12 coins and scale

Imagine that you have 12 coins and a balance scales. You know that one of the coins is a counterfeit, but you don't know whether it is lighter or heavier than others. The task is to isolate the counterfeit coin with 3 weightings.

Solution:
Let's mark coins with letters A, B, C, D, E, F, G, H, I, J, K, L. The idea is to observe three different outcomes from the second and third weightings and apply them to three groups of coins. Group 1 is the coins that were removed from the scales, Group 2 that was moved to the opposite pan, Group 3 that stayed on the same pan. If the counterfeit coin is in Group 1, the scale will balance, if in Group 2, the scale will change position, if in Group 3, the scale will remain in the same position.
First weighting is with 4 coins on each pan: A, B, C, D - E, F, G, H. If the scales are in balance (a), the counterfeit coin is one of the four remaining coins I, J, K, L otherwise (b) it is one of the eight coins on the scales.
(a) For the second weighting we use A, I - J, K. If the scales are in balance, counterfeit is L and we can spend the third weighting to our pleasure. Otherwise, we weight J - K. If the scales are in balance, the counterfeit is I, if position of the scales stays the same as in prior weighting, it is K, if scales change position, it is J.
(b) Second weighting is: I, J, B, E - D, C, F, G. If scales are in balance, the suspects are A, H, which were removed from the scales (c). If scales are in the same position as in prior weighting, the suspects are B, F, G that stay on the same pans (d), if scales change position, the suspects are E, C, D, that were moved between pans (e)
(c) Third weighting is A - I. If the scales are in balance, the answer is H, otherwise A.
(d) F - G. If in balance, than B, if stay in the same position, then G, if change position, then F
(e) C - D. If in balance, than E, if same position, then D, if change position, then C