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    Try this coin puzzle!

    You have six identical coins and a pair of scales. One of the coins differs slightly in weight (too small to detect by hand). You dont know if the coin is heavier or lighter than the rest. Can you determine which coin is different from the others and whether its heavier or lighter with only three or less weightings of the scales?

    36 Comments

    I read the answer to this this morning on some site. Can't remember it now!

    Original Poster

    Predikuesi;1662342

    I read the answer to this this morning on some site. Can't remember it … I read the answer to this this morning on some site. Can't remember it now!



    Shhh! Don't spoil it for others! ;-)

    Abvance;1662345

    Shhh! Don't spoil it for others! ;-)


    I wont. Anyway, I could not find the site again:thumbsup:

    Take the fox over to the other side of the river, then take the chicken, then take the fox back with you and then take the grain and the fox back at the same time.

    Put two coins on each side of the scales. There are two possible outcomes:

    1: The scales balance - the odd coin must be among the two coins not on the scales

    2: The scales are unbalanced - the odd coin is on the scales

    If 1: Put the two coins on the scales, they will be unbalanced. Switch one of the coins for one of the other four coins. If the scales balance, the coin that you just took off is the odd coin. If the scales remain unbalanced, the coin left on the scales is the odd coin.

    If 2: Switch two coins (from the heavier side, say) with the two coins not currently on the scales. If the scales balance, this means that the odd coin is among the coins you just took off the scale, and it is heavier than the other coins. If the scales remain unbalanced, the coin is still on the scale, and it is lighter than the other coins. From this you can place the two coins in question on the scales, and using your knowledge of whether the coin is lighter or heaver, you can find the odd coin.

    That is probably a difficult read. It's hard to put into words.

    I have another 'puzzle'. It's actually a question I was asked for a job interview. If you have two metal balls, identical size and mass, but one is hollow, how can you work out which is which? You don't need any tools (so to speak).

    jbarnett;1662470

    Put two coins on each side of the scales. There are two possible … Put two coins on each side of the scales. There are two possible outcomes:1: The scales balance - the odd coin must be among the two coins not on the scales2: The scales are unbalanced - the odd coin is on the scalesIf 1: Put the two coins on the scales, they will be unbalanced. Switch one of the coins for one of the other four coins. If the scales balance, the coin that you just took off is the odd coin. If the scales remain unbalanced, the coin left on the scales is the odd coin.If 2: Switch two coins (from the heavier side, say) with the two coins not currently on the scales. If the scales balance, this means that the odd coin is among the coins you just took off the scale, and it is heavier than the other coins. If the scales remain unbalanced, the coin is still on the scale, and it is lighter than the other coins. From this you can place the two coins in question on the scales, and using your knowledge of whether the coin is lighter or heaver, you can find the odd coin.That is probably a difficult read. It's hard to put into words.I have another 'puzzle'. It's actually a question I was asked for a job interview. If you have two metal balls, identical size and mass, but one is hollow, how can you work out which is which? You don't need any tools (so to speak).



    good I had the solution but didnt know how to put it into words so well done :thumbsup:

    split the coins, 3 each side.
    One side will be haevier than the other, take these three coins and one from the remaining three.
    Split therm 2each side. If the scales remain equal, then one of the remaining two is lighter than the rest.
    If the scales tilt then one of the coins is heavier than all the others, and is one of the two on that scale. The third move determines which of the two is either heavier or lighter.

    It should be possible in 2 weightings.

    Put 3 coins on one side of the scale, and 3 on the other.

    Whichever side weighs less has the light coin.

    So out of the 3 coins from that side, place 1 on each side of the scale. If one of them is the lighter coin the scales will show it. But if they weigh the same then the 3rd coin is the lighter one and you don't even need to weigh it.

    biff;1662508

    It should be possible in 2 weightings.Put 3 coins on one side of the … It should be possible in 2 weightings.Put 3 coins on one side of the scale, and 3 on the other. Whichever side weighs less has the light coin.So out of the 3 coins from that side, place 1 on each side of the scale. If one of them is the lighter coin the scales will show it. But if they weigh the same then the 3rd coin is the lighter one and you don't even need to weigh it.



    The coin might be heavier tho therefore on the other side!

    biff;1662508

    It should be possible in 2 weightings.Put 3 coins on one side of the … It should be possible in 2 weightings.Put 3 coins on one side of the scale, and 3 on the other. Whichever side weighs less has the light coin.So out of the 3 coins from that side, place 1 on each side of the scale. If one of them is the lighter coin the scales will show it. But if they weigh the same then the 3rd coin is the lighter one and you don't even need to weigh it.



    this doesn't take into account that the coin might be heavier, not lighter.

    I thought I'd point that out even though I don't know the answer

    jbarnett;1662470

    I have another 'puzzle'. It's actually a question I was asked for a job … I have another 'puzzle'. It's actually a question I was asked for a job interview. If you have two metal balls, identical size and mass, but one is hollow, how can you work out which is which? You don't need any tools (so to speak).



    Does it make a different sound when banging it (so to speak)?

    jbarnett;1662470

    I have another 'puzzle'. It's actually a question I was asked for a job … I have another 'puzzle'. It's actually a question I was asked for a job interview. If you have two metal balls, identical size and mass, but one is hollow, how can you work out which is which? You don't need any tools (so to speak).



    the hollow ball would be lighter.
    Mass should not be confused with Weight.

