 15:00
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    $\begingroup$ This would have been my guess as well, especially given the fact that it doesn't say that the person in the puzzle put the lid on. $\endgroup$
    – Onorio Catenacci
    Apr 21, 2016 at 16:30
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Working with Matt's excellent answer, you initially fill the barrel with:

Snow

This works because:

It's very easy to fill the drum with snow if there's a good snow fall outside.
Bring snow into the room in a wheelbarrow and simply shovel the snow into it into the drum until it's filled to the brim.
Now put the lid on, turn the heat on, lock the room and leave it a day.
New snow (immediately after falling in calm) has a density of 50-70 $\frac{kg}{m^3}$ compared to water at $1000 \frac{kg}{m^3}$.
So now that the snow has melted you can easily add another four litres of water into the drum without overflowing it.
In fact, since the mass of the snow might only account for 5% of the available space, you may even be able to add another $47\frac12$ litres of water.

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  • $\begingroup$ I assumed the density of solid ice, but your answer works too. Upvoted! $\endgroup$
    – cst1992
    Apr 21, 2016 at 5:38
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    $\begingroup$ I'd say this answer works better, as I think you'd be hard pressed to find a full barrel of solid ice fully melted by the next day (depending on ambient temperature). $\endgroup$
    – feelinferrety
    Apr 26, 2016 at 7:17
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On Monday, you fill the barrel with 50 litres of

ball bearings

The puzzle doesn't seem to exclude this. This link suggests you could manage nearly 13 litres of water on Tuesday.

Edit after comments: on Monday you...

put in 8.976 litres of water and then fill to the brim with ball bearings. The maximum packing density for spheres is 0.74048 (wikipedia) so after this action there is room for 4 litres (more) of water.

I grant that this is grammatical sophistry, but that seems appropriate for a lateral-thinking tag.

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  • $\begingroup$ Using this? Very clever. But no, it's a water drum. That's indicated in the title. $\endgroup$
    – cst1992
    Apr 21, 2016 at 5:41
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    $\begingroup$ @cst1992 So you discount his answer but accept when some else "fills" it with something other than water as well? That to me would suggest downvoting the question. $\endgroup$
    – Keeta - reinstate Monica
    Apr 21, 2016 at 13:51
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    $\begingroup$ @cst1992 Saying that it can only contain water because it's a water drum is like saying I can only put water in a water bottle. Or milk bottles in a milk crate. $\endgroup$
    – user16469
    Apr 21, 2016 at 20:35
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Perhaps

The drum is made of a flexible polymer that slowly expands under the pressure of 50L of water. When you return the next day, the drum has stretched enough that it can now hold 54L.

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    $\begingroup$ We already have that kind of polymer - it's what balloons are made of. $\endgroup$
    – cst1992
    Apr 21, 2016 at 8:21
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    $\begingroup$ Well, a typical balloon would expand too quickly. You'd need to be able to fill the drum over the course of a few minutes without having it expand immediately, but still have it stretch out over the course of several hours. $\endgroup$
    – Nuclear Hoagie
    Apr 21, 2016 at 8:53
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I'm posting this at the OP's suggestion, even though it doesn't work perfectly.

You filled the barrel with

boiling hot (100 °C) water — or 99.99°, if you prefer.  At a density of $0.9584~\mathrm{kg/\ell}$  (see Wikipedia), this is $$50~\ell \times 0.9584~\mathrm{kg/\ell} = 47.92~\mathrm{kg}$$ of water.  The next day, the water has cooled to the ambient temperature of 4 °C and contracted to a density of $0.99997~\mathrm{kg/\ell}$, and so it takes up $$47.92~\mathrm{kg} \div 0.99997~\mathrm{kg/\ell} = 47.9214~\ell$$ and there is more than enough room to add another two litres of water.

But, alas, not four.

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  • $\begingroup$ Wouldn't any evaporate? $\endgroup$
    – msh210
    Apr 21, 2016 at 17:05
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    $\begingroup$ @msh210: That would depend upon the ambient humidity. If the humidity was at 100% in both cases water would neither evaporate nor condense. If the room was at higher than atmospheric pressure, the water could actually be heated beyond 100C without any evaporating. I'm not sure what conditions, if any, would be needed for the density of liquid water to be adequately reduced for the puzzle's conditions. $\endgroup$
    – supercat
    Apr 21, 2016 at 18:13
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My answer depends on "fill the drum to the brim, the full 50 litres" meaning that the barrel contains 50 litres after filling, but not necessarily that 50 litres was added.

