A:
1. weigh coins 1,2,3,4 against 5,6,7,8  
if they are the same then {
   2. weigh coins 9,10 against 11,1 (1 is a good one)
   if they are the same, it must be coin #12 and then {
      3. weigh 12 against 1 to see if it is heavier or lighter
   }
   if they are different then {
      3. weigh 9 against 10
      if in weighing #2, the group (9,10) was heavier, then the heavier
       one is the odd coin, and vice versa.
      if they are equal, then 11 is the odd coin, and whether or not it is
       heavier or lighter is learned in weighing #2
   }
}
if they are different then {
   2. weigh coins 1,2,6 against coins 3,4,5
   if they are the same then {
      it must be either 7 or 8, and we know it is heavier or lighter from
       weighing #1
      3. weigh 7 against 8 to see which one it is.
   }
   if they are different then {
      if the (1,2,6) side is heavier or lighter in BOTH weighings #1 and #2
       that is, it stayed the same, then it must be either coin 
       1,2 or 5 that is the odd one, because these are the coins that we 
       DIDN'T move from weighing #1 to #2, 
       and then {
         3. weigh 1 against 2
         if they are even, then the odd coin is 5 and we know if it is 
          heavier or lighter from both #1 and #2
         if they are not even, then we know which coin it is because we 
          know whether the odd coin is heavier or lighter from both #1 and 
          #2
      }
   if the (1,2,6) side is heavier in one weighing but lighter in the 
       other, that is, it flip-flopped from #1 to #2, then it must be 
       either coin 3,4 or 6 that is the odd one, because these coins 
       we moved from one side to the other,
       and then {
         3. weigh 3 against 4
         if they are even then the odd coin is 6 and we know if it is 
          heavier or lighter from both #1 and #2
         if they are not even, then we know which coin it is because we
          know whether the odd coin is heavier or lighter from both #1 
          and #2
      }
   }
}