# Math Riddle: There are eight silver coins and one counterfeit coin…?

that looks like a silver coin but actually weighs slightly less than the others. By using a balance scale to compare coins (or groups of coins), how can you determine the counterfeit coin with just two weighings?

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Simple answer.

If the coin weights slightly less than the others. You must first weigh 3 coins vs. 3 coins. If they weight exactly the same, they you just need to weight the remaining two and figure out which one it is.

If they do not weigh the same amount. Then you have determined it has to be one of 3 coins. Pick any two and weigh them. If they weigh the same amount then you are done, and its the one you didnt weight. If they dont weight the same amount then you are done, and it is the one that weights less.

Take any 8 of the 9 coins, and load the scale up with four coins on either side. If the two sides are equal, then the remaining coin is the fake.

If however, the two sides are not equal, then that remaining coin is a real coin and the fake is in one side or the other of the scale.

The trick is that now you must unload at the same time a single coin from each side of the scales.

If the scales now balance, the bad coin is one of the two which you just withdrew.

If the scales remain unbalanced, the fake is still on the scales.

As you remove good coins you can just add them to the good coin pile which began with the first isolated coin.

Once you have found the two coins which when removed balance the scales, or if they are the final two and the scales are still unbalanced, you take one of those two and weigh it against a known good coin.

If they balance on this second loading of the scales, or if the donâ€™t, you have now with only two loadings of the scales correctly identified the fake coin.

weigh two groups of 3, if equal the light cion is in the other three. if they weigh unequal, the light group of 3 contains the light coin. so now its down to a group of 3 coins, weigh one vs one. if equal the other coin is it, if unequal, the light side one is it

With 9 coins total, all you have to do is the following:

Take 6 random coins, and weigh 3 and 3. One of two things are going to happen:

1) They will weigh the same. If this is the case, take the remaining 3 coins, and weigh 1 and 1. One of two things at this point is going to happen.

. . 1a) They will weigh the same. If this is the case, it will be the . . . . . . 3rd coin that is the counterfeit.

. . 1b) They will weigh differently. The lighter coin is the counterfeit.

2) They will weigh differently. If this is the case, take the lighter of the 3 coin stack, and take 1 and 1.

. . . 2a) If they weigh the same, the 3rd coin is the counterfeit.

. . . 2b) If they weigh different, the lighter coin is the counterfeit.

You take 8 coins and but then in the balance, if they are the same you found it, if not you keep taking 2 coins away from the balance until it is balanced, then you put the two coins alone in the balance and check which one is the fake.

say 8 coins A,B,C,D,E,F,G,H

Take ABC and DEF if it equal then take F and G to put in the scale —>the fake coin

If ABC lighter than DEF than take A and B to put in the scale —>fake coin