The barrel already contains salt, sugar or some other solute (perhaps Magnesium Sulphate?) Calcium Chloride. This dissolves overnight and the resulting solution has a higher density thus smaller volume than the constituent parts. I calculated common salt (NaCl) at solution of 22g/L would only allow 1.3 litres to be added, but perhaps there is another solute with the chemical properties to achieve the necessary 4 litres reduction in solution volume. 18Kg of Calcium Chloride will give a total solution volume of 45.86 L after dissolving, allowing the extra 4 litres of water to be added.

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  • $\begingroup$ Good one! I initially thought of something like this but didn't think I could manage 4 litres, so I went for ball bearings instead. $\endgroup$
    – NL_Derek
    Apr 22, 2016 at 12:48
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Another possibility:

The drum has a large cross-sectional area and forms a convex meniscus with water. Originally it was filled so that it was full/flat when the lid was on. Now the water has a convex top with the lid off. This would enable to water to stay in the drum without dripping.

1 litre of water has a volume of 0.001 cubic metres so the area may not be huge.

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The lid fits inside the drum. When you covered it, 4 litres of water were pushed out. You come back the next day, take the lid off, and see that you can add more water to the drum.

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  • $\begingroup$ Tell that to Walter White when he's doing his thing ;) $\endgroup$
    – cst1992
    Apr 21, 2016 at 5:41
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A variation on NL_Derek's answer: you filled the barrel with

sand

You would be able to add water without overflowing.

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  • $\begingroup$ And I've got an even better answer, except it doesn't work for four litres (but it works for two litres). $\endgroup$
    – Peregrine Rook
    Apr 21, 2016 at 3:05
  • $\begingroup$ You could post that separately. $\endgroup$
    – cst1992
    Apr 21, 2016 at 5:42
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The walls of the barrel are capable of absorbing at least 4 liters of water overnight. The exterior of the barrel is covered with some waterproof substance to prevent water from seeping out if the barrel is disturbed.

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    $\begingroup$ 'capable of absorbing' means the water will not seep out. Besides, the barrel's outer surface is made of plastic or painted with waterproof paint. $\endgroup$
    – soihu7
    Apr 21, 2016 at 13:43
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    $\begingroup$ You really should not ask lateral thinking questions and then downvote when someone gives an answer other than the one you already thought of. $\endgroup$
    – soihu7
    Apr 21, 2016 at 14:15
  • $\begingroup$ You do know that I am not the only one capable of downvoting, right? Any one of tens of thousands of users could have done it. Downvoting is not meant to be personal in any case - you should see if you could add anything to your answer that contributes to its value. $\endgroup$
    – cst1992
    Apr 21, 2016 at 14:16
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Nobody removed any water, but the drum has a leak and 4 liters or so leaked out.

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  • $\begingroup$ Edited question. $\endgroup$
    – cst1992
    Apr 21, 2016 at 5:50
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If you have a very very shallow barrel, than you can fill it to the brim and then some, using the surface tension. Don't know if 4 litres is pysically possible however

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Can be weird, but it's also work.

You can fill it initialy with hot water vapor. When it became liquid again, it takes far less than 50 liters and it's still water inside. I don't calculate how much water you can add.

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  • $\begingroup$ ISTM that this is every bit as valid as the accepted answer. $\endgroup$
    – Peregrine Rook
    Jun 19, 2016 at 22:11
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The room is in a zero (or very low) gravity setting, keeping together in the barrel with surface tension

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Already answered, but just for fun other valid answers

  1. You fill it with air or any other gas the first day.
  2. You fill it with any non-water the first day. Second day you remove the non-water and replace it with water, no water has spilled.
  3. The barrel is leak proof but is designed to drain the water anyways, using the water for some use case and needing refilled, or boiling the water for steam power.
  4. The barrel is moved to somewhere that would condense water, high pressure air, even different temperature of air could do it.
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  • $\begingroup$ I don't know about the 'high-pressure air' thing - water is basically incompressible at any pressures we are able to apply. $\endgroup$
    – cst1992
    Aug 6, 2016 at 10:11

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