# How to solve this problem?

You have 9 identical coins. Eight coins are real and one is counterfeit (fake). You are

not able to tell them apart by looking at them or touching them. But, you have a balance

scale that can detect the counterfeit coin. This scale can detect that the counterfeit coin

is lighter in weight than the real coins. You can place the coins on the balance scale in

any combination but you must do it in only 2 weighings.

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Seperate tha nine coins into three batches A, B, and C, each consisting of three coins.

Then weight two of the batches against one another, say A and B.

If they are equal you know the counterfeit coin is in batch C, if A is lighter than its in batch A, so on.

Take the lighter batch of 3 coins.

Weight 2 of them, no matter which one. If they are equl than you know that the counterfeir coin is the one you didn’t weight. If they are not than you see which one is lighter and thats the counterfeit coin.

Ok here’s how to do it. Separate the coins into 3 groups with 3 coins each. Put 1 group on one side and one group on the other. Leave the third alone. If the scale is equal then the other group has the counterfeit coin (because all the coins weigh the same). If one is higher then keep that group and set the other groups aside. Put now out of the 3 coins in that group put 1 coin on one side of the scale and 1 coin on the other. It’s now just like the time before. If the scale stays the same then you know it’s the final coin (because the real coins weigh the same). But if one goes up then you know that’s the coin. And you know which coin is counterfeit!

weigh any three coins against any other 3. If they’re equal, you have 3 coins left, weigh 2 of those. If they’re the same, the remaining one is counterfit, if they’re not, you’ve still found the counterfit.

If the 3 against 3 are not even, take the light stack of 3 and weigh one against one. If they’re even, the one left over is the counterfit, if they’re not even, the lighter one is the counterfit.