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If I'm reading this [0] right, the heavier/lighter factor can be determined within 3 weightings... [0] https://suresolv.com/brain-teaser/find-fake-ball-among-12-id...

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Of course it can. There are 24 possible states and you get enough information to uniquely identify one of 27 states. This was already stated in the root comment.

I'm confused how the response to "you must identify whether the odd ball is heavier or lighter" can be "the key to this is realizing you don't need to know whether the odd ball is heavier or lighter, which is good because that's impossible anyway".

Sorry, yes I saw your confusion. If you read back to your Huh comment you might forgive me for reading it as that you were unsure of the truth yourself. The one word 'huh?', spoke to me as "which one of these is true?". Whereas a person who was sure of the true answer, I would expect to say "Hey that's incorrect", if they encountered an obviously mistaken quote.

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