28 Aug 2022 10:59 am
I see how your logic works if the scales are tilted on the 1st weighing.
What if the 1st weighing is even? Now you have 2 more chances, and only moving 2 marbles from side b to side a will not resolve it every time. You need to move 3 marbles in order to only leave one control marble for the final step.
If you put yellow marbles on both sides on step 2, you're not resolving anything if the scale tilts, because you don't know if one of those 3 yellow marbles is heavier or lighter, and you're left with one more chance. You can't put the yellows on both sides. It has to be on one side, and therefore you have to put all 3 on one side.