Thursday Solution

Several commenters correctly solved yesterday’s puzzle…..

$100,000 in hundred dollar bills weighs about two pounds on earth. So does a cubic yard of air.

On earth, when you weigh a lockbox full of air on a balance scale, you’re weighing just the lockbox, not the air — because there’s an equal amount of air pushing down on the other side.

But on the moon, when you weigh a lockbox full of air on a balance scale, you’re weighing both the lockbox *and* the air (because no air is pushing down on the other side). So the lockbox should balance against two more pounds on the moon (or, to be more precise, if on earth it balances against 100 little weights each weighing a pound, then on the moon it will balance against 102 of those little weights).

Since the lockbox on the moon balances against 100 pounds, instead of the expected 102, two pounds worth of something must have been removed — before Barb ever came into the picture. Unless Al somehow let the air escape from the box, he’s the one who stole your two pounds of money.

Hat tip to a person called jitter.

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37 Responses to “Thursday Solution”


  1. 1 1 Advo

    The explanation is a bit confusing in one regard – whether the lockbox contains air, and how much air, is quite irrelevant.
    It could be filled with helium, vacuum or fluffy kittens, all that matters is that in a closed state it DISPLACES one cubic yard of air, which means that it experiences buoyancy of 2 lbs.

  2. 2 2 Harold

    #1. This was mentioned yesterday, but the mass of air it contains is significant – we cannot ignore mass. If it contained a vacuum it would weigh 2lbs less than a box full of air. This is why helium balloons float. The air it contains is balanced by the buoyancy on Earth.

  3. 3 3 Bob Lince

    In all the banks I’ve been in, I’ve yet to come across a single airtight lockbox.

    Just sayin’….

  4. 4 4 David Grayson

    Advo’s explanation in comment #1 makes a lot more sense to me than the one in the original post.

    The original post said “because there’s an equal amount of air pushing down on the other side” which doesn’t make sense to me. The way I picture that comment is that on one side of the balance scale there is a platform for putting weights, and there is air that is pushing down on the platform. That is true, but there is also air below the platform pushing the platform up, so those forces largely counteract. The difference between those two forces would be buoyancy force of the platform itself, and it should be pretty small, but it would be in the opposite direction that Steve is supposing; it would push the platform upwards.

  5. 5 5 Ken B

    Advo is right in 1. The kittens were already part of the weight of the 100 lbs. What matters is not what’s in the box, but what’s not in the space the box occupies. On Earth that corresponds to displaced air, and on the moon it doesn’t.

    As I remarked on the other thread, this is easier to see if you imagine water instead of air. But the principle is the same.

  6. 6 6 Harold

    #5 – but kittens would still be in the box after it was opened on the moon, although they would not be very well. The mass of the box plus contents is different after opening it on the moon because the air escapes. If it contained a vacuum at the start and weighed 100lbs, then it would weigh 102lbs on the moon, and the puzzle doesn’t work. Conversely, if we filled it with air at 500 bar pressure, it would weigh 200kg on Earth, then 100kg on the moon.

  7. 7 7 Ken B

    You have a sealed lockbox about a cubic yard in volume, containing gold coins. You weigh it at the bottom of your filled swimming pool. Your balance scale tells you that the box (with the money inside) balances your lead weight. You leave Al alone with the box while you, taking your scale to prevent tampering, leave to pull the plug and drain the pool.
    Upon your return, you retrieve the sealed box, put it on the balance scale and verify that it still matches the lead weight.

    You see Al took your gold, right? You’ve lost bouyancy and your box should tilt the scales. It doesn’t because Al took some of the gold.

    This is all still true if you repeat with kittens or helium in the box from the get-go.

  8. 8 8 Ken B

    David Grayson: “The original post said “because there’s an equal amount of air pushing down on the other side” which doesn’t make sense to me.”

    Nor should it. The 2lbs force Advo is talking about is pushing UP on your box. It’s the reactive force from the displaced fluid air.
    Put the box in water. It feels lighter. Because the force is on the box not on the other side of the scale.

  9. 9 9 Ben

    HT to everybody who says buoyancy.

    Pressure increases with depth. The mechanism of the Archimedes principle is the pressure exerted by the fluid at the surface of the object. It can be proved that this is equal to the mass of the volume displaced.

