To work through an example using your method:
Let A,B,C,D,E,F,G,H,I,J,K,L be the set of 12 coins. Let L have a heavier weight.
X = A,B,C,D
Y = E,F,G,H
Z = I,J,K,L
(1) X vs Y => Balance. (1st weighing)
==> a) Discard X and Y.
(2)
a) Split Z into groups of 2:
Z1 = I,J
Z2 = K,L
Place them on the scale (2nd weighing).
Z1 is the lighter side.
(3)
a) Replace the lightest scale's coin (there are two of them aren't there???) with any previous coins. I'll assume you mean replace one of the two coins.
Z1 = A,J (replacing I with A).
Z1 vs Z2 => Z2 is heavier. (3rd weighing).
Now you are stuck with Z2, and no way of knowing which is the heavier coin.
Also, what if the coin was a lighter one, and in step 3a you replace a normal coin with a normal coin? This means you have no idea whether the odd coin is on the heavy side, or the other coin on the lighter side.
Let A,B,C,D,E,F,G,H,I,J,K,L be the set of 12 coins. Let L have a heavier weight.
X = A,B,C,D
Y = E,F,G,H
Z = I,J,K,L
(1) X vs Y => Balance. (1st weighing)
==> a) Discard X and Y.
(2)
a) Split Z into groups of 2:
Z1 = I,J
Z2 = K,L
Place them on the scale (2nd weighing).
Z1 is the lighter side.
(3)
a) Replace the lightest scale's coin (there are two of them aren't there???) with any previous coins. I'll assume you mean replace one of the two coins.
Z1 = A,J (replacing I with A).
Z1 vs Z2 => Z2 is heavier. (3rd weighing).
Now you are stuck with Z2, and no way of knowing which is the heavier coin.
Also, what if the coin was a lighter one, and in step 3a you replace a normal coin with a normal coin? This means you have no idea whether the odd coin is on the heavy side, or the other coin on the lighter side.
