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 Post subject: Fools Gold
PostPosted: May 20th, 2010, 8:33 am 
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Acolyte
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Joined: April 29th, 2010, 7:35 pm
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Location: Near London
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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 Post subject: Re: Fools Gold
PostPosted: May 20th, 2010, 9:11 am 
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Joined: April 30th, 2010, 4:36 pm
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I guess the answer is: 1
But you must have luck. Take 7 bars in each scale. If the scales are in balance the 15th (not weighed) bar must be the lightest.


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 Post subject: Re: Fools Gold
PostPosted: May 20th, 2010, 9:13 am 
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Acolyte
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Joined: April 29th, 2010, 7:35 pm
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Location: Near London
Quote:
I guess the answer is: 1
But you must have luck. Take 7 bars in each scale. If the scales are in balance the 15th (not weighed) bar must be the lightest.
If you are lucky, yes. What is the fewest if you are unlucky?


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 Post subject: Re: Fools Gold
PostPosted: May 20th, 2010, 9:23 am 
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3?

1) Take 7 bars in each scale. The scale which is lighter must continue the light bar. If they are in balance --> see my first answer.
2) Take 3 bars of the remaining 7 in each scale. The scale which is lighter must continue the light bar. If they are in balance the 7th one (not weighed) must be the light one.
3) Take 1 bar of the remaining 3 in each scale. Either the scales are in balance, then the 3rd one must be the light one, or they are not in balance, then you can also identify the lighter one.

I want a prize now for translating this stuff into English!!! :mrgreen:


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