Hear Ye! Since 1998.
Please note: This post is at least 3 years old. Links may be broken, information may be out of date, and the views expressed in the post may no longer be held.
5
May 00
Fri

Riddle Ye! VI Solution

I take it that since there are no posted riddle solutions, you haven’t received any…that is really really poor!! Shame on them.

(I am somewhat unwilling to provide this as noone even had an attempt…)
Let us split the coins up into 3 piles of 4. We weigh two of them against each other.

Case 1 – They weigh the same.
That means the counterfeit is among the remaining four. Take two of them, and weigh them one against the other.
If they are equal, take off one and put on one of the remaining 2. If they are still equal the remaining one is fake, if the one you put on is heavier or lighter then that is the fake. (3 weighings)
If they aren’t equal, take off one and replace it with a real coin. If the scales don’t shift, then the one left on them is fake, if they balance out, the one you removed is a fake. (3 weighings)

Case 2 – They are not the same.
That means that the 4 remaining coins are real, and the counterfeit is among those eight. One side of the scales will be higher than the other. We then take 3 coins from the bottom plate and put them aside, take 3 coins from the top plate and put them on the bottom plate, and take 3 real coins (from the 4 we haven’t weighed) and put them on the top plate.
If nothing happens, the counterfeit is one of the 2 we didn’t move. Weigh one against a real coin – if the same, the other is fake, if different, it is fake. (3 weighings)
If the scales balance out, that means we have removed the real coin, and therefore it is one of the 3 we removed, and heavier than a real one (as they were off the bottom plate). Then, weigh two of the 3 against each other – if one is heavier, that’s the fake, if they are the same, the third is the fake. (3 weighings)
If the scales change (ie. the top plate becomes the bottom one), then we have moved the counterfeit coin from the (former) top to the (former) bottom. Therefore it is one of the 3 we moved thus, and it is lighter than a real coin (it was on the top plate). Then, weigh 2 of the 3 against each other. If the same, the third is fake, if one is lighter, it is fake. (3 weighings).

There you go…not that hard now was it?
Bonhomme de Neige

s