September 13th, 2010 at 11:31:25 AM
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This is another "oldie but goodie".

You have 13 piles of silver coins. Each pile contains 13 coins. No one coin is in any way visibly distinguishable from any other. Twelve of these piles contain pure silver coins and a pure silver coin weighs precisely 10 grams. One of the piles contains coins which are not pure silver and each of these impure coins weighs only 9 grams. Using a simple scale (not a balance but a scale that measures in grams), what is the smallest number of weighings required to determine which pile of silver coins is impure?

You have 13 piles of silver coins. Each pile contains 13 coins. No one coin is in any way visibly distinguishable from any other. Twelve of these piles contain pure silver coins and a pure silver coin weighs precisely 10 grams. One of the piles contains coins which are not pure silver and each of these impure coins weighs only 9 grams. Using a simple scale (not a balance but a scale that measures in grams), what is the smallest number of weighings required to determine which pile of silver coins is impure?

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September 13th, 2010 at 11:58:00 AM
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Since you have piles and a scale that measures in grams... I say one.

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September 13th, 2010 at 12:05:17 PM
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the answer better not be 30 pieces of silver [if you know your Bible] [g]

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September 13th, 2010 at 12:34:12 PM
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None. The difference between 130 grams and 117 grams is easy to detect manually without weighing.

Otherwise, the answer is one. Is there a way to do hidden spoilers on here?

Otherwise, the answer is one. Is there a way to do hidden spoilers on here?

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September 13th, 2010 at 12:34:44 PM
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Seven weighings?

September 13th, 2010 at 12:40:37 PM
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One.

Number the piles 1-13

taking care to keeping them from mixing, take one coin from pile one, two coins from pile two, three from pile three, and so on until you take the entire 13 from pile 13 an place them all on the scale.

The difference in the weight from 910g will tell you which pile has the phonies (e.g., if the pile weighs 908 grams, there are two coins off, so the impure are in pile #2).

Number the piles 1-13

taking care to keeping them from mixing, take one coin from pile one, two coins from pile two, three from pile three, and so on until you take the entire 13 from pile 13 an place them all on the scale.

The difference in the weight from 910g will tell you which pile has the phonies (e.g., if the pile weighs 908 grams, there are two coins off, so the impure are in pile #2).

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September 13th, 2010 at 1:25:22 PM
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clever. I didn't read it carefully enough.

September 13th, 2010 at 2:01:01 PM
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Quote:MathExtremistNone. The difference between 130 grams and 117 grams is easy to detect manually without weighing.

Otherwise, the answer is one. Is there a way to do hidden spoilers on here?

The difference between piles can not be visibly detectable since all coins are indistinguishable.

September 13th, 2010 at 2:07:39 PM
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Quote:AyecarumbaOne.

Number the piles 1-13

taking care to keeping them from mixing, take one coin from pile one, two coins from pile two, three from pile three, and so on until you take the entire 13 from pile 13 an place them all on the scale.

The difference in the weight from 910g will tell you which pile has the phonies (e.g., if the pile weighs 908 grams, there are two coins off, so the impure are in pile #2).

I lost you a bit here. You have 13 separate piles untouched and then you start pulling coins one from Pile 1, 2 from Pile 2, so on and so forth. Don't you mean the following:

a.) 13 Piles Untouched

b.) You pull 1 coin from each pile 1 at a time and place on the scale. The moment you get a reading that does not equal 0 in the unit's digit space, you know the pile that contains the odd weighing impure silver. This is because pure silver weighs 10grams here and impure weighs 9 grams.

c.) Example: (coin 1 from pile 1 = 10grams + coin 2 from pile 2 = 20 grams)+ coin 3 from pile 3 = .9 grams ...ahh haha. Pile 3 it is.

September 13th, 2010 at 2:09:35 PM
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If adding 1 coin to the scale from each pile until we find the odd number units digit counts as a "weigh in", then I believe the answer to the minimum number of weigh ins is 12 to guarantee that out of 13 piles, we find the impure pile.