27 12 Identical Balls 
27 

12 Identical Balls 
54 

All the King's Wine 
12 Identical Balls
I found an alternate solution to this one: The first step is the same, but in step 2, when you've got 14 and 58 as containing the odd one out, weigh (1,2,5) x (3,4,9). If they're equal, then 6,7,or 8 is the light one, so weigh one against another. Otherwise, there are two outcomes: 1) if (1,2,5) is lighter, then either (1,2) is heavy, or 5 is light, so weigh (1) x (2). 2) if (1,2,5) is heavier, then either (1,2) is heavy, so again weigh (1) x (2) to find out which. context 