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  1. #1

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    A bag contains two marbles, each black or white.
    The marbles are identical in all respects other than color.
    The marbles were randomly selected from an indefinitely large pool where half of the marbles were black and half of the marbles were white.
    The pool is unavailable for inspection counts at any time.
    How do you figure out the colors of the marbles?



    ed... I'm updating this description of the puzzle as the need for clarification arises.

    Clue #1 now appearing in post #29
    Clue #2 obliquely revealed in post #41 (with more about Clue #2 in post #47)
    Last edited by pauln; 05-26-2020 at 11:15 PM.

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    The Jazz Guitar Chord Dictionary
     
  3. #2

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    So there are either two white marbles, two black marbles, or one white and one black marble?

  4. #3

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    I don't know Iv'e lost mine.

  5. #4

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    Open the bag.

    Unless the bag is transparent of course.

  6. #5
    Quote Originally Posted by BigDaddyLoveHandles
    So there are either two white marbles, two black marbles, or one white and one black marble?
    Yes!

  7. #6
    Quote Originally Posted by grahambop
    Open the bag.

    Unless the bag is transparent of course.
    No, the point is to figure it out without looking.

  8. #7
    I should not have stipulated nothing known about the selection of the marbles in the bag; you may take it as given and know for certain that they were randomly selected from a large pool that had equal numbers of black and white marbles. I have corrected the initial post.

  9. #8

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    Quote Originally Posted by pauln
    No, the point is to figure it out without looking.
    Ask a friend?

  10. #9
    Quote Originally Posted by BigDaddyLoveHandles
    Ask a friend?
    It's not tricky like that. It uses probability calculations.

  11. #10

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    Check the remaining marbles in the pool. If there's an equal amount of black and white then the marbles in the bag are 1 white and 1 black. If there are 2 extra white marbles then the bag has 2 black ones. The opposite if there are 2 extra black ones. Anyway, that's how I'd do it.

  12. #11

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    Quote Originally Posted by Jack E Blue
    Check the remaining marbles in the pool. If there's an equal amount of black and white then the marbles in the bag are 1 white and 1 black. If there are 2 extra white marbles then the bag has 2 black ones. The opposite if there are 2 extra black ones. Anyway, that's how I'd do it.
    That is the correct way to do it IF one is 'allowed'; otherwise there is a 25% chance of either all white or all black and 50% chance of both.

  13. #12
    Quote Originally Posted by Jack E Blue
    Check the remaining marbles in the pool. If there's an equal amount of black and white then the marbles in the bag are 1 white and 1 black. If there are 2 extra white marbles then the bag has 2 black ones. The opposite if there are 2 extra black ones. Anyway, that's how I'd do it.
    That is excellent; but it's not tricky like that either; let's additionally stipulate that the remaining pool is unavailable (lost or destroyed, and we never knew how many marbles).

  14. #13
    Quote Originally Posted by jameslovestal
    That is the correct way to do it IF one is 'allowed'; otherwise there is a 25% chance of either all white or all black and 50% chance of both.
    Updated to stipulate the pool is unavailable for inspection counts.
    Your probabilities are correct and part of the path to the answer.

  15. #14

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    Will the solution be probabilistic, or certain?

  16. #15
    Quote Originally Posted by BigDaddyLoveHandles
    Will the solution be probabilistic, or certain?
    Oh yes; the answer appears to be surprisingly impossibly absolutely certain, describing the marbles in the bag as one of WW, BW, or BB.

  17. #16
    I have a clue but I'l hold it until needed...

  18. #17

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    Do all the marbles have the same weight, shape and size?

  19. #18
    Quote Originally Posted by Tal_175
    Do all the marbles have the same weight, shape and size?
    Yes, and same density, temperature, charge, magnetism, etc. Nothing tricky about the marbles.

  20. #19

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    Is Schrödinger's cat involved in this ?

  21. #20

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    Since the contents of the bag can be any of BW, BB or WW it is impossible to be certain which one of these three possibilities is true while the marbles are concealed in the bag, without a further test.

    The marbles are identical in every respect but colour.

    The test for colour is visual.

    We are not allowed to open the bag.

    If it is possible to determine the colour visually without opening the bag, it must follow either that the bag is not opaque or (and/or) that it is truthfully labelled to identify its contents.

    What do I win?
    Last edited by pcjazz; 05-26-2020 at 06:51 PM.

  22. #21
    Quote Originally Posted by 339 in june
    Is Schrödinger's cat involved in this ?
    Nope, no Schrodinger's cat, no many worlds, etc.

  23. #22
    Quote Originally Posted by pcjazz
    Since the contents of the bag can be any of BW, BB or WB it is impossible to be certain which one of these three possibilities is true while the marbles are concealed in the bag, without a further test.

