# Coin Problem-1?

Suppose that u have eight coins and r told that one is counterfeit and has a different weight (heavier or lighter)than the other seven.Determine which coin is different in no more than three weighings.

[hint:weigh 3 coins in the left pan against 3 in the right.]

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Start off, as suggested, with three on the left and three on the right. Label them A,B,C and D,E,F.

If they balance, then one of the other two is the counterfeit one. Swap F with one of the other two coins (call it G). If they still balance, then H is the counterfeit - if they donâ€™t then G is the counterfeit. That takes only two weighings.

If the original six do not balance, then one of the six must be counterfeit, and in this case, you know that G and H are genuine.

Take two off the heavier side (letâ€™s call them A and B) and two off the lighter side (D and E).

If C remains heavier than F, then ABDE are all genuine, and one of CF is fake. Balance either F or C against any of the known genuine coins, and if it balances, then it too is genuine, and you can have isolated the fake.

If, after removing two from each side, and you balance C and F so the scales move to level, then you know that one of ABDE is fake. You will also know that either A or B is heavier than a real coin, or D or E is lighter. However, Iâ€™m stuck at this point, and I hope somebody else can step in and finish the answer!!

The answer given by the previous contributor works if you know that the counterfeit is definitely heavier - but your question said it could be lighter OR heavier, so Iâ€™m not sure if the answer will satisfy your question.

With your hint this becomes easy.

Weight 3 in left and 3 in right.

If equal then weigh the other 2 to see which is heavier.

If one side is heavier - weigh 2 of the three fromthe heavier pan.

If they are equal then the third is the counterfeit. If one is heavire, than that one is counterfieit.

2 weighings is all it takes