Find the Fake Gold Coin - a brain teazer - just for fun

1630Boston

There are 12 gold coins. One of the coins is fake. It is known that a fake coin weighs either slightly less or slightly more than a real coin. Using a balance scale, how can you find the fake coin, and determine if it weighs less or more than a real coin, in only three weighings?

Answer:

Divide the coins into three groups of 4 coins each. First, weigh two of the groups. If they balance, then the fake coin is in the third group, so take three of the coins, and weigh them against three of the coins that we know for sure are real (from the first 8 coins). If they balance, then the remaining coin is the fake one, but we still don't know if it is lighter or heavier, so weigh it against a real coin to determine that. But if it didn't balance, then we know that the fake coin is one of the three, and we also know if it is lighter or heavier, because we know which side had the real coins. So weigh two of the coins against each other, if they balance then the third coin is fake, if they don't balance we know which coin is fake, because we already know if it is lighter or heavier.
Now let's go back to the first weighing; if the two groups didn't balance, we know that the fake coin is in one of the groups, but we don't know which group. Let's mark the group that was heavier as group A, and the group that was lighter group B. For the second weighing, weigh two coins of group A and one coin of group B, against the other two coins of group A and one coin of group B. If they balance, the fake coin must be one of the remaining two, and a weigh between them will tell us which one (they are both from group B so we know that it's lighter). If the second weigh didn't balance, look at the side that is heavier: Either the fake coin is one of the two group A coins, or it can the group B coin on the other side of the scale. Take the two group A coins, and weigh them against each other. If they balance, then it is the group B coin that is fake, and if they don't balance, then the heavier one is the fake coin.
And that's that. We have covered all possibilities.

Namvet69

Whew! Peace Roy

Insider2

Thanks, this is a fun math puzzle. All possibilities except one...Unfortunately many fakes are of the correct weight. Add, "old underweight C/F" to the tease next time.

Timbuk3

Wow !!!

1630Boston

@Insider2 said:
Thanks, this is a fun math puzzle. All possibilities except one...Unfortunately many fakes are of the correct weight. Add, "old underweight C/F" to the tease next time.

I think you arrived at the correct answer

ricko

An exercise in logic.... so rare among people today... Well, at least rare among the younger adults - absent in juveniles. When my wife was teaching at the college, one of her courses was in critical thinking. It was amazing how many of her students had their minds blown... comments such as "How come we were not taught this before?", and "Wow....now I can think." Just amazing to see the level of learning coming out of public schools today. Cheers, RickO

AUandAG

Sure, here's another solution assuming that the CF is lighter than the real:

1. Divide the 12 coins into two groups of 6. Weigh.
2. Take the group that was lightest and split into two groups of 3 and weigh.
3. Take two of the coin in the lightest group of three and weigh. If they weigh the same the odd coin out is the fake and if one is lighter than the other that is the fake.

bob

RogerB

Put them in a boat and take them across the river before the wolf can swim over and eat the good ones.....

The alternate method is to put them all on one side of a balance and weight them against your thumb, then put the group in a paper wrapper, a CC coin on one end, and sell the whole group on ebay as an original bank wrapped short-roll.