    If you integrate the air pressure vector over the surface of an object, you get buoyancy equivalent to the volume of air displaced – i.e. assuming a cuboidal box placed horizontally, the pressure on the sides cancels out because they are in opposite directions, so the buoyancy is the difference between the air pressure on the top of the box which pushes down, and the air pressure on the bottom which pushes up, which is equal to the weight displaced.

    (I say it can be proved for any shape, but I can’t be bothered. A cuboid can be done in your head as above. I once did the exercise for a sphere and that was enough to satisfy me.)

  10. 10 10 Ben

    Readers, please substitute “weight” for “mass” in the second paragraph above.

  11. 11 11 Harold

    Advo, Ken B: I had it right the first time Wednesday when I said the box on the moon contains 198 lb box plus 2 lb air, then went off on a tangent Thursday somehow thinking the air had escaped from the box before re-weighing on the moon. You are correct, it matters not what was in the box as long as it is the same on the moon as on the Earth, and the displaced air has the same mass as the money.

  12. 12 12 Ken B

    @10: Still wrong I’m afraid. Pressure vs force.

  13. 13 13 Advo

    @11:
    You don’t know that the box contains 2 lbs of air. What you know is that it displaces 2 lbs. of air. That is also the only thing that matters.

  14. 14 14 Dave

    The official answer and the commentors have the physics right, but I am not very satisfied with this puzzle, because it makes two assumptions that seem to me improbable: a) that the box is airtight (to 1 atm pressure); b) that the weighing happens in vacuum rather than in an artificial, pressurized environment. Both have to hold for the solution to work out as presented.

  15. 15 15 Martin-2

    Just because I’m using a balance scale doesn’t mean I’m going to get sloppy with my terminology. 100 pounds on the moon equates to around 603 pounds on Earth, so what really happened is Al tried to use my lockbox to launder 250,480 Benjamins leading Barb, a detective, to confiscate all the money citing reasonable suspicion. My court date is next week.

  16. 16 16 Harold

    #13. You don’t know or need to know it contains 2lb of air, but it does. As you say, it doesn’t matter what it contains, as long as it is the same on the Earth and the moon, except for the missing money.

  17. 17 17 Jim W K

    Steve,

    As this is a puzzle thread, here’s a fun thought I had that you might like to blog about:

    AN INTERESTING PERSPECTIVE ON THE RATIO OF SUFFERING TO DIVINE BLESSINGS
    If you were offered 10,000 years of blissful pleasure and happiness, and to attain this you only had to suffer 3 seconds of pain and sadness, my guess is you’d take it, as it sounds like an awesome deal. As an analogy to earthly life and heavenly paradise, enduring 50-100 years of earthly travails to attain eternity in heavenly paradise is a much better deal than 3 seconds of pain and sadness to attain 10,000 years of blissful pleasure and happiness. That is to say, 50-100 years into eternal paradise is a much more favourable ratio compared with 3 seconds into 10,000 years, yet I’ll bet everyone who complains that there is too much suffering in the world for there to be a God would willingly take 3 seconds of pain and sadness to attain 10,000 years of blissful pleasure and happiness.

    Although there are many things this doesn’t show, it does at least show that it is irrational to accept 3 seconds of pain and sadness to attain 10,000 years of blissful pleasure and happiness and yet at the same time reject God on grounds of too much human suffering in our earthly lives.

  18. 18 18 Ron

    I reasoned exactly the same as Dave @14. Two unlikely things have to be truernin order to get the official “correct” answer.

  19. 19 19 Harold

    #17 If I had the choice of 3 seconds of pain or no seconds of pain, I would choose no pain. If God is all powerful, the point is the same however much bliss and happiness is on offer – why not do it without the suffering?

  20. 20 20 Dave

    Harold #19 – because Jim that would completely dfeat Jim’s straw man argument.

  21. 21 21 Jim W K

    The observation is ingenious, actually Dave – it puts an end to the issue of the suffering = no God fallacy if you choose 3 seconds of pain for 10,000 years of pleasure. If a man accepts the latter he behaves irrationally by imputing the suffering = no God argument.

  22. 22 22 Dave

    Jim – not that I can speak for every atheist but I don’t think I have ever heard the argument that “because there is suffering, that proves there is no god”.rnrnWhat I have heard is that given the amount of suffering in the world, it puts into doubt the idea that there is a god that is simultaneously all knowing, all loving and all powerful.rnrn9 year old girls get raped and killed all the time. That doesn’t mean that there isn’t a god. There could be a god but he just doesn’t know about these incidents. Or he doesn’t care about them (maybe he even enjoys it when they happen). Or he has no power to stop them from happenning.rnrnThat’s why I called it a straw man argument.

