Even harder riddle

[AztecWarrior]

You have 12 coins. These are the most valuable coins, ever. Don't ask what's in them. However, one of them is impure by just a tiny bit. However, you do have The World's Best Scale to help you. TWBS can sense impurity to a bajillionth of a gram and will exxagurate the difference between two objects of different mass so that one that is even slightly off in weight will be shown by a big change.

However, the guy who owns it is a total prick, and you only have enough money to use it THREE times.

Furthermore, you don't know if the impurity is a lighter or heavier substance- meaning that if one coin is heavier than the other, you know nothing.

Come up with a straightforward strategy to find the coin.

ONE guy solved this in our Physics class.

[WritheNC]

I'm not doing your homework for you because...I don't know! :)

[AztecWarrior]

It's not homework. By the way, I found an alternate way to solve this.

Because nobody on Earth will get this, I will allow you to post the answer in the thread.

[MrPaul]

You have the worlds most valuable coins evar and you only have enough money to use the scales 3 times? sheesh.

I can only think of an answer for it you knew if it was heavier or lighter. I bet it's similar to this...

[Triggar]

Didn't Martyr post a variation of this riddle a few weeks ago?

[Mr1337Duck]

Very very simple.

12 coins, 3 scale uses.

Look at the thing that shows a graph. If it's a straight line, weight going up by a steady amount with each coin being added...


Ah hell, shoot the owner, take the coins, torch the scales. Nobody else will be able to tell which is fake.

[Derfud]

I put all the twelve coins, 6 on each side, on the scale one at a time, as soon as there is a difference, I stop, then begin to remove two from each side until the difference is gone, on the two coins I took away when it was gone, I weigh them both opposite each other, then one final time, I weigh the heavier coin, against a different coin, knowing it is authentic. Whether the scale stays the same when I replace the last coin, or whether is changes, affects which coin I will determine to be fake. Obviously, if in the final use of the weighing both coins were the same, then the coin I removed is obviously fake. If not, then it is the coin I didnt remove.

Technically speaking, placing the coins down two by two, is using it only once.

[Rbstr]

you can only use it thre times Defud

put 6 coins on each side, take note of the differences
take 3 coins of each side.
if the sides are the same you know, besause of the difference recorded above and the mass of these times 2, witch group of three(not on the scale) is the one with the impure coin.
if the sides are not the same you know for the same reasons above, what group of 3(on the scale) is the one with the impure coin.

then put a coin on each side of the scale, if they are the same the on not on the scale is the impure one, if one is different based on results before you can figure out witch is witch.

[Derfud]

I only did use it three times, look at my explination.

[UncleDynamite]

Answer

For now, let's say that we only have 9 coins. We can find the fake coin in three weighings, the first two as follows:

Coins 1 2 3 against Coins 4 5 6
Coins 1 2 3 against Coins 7 8 9

That'll let us know which group has the fake coin. For example, if groups 1 2 3 and 4 5 6 balance out, but if group 1 2 3 falls while group 7 8 9 rises, we know the fake coin is in 7 8 9. Now, we do the third weighing to find the fake coin by putting a coin from each group on either side.

Coins 1 4 7 against Coins 2 5 8

For 12 coins, we simply add three more coins to our groupings:

1 2 3 10 against 4 5 6 11
1 2 3 11 against 7 8 9 10
1 4 7 10 against 2 5 8 12

That should let you discover the fake coin.