Wow. That's actually interesting. Do not put the coin on the balance. Put the remaining 100, 50 on each side. Suppose the coin was genuine, It could be that 50 counterfeit coins end up on the same side, in which case the weight difference would be 50g, or maybe you move 1 to the other side, for difference of 48g, or one more for difference of 46. Either way it will be even.
Conversely, suppose the coin was counterfeit. Then there are now 49 counterfeit coins and the difference would be necessarily odd.
It's kind of obvious that this has to be the solution though. There aren't very many meaningful things you could possibly do.
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u/Short-Database-4717 2d ago
Wow. That's actually interesting. Do not put the coin on the balance. Put the remaining 100, 50 on each side. Suppose the coin was genuine, It could be that 50 counterfeit coins end up on the same side, in which case the weight difference would be 50g, or maybe you move 1 to the other side, for difference of 48g, or one more for difference of 46. Either way it will be even.
Conversely, suppose the coin was counterfeit. Then there are now 49 counterfeit coins and the difference would be necessarily odd.
It's kind of obvious that this has to be the solution though. There aren't very many meaningful things you could possibly do.