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Math Help - Riddle me this Riddle me that...

  1. #1
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    Riddle me this Riddle me that...

    You have 15 tiny gold bars and a balance scale. One of the bars is lighter than the others, but you can't tell the difference by feel. What is least number of times you could use the scale to determine which one is the light one?
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    Quote Originally Posted by qbkr21 View Post
    You have 15 tiny gold bars and a balance scale. One of the bars is lighter than the others, but you can't tell the difference by feel. What is least number of times you could use the scale to determine which one is the light one?
    1)Take any 7, and take any 7.
    2)Weigh them.
    a)If equal then the remaining coin is lighter.
    b)If unequal take the lighter one.
    3)Spilt 3 with 3.
    a)If equal then remaining coin is lighter.
    b)If unequal take the lighter one.
    4)Split 1 with 1
    a)If equal the remaining coin is lighter.
    b)If unequal take the lighter coin as the solution.
    The worst case is 3 weighings.
    ----
    Does anybody know how to do this problem with math?
    Looks like a graph theory problem, but I do not know.
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  3. #3
    Grand Panjandrum
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    Is there an award for the most moved post?

    I moved this from Advanced Topics to Gerneral HS Maths Help, now
    moderator or moderators unknown have moved it here

    RonL
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    Quote Originally Posted by CaptainBlack View Post
    Is there an award for the most moved post?

    I moved this from Advanced Topics to Gerneral HS Maths Help, now
    moderator or moderators unknown have moved it here

    RonL
    The reason why I move so many threads is because of obsessive-compulsive disorder. I just cannot keep them if the wrong place.
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  5. #5
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    Quote Originally Posted by ThePerfectHacker View Post
    The reason why I move so many threads is because of obsessive-compulsive disorder. I just cannot keep them if the wrong place.
    I know the prank the rest of us are going to play on you on April Fools...

    Hehe
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  6. #6
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    Quote Originally Posted by anthmoo View Post
    I know the prank the rest of us are going to play on you on April Fools...

    Hehe
    He hasn't noticed the prank we have been playing on him since last April first yet

    RonL
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  7. #7
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    Quote Originally Posted by CaptainBlack View Post
    He hasn't noticed the prank we have been playing on him since last April first yet

    RonL
    Now that's going to mess with his head! He'll create 100 forum bots, each to carry out a separate, unique algorithm on every single post for deviations from the normal posting habits.

    ..This is the sort of thing that he'll cover his bedroom walls with...in blood!
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  8. #8
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    Quote Originally Posted by qbkr21 View Post
    You have 15 tiny gold bars and a balance scale. One of the bars is lighter than the others, but you can't tell the difference by feel. What is least number of times you could use the scale to determine which one is the light one?
    Here is one way.

    So the odd bar is lighter than any of the rest.

    Divide the 15 bars into 3. We now have 3 groups of 5 bars each, say, A, B and C.

    Weigh A and B. -------1 weighing.
    a) If the scale is balanced, then the lighter bar is in group C.
    a.1) Separate the 5 bars in C into 2-2-1
    Weigh the 2 and 2. -------another weighing.
    a.11) If they are balanced, then the 1 is the lighter bar. ------hence, 2 weighings only altogether.

    a.12) If not balanced, the 2 that is lifted has the lighter bar.
    a.121) Weigh the those 2. -----another weighing.
    The bar that is lifted is the lighter bar.
    Hence, 3 weighings altogether.

    --------------------------
    b) If in weighing groups A and B, they are not balanced, say group B is lifted, then the lighter bar is in B.
    Same procedure,
    b.1) Separate the 5 bars in B into 2-2-1
    Weigh the 2 and 2. -------another weighing.
    b.11) If they are balanced, then the 1 is the lighter bar. ------hence, 2 weighings only altogether.

    b.12) If not balanced, the 2 that is lifted has the lighter bar.
    b.121) Weigh the those 2. -----another weighing.
    The bar that is lifted is the lighter bar.
    Hence, 3 weighings altogether.

    ----------------
    Therefore, the "maximum" number of times to use the scale to determine the lighter bar is 3 times. The "minimum" number is 2 times only.

    But which of those is the " least number of times you could use the scale to determine which one is the light one?"

    I'd say three times. -------------answer.
    Last edited by ticbol; January 17th 2007 at 12:23 PM.
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  9. #9
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    I would say once...

    1) Pick 2 at random (In this situation you pick the light one and a normal one so you are very lucky!)
    2) Put them each on a balance
    3) They unbalance and woohoo you find the lightest one.

    Not mathematically sound but there is a probability that this could happen therefore this would count as the least weighings you could have to determine the lighter one.
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    Quote Originally Posted by anthmoo View Post
    I would say once...

    1) Pick 2 at random (In this situation you pick the light one and a normal one so you are very lucky!)
    2) Put them each on a balance
    3) They unbalance and woohoo you find the lightest one.

    Not mathematically sound but there is a probability that this could happen therefore this would count as the least weighings you could have to determine the lighter one.
    If you are going to play such games, we could ask for a weighing algorithm
    which minimises the expected number of weighings.

    RonL
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    Quote Originally Posted by CaptainBlack View Post
    If you are going to play such games, we could ask for a weighing algorithm
    which minimises the expected number of weighings.

    RonL
    Games? I think the laws of probability allow this to happen giving one as the least number of weighings! The riddle says nothing about the person doing the weighing being constantly mathematically unlucky

    EDIT: And doesn't your model base itself on the person weighing being lucky too?
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    What? No one dare to challenge me on this?
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  13. #13
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    Quote Originally Posted by anthmoo View Post
    Games? I think the laws of probability allow this to happen giving one as the least number of weighings! The riddle says nothing about the person doing the weighing being constantly mathematically unlucky

    EDIT: And doesn't your model base itself on the person weighing being lucky too?
    Worst case analysis of algorithms assumes that you are always unlucky.

    RonL
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  14. #14
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    Quote Originally Posted by anthmoo View Post
    What? No one dare to challenge me on this?
    So you are told to find the lighter bar from among the 15 bars. At least how many times do you have to use the balance scale to find it.

    If once, then you are lucky.
    Suppose you can not do it in one time? Then you can't solve the problem.

    If you can do it in two times, then you are lucky again.
    Suppose two times using the balance scale does not do it?
    You stop?

    Then 3 times solves the problem.
    Therefore, you need at least 3 times to solve the problem.

    ---------------
    If that doesn't challenge your lucky guess, then at least it explains why you need at least the "highest" possible times to use the scale to solve the problem.
    Last edited by ticbol; January 18th 2007 at 11:40 AM.
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  15. #15
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    Quote Originally Posted by ticbol View Post
    Then 3 times solves the problem.
    Therefore, you need at least 3 times to solve the problem.
    at most 3 times

    RonL
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