How to Determine Counterfeit Coins with Only One Weighing

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To determine the number of counterfeit stacks among seven stacks of coins, each containing 100 coins, only one weighing is needed. The method involves taking a different number of coins from each stack: one coin from the first stack, two from the second, three from the third, and so on, up to seven coins from the seventh stack. This results in a total of 28 coins weighed together. Since real coins weigh 10 grams and counterfeit coins weigh 11 grams, the total weight will indicate how many stacks are counterfeit. If the total weight deviates from the expected 280 grams (28 coins x 10 grams), the difference in grams can be directly correlated to the number of counterfeit stacks. For example, if the weight is 283 grams, it indicates three counterfeit stacks. This approach efficiently identifies both the number and specific stacks containing counterfeit coins in just one weighing.
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There are seven stacks of coins, each consisting of 100 coins.
You know that real coins weigh 10 grams, but counterfeit coins weigh 11 grams.
You have an analytical scale that is accurate to .1 gram.
Each stack consists of either all real coins or all counterfeit coins, none of the stacks are mixed.
You do not know how many stacks are counterfeit or even if any of them are.
You want to determine how many stacks are counterfeit (if any), and precisely which ones are.
You want to do this in the least possible amount of weighings.

Whats the fewest number of weighings you need to make?
And how do you do it?
 
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Is there a catch? I make it 1.

Take 1, 2, 4, 8, 16, 32, 64 from each pile, measure the excess weight and convert it to a binary number
 
Jonathan Scott said:
Is there a catch? I make it 1.

Take 1, 2, 4, 8, 16, 32, 64 from each pile, measure the excess weight and convert it to a binary number

I'm impressed. :-p That was fast!
 
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