
Step 1. Compare the two 2buckazoid coins. They
either balance (diagram A1) or they don’t (diagram B1). We treat each
possibility differently. If they balance, go to step 2, if they don’t
balance, go to step 3.
Step 2. We know that both 2buckazoid coins are real, so the fake one
is either the 1 or the 3buckazoid coin. Weigh the 1buckazoid and
the 3buckazoid coin against the two 2buckazoid coins. Obviously,
they won't balance. We now know whether the fake is too heavy (diagram
A2) or too light (diagram A3). Now put the 3buckazoid coin in one
pan, and one of the 2buckazoid coins and the 1buckazoid coin in the
other. If the fake is lighter, then the lighter pan contains the fake
 this is the 3buckazoid coin in diagram A4 and the 1buckazoid coin
in diagram A5. If the fake is heavier, then the heavier pan contains
the fake  this is the 1buckazoid coin in diagram A4 and the
3buckazoid coin in diagram A5.
Step 3. One of the 2buckazoid coins is fake, and both the 2 and
3buckazoid coins are real. Put the 3buckazoid coin in one pan, and
one of the 2buckazoid coins and the 1buckazoid coin in the other,
and this will tell which of the 2buckazoid coins is fake. If both
pans balance, then the remaining 2buckazoid coin is the fake 
diagram B2 (from remembering the result of the weighing in diagram B1
we can say if the fake is lighter or heavier). If the pans don't
balance, the 2buckazoid coin in the pan is the fake (diagram B3)  in
case the pan is lighter the fake is lighter, and in case the pan is
heavier the fake is heavier. 
