You have 12 coins, six weigh 24 grams and six weigh 25 grams. You also have the broken scale from Five Weights and a Broken Scale
Sort the 12 coins into the group of 24g coins and the group of 25g coins using that broken scale no more than 9 times.
I still think you're overanalyzing the problem, but I see what I messed up on my original solution.
Take four coins from the pile of twelve. Weigh them AB/CD, AC/BD, and AD/BC. One of them will show a lighter weight, as 50g is more than 1.5g heavier than 48g. Repeat three times. Nine weighings, sorted out.
Note: This might not work. There is a problem with my logic that yes, could be fixed if I used a computer program. But I prefer to sort things out like this. Makes me feel all warm and fuzzy inside. With two coins on each side, the only way the scale would even register is if one side is both 24g, and one side is both 25g. Anything else is less than 1.5g apart. I took that into consideration.