# I hav 9 gold coins that r identical exept for 1(counterfeit), how do I find it w 2 tries on a balanc scale?

I have 9 gold coins that are identical in appearance. However, one is counterfeit and weighs slightly less. Using a balance scale, how can I find the counterfeit coin in just two weighings?

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I was on the same track but the previous answer only works if there are 7 coins.

4+3= 7

Otherwise I would start with 4 coins on each side and the follow the previous answer. Of course that only allows you to solve it in 3 tries.

Okay

First, you put 2 coins on one side and 2 coin on the other side.

Case 1:

If one side goes up, you know that side contains the counterfeit coin.

Now you know one of the coins on the "lighter" side is counterfeit.

Take those two coins and put them on opposite sides of the balance.

The lighter coin is the counterfeit one.

Case 2:

If after you put 2 coins on one side and 2 coins on the other side, and the balance does not move, then you know that neither of those coins are counterfeit.

Put those coins on the side and pick 2 of the remaining 3 coins.

Place those one of those coins on one side of the balance and one coin on the other.

If one side moves up, that is your counterfeit coin.

If neither side moves up, the one remaining coin is your counterfeit.

edit:

Right… it was a little late for me when I was coming up with this answer… …and I thought I was being smart! =)

edit again:

Figured it out:

But 3 coins on either side of the scale

If one side is lighter, take two of those coins and put them on either side of the scale. If one side is lighter, that is your counterfeit coins. If both sides are equal, the coin you did not put on the balance is your counterfeit coin.

If when you weight your three coins on each side (six total), they all balance, place two of the three coins not balanced on the balance. If those two coins balance out, the one remaining coins is counterfeit. If one side is lighter, that is you counterfeit coin!