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Nasty lateral thinking problem

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  • Nasty lateral thinking problem

    I've been given this problem by someone and it made my head hurt, i couldn't figure it for 3 days so i though i'd share

    Here goes:

    I have in front of me 10 pill boxes,numbered 1 to 10, each containing 10 pills.
    All the pills weigh exactly 1 gram each except
    one out of the 10 boxes contains 10 pills that weigh 1.1 grammes each.

    I have a set of accurate digital scales.
    How can i find the box that contains the 1.1 gram pills ?
    I am only allowed to use the scales once.

    Stacking them up and taking them off again constitutes more than one weigh.
    The boxes are identical,apart from the numbers. The pills are identical.

    Good luck, i'll pop back later but i'll look a real idiot if someone gets it straight away.

  • #2

    There is only one way, I suppose. Why not take n pills from every nth pill box, and weigh them all together, e.g.:
    - take 1 pill of the 1st box,
    - take 2 pills of the 2nd box,
    - ...
    - take 10 pills of the 10th box,
    - put them all together and weigh them.

    You have now 55 pills. You can determine which box contains the 1.1 gram pills:

    If the first box has the 1.1 gram pills, the weigh would be 55,1 gram.
    If the second box [...] => 55,2 gram.
    The Boardzombie's website.


    • #3
      Well done !!!!!!