Hmm. I solved this a slightly different way. The first step was the same, (ABCD v EFGH), but all subsequent stages were different (for instance, if the scale ti

Hmm. I solved this a slightly different way. The first step was the same, (ABCD v EFGH), but all subsequent stages were different (for instance, if the scale tilts left, I'll then weight ABCEF against IJKLD). I'm sure there are multiple solutions. The key is that given there are 24 possibilities, and 3 possible outcomes from the scale, at each stage you must choose balls in order to maximize the amount of information gained. After the first weighing, you've reduced the possibilities to 8 (whatever the outcome). Since, on the final weighing there are only 3 possible outcomes, you need to devise a second weighing that ensures that the 8 possibilities are split into 3,3,2 - (ie. no result of the second weighing can yield an outcome where more than 3 possibilities remain).