    The marbles are identical in every respect but colour.

    The test for colour is visual.

    We are not allowed to open the bag.

    If it is possible to determine the colour visually without opening the bag, it must follow either that the bag is not opaque or (and/or) that it is truthfully labelled to identify its contents.

    What do I win?
    Not yet.
    The marbles in the bag cannot be seen.
    The bag is not labeled or otherwise marked indicating contents.

  24. #23

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    Was the original pool mixed, or divided by color, say, left and right?

    Also, when we say "randomly selected," are we to assume the pick for the bag was done blind? Or was the instructions to the picker "choose any two marbles" with no further instruction as to what would be done with them?

  25. #24

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    Chocolate and vanilla!

  26. #25
    Quote Originally Posted by mr. beaumont
    Was the original pool mixed, or divided by color, say, left and right?

    Also, when we say "randomly selected," are we to assume the pick for the bag was done blind? Or was the instructions to the picker "choose any two marbles" with no further instruction as to what would be done with them?
    The pool was well mixed.
    Marbles were picked and placed in the bag without knowing their colors.
    Nothing tricky about the pool or the marbles handing.

  27. #26
    Quote Originally Posted by BigDaddyLoveHandles
    Chocolate and vanilla!
    If that be your answer I may quote from scene 19; "You know much that is hidden".

    Clue #1 coming soon...

  28. #27

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    Dark colours absorb more light energy than light colours. What if I shine a light (of some wavelength, IDK) on the bag and observe how much energy is absorbed. From that, a smarter person than me could tell you the colours, assuming the bag doesn't block the light.

  29. #28
    Quote Originally Posted by BigDaddyLoveHandles
    Dark colours absorb more light energy than light colours. What if I shine a light (of some wavelength, IDK) on the bag and observe how much energy is absorbed. From that, a smarter person than me could tell you the colours, assuming the bag doesn't block the light.
    Does not involve tricky physics principles like that.
    All the tricky part is logical.

  30. #29
    Quote Originally Posted by ragman1
    Based on what's been said, the only way to be certain is to open the bag and look. Otherwise it's guesswork.
    Looks like time for a clue. Clue #1 is a little long winded...

    ================================================== =================
    This is clue #1
    Scroll down the page to ponder it, or not for those wishing to proceed without it.
    ================================================== =================



























































    here it comes...























    ================================================== =====


    Clue #1


    Forget the puzzle for a moment and consider two scenarios below.


    Scenario A


    Imagine that I inform you I have exactly two black marbles and one white marble in a bag. If I ask you draw one marble from the bag, what is the probability of selecting a black marble?


    You reply that if there are only three marbles and two are black and one is white, then the probability of selecting a black marble MUST be 2/3.


    Scenario B


    Imagine that I inform you I have exactly three marbles, each is black or white, in a bag, and I inform you that the probability of drawing a black marble is 2/3. I ask you what are the colors of the marbles?.


    You reply that if there are three marbles and the probability of selecting a black one is 2/3, then the colors of the marbles MUST be two blacks and one white.

    ------

    The two scenarios were just to produce the two replies:

    A - Knowing the colors (BBW) and quantity (3) of the marbles reveals the probability (2/3) of selecting a black marble.
    B - Knowing the quantity of marbles (3) and probability of selecting a black marble (2/3) reveals the colors of the marbles (BBW).

  31. #30

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    Probability answers are not a correct, definite and exact answer. You'd still have to check the bag to know if you were right.

    Unless it was you who selected the marbles, of course :-)

  32. #31
    Quote Originally Posted by ragman1
    Probability answers are not a correct, definite and exact answer. You'd still have to check the bag to know if you were right.
    The answer describes the marbles colors in the form BB, BW, or WW.
    Probabilities are abused to get the answer, but the answer is not a probability.

  33. #32

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    OK Pauln, I have 6 black and 6 red Jazz III picks in a jar. I randomly picked 2 Jazz III picks and holding them in my closed fist. Since presumably you can answer the puzzle you posted, you should be able to tell me the colors of the 2 picks I'm holding. I'm waiting for your answer.

    Am I missing something?

  34. #33

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    What's the probability I'm cracking open a beer right now?

    .
    .
    .
    .

    100%!

  35. #34

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    The most likely scenario is BW, because when the first marble is chosen, it is either black or white.
    Now when the second marble is randomly chosen, the pool has more of whatever the opposite color is.

  36. #35

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    Sounds a bit like the old ‘Monty Hall’ problem.

  37. #36

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    Quote Originally Posted by pauln
    The answer describes the marbles colors in the form BB, BW, or WW.
    Probabilities are abused to get the answer, but the answer is not a probability.
    You can't work out the answer even with probability because there's no information to work with.