  23. 23 23 iceman

    Course there’s one other possibility – he’s all-everything but also gave us free will? But that would only speak to “why do bad things happen?”; personally I don’t really care much for the idea that bad things MUST happen for us to earn some reward.

  24. 24 24 Ken B

    @iceman: what if your not caring is one of the bad things that must happen for the rest of us to earn rewards?

  25. 25 25 Dave

    There are limits to your free will (if you have it at all – see http://www.youtube.com/watch?v=pCofmZlC72g)rnOtherwise we would all be living the dream.rnGiven that he creates these limits, why would an all knowing, all powerful, all knowing god allow so much suffering within those limits? Where’s the love bro?

  26. 26 26 iceman

    25 – I’m not endorsing the analogy, just pointing out it’s not necessarily a straw man – could be plenty of love, along with a recognition that a capacity for virtue requires the possibility of vice.rn24 – No fair, the only reason you knew of (= felt any impact from) my preference is because I told you

  27. 27 27 Dave

    Iceman 26.rnrnrnIn response to your response to 24 – yes but you had no choice in the matter :prnrnrnIn response to your response to my 25 – a recognition that a capacity for virtue requiring the possibility of vice is surely a rule that can be created and amended by an all powerful god. If he was all loving and all knowing as well, why would he create that requirement? That’s why it’s a straw man.

  28. 28 28 iceman

    Don’t ask me ask him…I’m asking you why he can’t *possibly* be all knowing and loving, and also a Sting fan? (Free free, set them free

  29. 29 29 Ken B

    I have a proof there is no free will. I’d like to post it but for some reason find myself unable to, as if I had no control over the matter …

  30. 30 30 Dave

    1) Because he supposedly sets the boundaries in which your free will operates. If life was unbearable physical torture for everyone from cradle to grave surely you couldn’t say that god is loving because he gives you the free will to choose between screaming your head off and suffering in silence?rnrn2) not all misery is caused by the act of other humans exercising their free will. Example the Boxing Day tsunami. Remove pain created by others and you are still left with having to explain why an all loving and all powerful god would inflict so much misery via natural disasters that only he could be responsible for. rnrnI’m sure if there is a god his favorite sting song would probably be “every breath you take”

  31. 31 31 Dave

    Prof landsburg. rnrnSomething is weird with the comments section on your blog. Whenever I hit return it prints out “rn” without any spacing. rnrnJust doing my bit of community servicernrnrnDave

  32. 32 32 Harold

    Da do rnrnrnDa do

  33. 33 33 Dave

    Harold that made me laugh more than it should have. Pity the bug didn’t pick up the last 2 times you hit enter (supposedly it ignores blanks?)

  34. 34 34 Harold

    Yes, maybe I should have put in a full stop.

  35. 35 35 iceman

    All I want to say to you both is…da doo doo doo, da da da da

    Also this:

    Again, supposing a higher being exists, what if ‘he’ thinks it’s better not to set boundaries? You seem to be saying we can’t possibly experience joys and sorrows from events that are allowed to unfold “randomly” by a loving god who generally doesn’t intervene (but how would we know things couldn’t have been worse?), e.g. because he believes character is formed by how one responds to both emotions. I say any parent knows that’s not categorically true. (I hope the Russians love their children too…)

    Note that I don’t necessarily believe anything I just said, but I don’t see how you can “logically” dismiss it.

  36. 36 36 Dave

    lol

    (not sure if that worked). I’m not dismissing it per se….just saying it raises the question…If he’s all powerful he can make your character form however way he likes. If he’s all loving, why would he require such unbearable pain and misery be part of that formation when he could just as easily give you that character without having to go through all that crap? And that 2 year old that was just raped to death? What exactly is the character that he supposedly formed before crying out that last whimper? It just raises the question is all. My original point is that Jim set up a straw man argument by saying (and I know I’m dramatizing here but I do like effect) “Atheists say that there is no god because there is misery in the world but the payoff is so large that it’s worth it so there is a god checkmate atheists”. I’m saying that that he built that strawman himself, knocked the crap out of it, and then proudly declared victory to the point we can all move on and praise the lord for eternity. (I know I’m putting words in his mouth here but it’s fun and I don’t think I’m that far off).

  37. 37 37 iceman

    Gotcha. If you haven’t done so, treat yourself to George Carlin’s rant on religion on his album “You Are All Diseased”

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