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12 balls part 2

You can actually do this problem with just a single weigh. You take all of the first ball 1/2 of the second 1/3 of the third 1/4 of the fourth etc all the way to 1/12 of the final ball. The total weight if each ball was 10 grams should 31.032. Then depending on which ball is 9 grams you will be off of that by 1,1/2,1/3,1/4,1/5... etc. So based on the difference between the measured weight and 31.032 you will know which ball was 9 grams. If the ball was 11grams instead then ur just increased instead of decreased.