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Mistershine said:
Can I sit on the scale and pick up 1 coin at a time?

Also just picking up the coins will tell you which ones are heavier.

It might, but you need scientific logical proof.  There is a way to do it even if the difference was 2 kilograms to 2.1 Kilograms.  The 2 kilograms vs 1 kilograms thing is just to make it less complicated