  38. #37
    Quote Originally Posted by Tal_175
    OK pauln, I have 6 black and 6 red Jazz III picks in a jar. I randomly picked 2 Jazz III picks and holding them in my closed fist. Since presumably you can answer the puzzle you posted, you should be able to tell me the colors of the 2 picks I'm holding.

    I'm waiting for your answer. Am I missing something?

    I don't wish to confound the liberty of others working the puzzle. Clue #1 appears in post #30.

  39. #38
    Quote Originally Posted by ragman1
    You can't work out the answer even with probability because there's no information to work with.
    All the information needed has been provided in post #1, by jameslovestal's post #11, and clue #1 in post #29.
    Last edited by pauln; 05-26-2020 at 11:17 PM.

  40. #39
    Quote Originally Posted by wengr
    The most likely scenario is BW, because when the first marble is chosen, it is either black or white.
    Now when the second marble is randomly chosen, the pool has more of whatever the opposite color is.
    That is excellent, but let's stipulate that the pool is large enough that effect approaches zero.

  41. #40

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    Quote Originally Posted by ragman1
    Sorry, impossible.

    Random selection from an equal pool of two colours. Either one is white and one is black, or both are the same colour. There's no probability to give the answer. It needs at least one more element in the equation to point to a probable combination.

    In any case, probability answers are not the right answer. You'd still need to check in the bag. Guaranteed.
    yes, even knowing the colour of the first marble won’t tell you the colour of the second in this case.

  42. #41
    Quote Originally Posted by ragman1
    Sorry, impossible.

    Random selection from an equal pool of two marbles. Either one is white and one is black, or both are the same colour. There's no probability to give the answer. It needs at least one more element in the equation to point to a probable combination.

    In any case, probability answers are not the right answer. You'd still need to check in the bag. Guaranteed.
    Now see, you've actually revealed Clue #2. That's progress.
    Take a look at Clue #1; there is more probability there.

  43. #42

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    A probable answer is not the right answer.

    I think I'll go and do something sensible, like play the guitar, and come back when all is revealed. I may have to grovel. I may not :-)

  44. #43

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    Were the two marbles selected sequentially or simultaneously?

  45. #44

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    As a logic problem the puzzle has no solution. May be there is a word trick somewhere that deliberately disguises the true premise of the puzzle.
    Puzzle solver is allowed to make reasonable assumptions about the premise, otherwise a puzzle can never be told. It will take forever to describe the complete situation by listing everything that's true and everything that's false about the premise.

  46. #45
    Quote Originally Posted by wengr
    Were the two marbles selected sequentially or simultaneously?
    With an indefinitely large pool, we can always make the pool large enough that it won't matter. We may assume they were selected simultaneously; in any event nothing is tricky about their selection so we take jameslovestal's post #11 probabilities as correct.

  47. #46
    Quote Originally Posted by ragman1
    A probable answer is not the right answer.

    I think I'll go and do something sensible, like play the guitar, and come back when all is revealed. I may have to grovel. I may not :-)
    OK, but may I suggest while playing you work with triads and let Clue #1's conclusions A and B concerning both their symmetrically invariant initial quantities of marbles (3) run in the background of your mind.

  48. #47
    Quote Originally Posted by pauln
    Now see, you've actually revealed Clue #2. That's progress.
    Take a look at Clue #1; there is more probability there.
    More about Clue #2

    Clue #2 is about how to use the certainty about three marbles in the two statements A and B in Clue#1 in order to make a certain answer about the two marbles of the puzzle. Notice that in neither scenario A or B is the set of three marbles originating from a random selection; in A the arrangement is given as two blacks and one white, in B the arraignment is given by the probability.
    Last edited by pauln; 05-26-2020 at 11:14 PM.

  49. #48

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    Quote Originally Posted by pauln
    A bag contains two marbles, each black or white.
    The marbles are identical in all respects other than color.
    Using simple logic from just these two sequential clues, which are presented to be facts, you just paraphrase the facts and come to a conclusion.

    A bag contains two marbles, identical in all respects OTHER than color.......so, the colors are NOT identical, one must be black, and one must be white for this to be true.

    All other info is to misdirect.

  50. #49

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    Cosmic -

    That's the most intelligent answer so far. Someone else suggested that it was one of those description puzzles that you have to read very carefully. On that basis your answer's correct.

    Unfortunately Paul has said the puzzle uses probability:

    Quote Originally Posted by pauln
    It's not tricky like that. It uses probability calculations.
    As the puzzle setter he's not allowed to say that unless it's true.

  51. #50

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    each black or white. Semantic trick: they can be either, but not both, ergo one black, one white.