13 piles of silver coins problem

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?

Since you have piles and a scale that measures in grams... I say one.

the answer better not be 30 pieces of silver [if you know your Bible] [g]

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?

Seven weighings?

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).

clever. I didn't read it carefully enough.

Quote: MathExtremist

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?

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

Quote: Ayecarumba

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).

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.

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.

Quote: Asswhoopermcdaddy

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.

Actually, with my method, you only "weigh" the lot one time (but you need to be careful to keep the coins you pulled off each pile separated so that you can put the bad ones back after the weigh in.)

If every coin were pure you would have 1+2+3+4+5+6+7+8+9+10+11+12+13 = 91 coins that should all weigh 10 grams each, or 910g total. The impure coins will each be off by one gram, so the number less than 910g; when you weigh the whole lot of 91 coins one time, will tell you which pile they came from.