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Preliminary answer. The work to get a definitive answer is more than I have time for. As OP points out: Also, as OP pointed out: As with all such problems, the goal is to try to have each test divide the remaining set of possibilities into 3 groups, as evenly as possible. The only possible option for the first test is to weigh N coins on the left versus ...


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Here is mine to kick it off: Sentence: They're there to show their wordplay is too much fun for only two to four people, so come to the fore and join in the play by making a play or go buy a room at an inn. Homophone groups: they're, there, their (+3); too, to, two (+3); for, four, fore (+3); play, play (+2); by, buy (+2); in, inn(+2). Score: 15 [Note: ...


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