The Odd Ball !

Discussion in 'Off-Topic Chat' started by impycornet, Nov 3, 2004.

  1. impycornet

    impycornet Member

    Following on from the Rope Question Try this one :shock:

    The Odd Ball Problem

    There are twelve identical-looking balls, but one is either heavier or lighter than the other eleven. How can you determine which is the odd ball and find out whether this ball is heavier or lighter than the others using only three weighings with a balance?


    Enjoy :p
     
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  3. lynchie

    lynchie Active Member

    I take it this is a "pm your answer" jobby...
     
  4. impycornet

    impycornet Member

    Yeah go on then !!

    Will post the answer Friday/Saturday

    Solved it already then ??
     
  5. TuTuKu

    TuTuKu Active Member

    Our maths teacher gave us this problem about a week ago.. made us talk it through and discuss it for about half an hour.. and then he forgot the answer! He said the answer's on then net somewhere!
     
  6. impycornet

    impycornet Member

    Excellent teacher then !!
     
  7. TuTuKu

    TuTuKu Active Member

    lol, no, he's good really... we'd finished our work so it was something he remembered off the top of his head to amuse us!
     
  8. lynchie

    lynchie Active Member

    I swear I need one more move.... hmmm... brain doesn't seem to be very well engaged this week...
     
  9. six pints

    six pints Active Member

    i know how its done but cant be bothered to write it out yet... ill pm you at some point just to prove it tho!
     
  10. flugelgal

    flugelgal Active Member

    My workings so far are one side of A4 but I think I'm getting there... :shock:
     
  11. davidquinlan

    davidquinlan Member

    **************************

    :)

    Edit: Have removed the URL which linked to the answer....
     
    Last edited by a moderator: Nov 4, 2004
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  13. T-Horn

    T-Horn Member

    well i've given up on this one. so you better give the answer soon!!
     
  14. MICKTHEEUPH

    MICKTHEEUPH Member

    It's easy!
     
  15. T-Horn

    T-Horn Member

    finally worked it out. i just hope that its right now!
     
  16. impycornet

    impycornet Member

    The answer.....


    If you don't want to know then look away NOW !!

























    Answer:



    Label the balls from 1 to 12 to identify them.

    Weigh 1, 2, 3, 4 against 5, 6, 7, 8:
    1. If they balance, 9, 10, 11, 12 contain the odd ball.
      Weigh 6, 7, 8 against 9, 10, 11.
      1. If they balance, 12 is the odd ball. Weigh 12 against any other ball to discover whether it is heavy or light.
      2. If 9, 10, 11 are heavy, they contain an odd heavy ball. Weigh 9 against 10. If they balance, 11 is the odd heavy ball, otherwise the heavier of 9 and 10 is the odd ball.
      3. If 9, 10, 11 are light, we use the same procedure to reach the same conclusion for the odd light ball.
    2. If 5, 6, 7, 8 are heavy, either they contain an odd heavy ball or 1, 2, 3, 4 contain an odd light ball.
      Weigh 1, 2, 5 against 3, 6, 10.
      1. If they balance, the odd ball is 4 (light) or 7 or 8 (heavy). Weigh 7 against 8. If they balance 4 is light, otherwise the heavier of 7 and 8 is the odd heavy ball.
      2. If 3, 6, 10 are heavy, the odd ball can be 6 (heavy) or 1 or 2 (light). Weigh 1 against 2. If they balance 6 is heavy, otherwise the lighter of 1 and 2 is the odd light ball.
      3. If 3, 6, 10 are light, the odd ball is 3 and light or 5 and heavy. We thus weigh 3 against 10. If they balance, 5 is heavy, otherwise 3 is light.
    3. If 5, 6, 7, 8 are light we use a similar procedure to that in II.
    Confused yet ??????? :)
     
  17. flugelgal

    flugelgal Active Member

    I'd gotten as far as 1., but had to get on with some work and never managed to work out the rest. (I also ran out of paper - how on earth did you manage to get all my one side of A4 into about 4 lines???).
     
  18. lynchie

    lynchie Active Member

    ah right... all makes sense now...
     
  19. WhatSharp?

    WhatSharp? Active Member

    AAAH! A binary sort algorithm in practice! (well kind of anyway)
     

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