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KöMaL 2020 B5070

    There are two kinds of people living on an island: some always tell the truth, while some always lie. Ten inhabitants of the island were numbered as 1,2,…,101,2,\ldots,10. Then everyone was asked the same three questions: Is your number even?'', Is your number divisible by 4?'', Is your number divisible by 5?''. The number of those saying Yes'' was three, six, and two, respectively in the three cases. Which numbers were assigned to liars?

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