    Benjimoron;1662557

    Does it make a different sound when banging it (so to speak)?



    Nope. I tried that in the interview, and neither ball rang at all. Ultrasonic and X ray both would work (and were suitable answers in the interview), although it's not what I'm looking for here.

    PapaSmurf;1662592

    the hollow ball would be lighter. Mass should not be confused with Weight.



    No, they're the same mass, and assuming the same gravitational field is acting on them, they both have the same weight. Think about it.

    Oops didn't read the question correctly :oops:

    Original Poster

    jbarnett;1662470

    I have another 'puzzle'. It's actually a question I was asked for a job … I have another 'puzzle'. It's actually a question I was asked for a job interview. If you have two metal balls, identical size and mass, but one is hollow, how can you work out which is which? You don't need any tools (so to speak).



    I would have said put them in water to see which one floats but they are both metal and will sink.

    They're the same mass and volume, so their buoyancy is identical anyway.

    I think this is quite hard actually, and not just a test of logic. You need to have some certain science/applied maths/engineering knowledge to be able to answer it, just so you know.

    Original Poster

    Was this for an Engineering job or something?

    Yeah it was.

    Cut it in half, or drill a hole in it?

    Do they bounce to different heights?

    No, and I'm not sure about that. I don't think they'd bounce at all really.

    Do you roll them? The hollow ball should go slower.

    nightswimmer;1663435

    Do you roll them? The hollow ball should go slower.



    Care to explain?

    jbarnett;1663468

    Care to explain?



    Gawd, now your asking. I can't remember the actual physics, but it's something to do with their rotational properties. Gah, is it inertia? I just seem to remember doing this experiment many years ago. :oops:

    spin them?

    Hollow one goes for longer?

    Yeah, it's the moment of inertia (ie rotational inertia) of the spheres. The hollow sphere has the same mass as the solid sphere, but it's 'nearer the outside', so the M of I is higher. So, for example if you were to roll them down a slope, the solid sphere would accelerate faster than the hollow ball (in the interview I lifted the table and let them roll down).

    You were pretty much right, I just asked for clarification because you could also say that the hollow sphere would lose less speed if both spheres were rolled at the same speed to start with.

    Benjimoron - that works as well :thumbsup:

    Benjimoron;1663532

    spin them?Hollow one goes for longer?



    That's also how you tell the difference between a raw egg and a hard boiled egg. :thumbsup:

    Sort of. Except if you spin a sphere and stop it, it won't start spinning again when you let go.

    jbarnett;1663553

    Yeah, it's the moment of inertia (ie rotational inertia) of the spheres. … Yeah, it's the moment of inertia (ie rotational inertia) of the spheres. The hollow sphere has the same mass as the solid sphere, but it's 'nearer the outside', so the M of I is higher. So, for example if you were to roll them down a slope, the solid sphere would accelerate faster than the hollow ball (in the interview I lifted the table and let them roll down).



    Ah. Thanks for the explanation. Wish I could of remembered all that instead of just remembering watching the balls rolling. :oops:

    If you have 2 metal balls of identical size and mass but one of them is hollow then they must be different densities so different metals, so identify the metals through chemical tests, then work out the expected mass for solid spheres - the deficient one is hollow.
    Where did I go wrong?

    It hurt my head just reading that puzzle! long day at work! might give it to my son to figure out though...

    Original Poster

    I think I'll post another one soon...

    chesso;1664191

    If you have 2 metal balls of identical size and mass but one of them is … If you have 2 metal balls of identical size and mass but one of them is hollow then they must be different densities so different metals, so identify the metals through chemical tests, then work out the expected mass for solid spheres - the deficient one is hollow.Where did I go wrong?



    That is definitely a valid method, but it wasn't what I was looking for.

    Once I'd established that the spheres were made of different materials, I was informed that they were aluminium and steel. But the spheres were coated in plastic so I couldn't tell which was which by looking.

    i was asked this question on my interview !!!!! Didn't get it right cos nerves kicked in and I had a breain freeze but still got the job. I remember the answer being 3 on each side. Whichever heavier, take two and weight. etc etc

    you the the idea ! Too tired to type.

    jbarnett;1664393

    That is definitely a valid method, but it wasn't what I was looking … That is definitely a valid method, but it wasn't what I was looking for.Once I'd established that the spheres were made of different materials, I was informed that they were aluminium and steel. But the spheres were coated in plastic so I couldn't tell which was which by looking.



    magnet?
    Or did they only want a mechanical solution? I suppose that, as you got the job it was all fine anyway!

    It was more of a 'think out loud' question, rather than one with a specific answer. I literally just listed everything that came to mind, but as far as I know, rolling them was the only one that could be done there and then, and I guess that was the answer they were looking for ultimately.

    I think I suggested:

    Cut it in half
    Ultrasonic
    X Ray
    Magnetism
    Chemical testing (ie steel would rust)
    Visual inspection (upon removal of plastic coating)
    Rolling them
    Testing the heat capacity

    By the way, I'm sorry to have hijacked your thread Abvance! Thanks for posting the puzzle in the first place, it definitely got me thinking.
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