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This notion generalizes the classical Oddtown and Eventown problems.\n  We prove that $m_{k,n}(a,b)\\leq n$ whenever $a\\not\\equiv b\\pmod{k}$, thereby resolving a conjecture of Veselinov and Marinov. We also disprove another conjecture of theirs by showing that $m_{3,11}(2,2)>m_{3,11}(1,1)$. 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This notion generalizes the classical Oddtown and Eventown problems.\n  We prove that $m_{k,n}(a,b)\\leq n$ whenever $a\\not\\equiv b\\pmod{k}$, thereby resolving a conjecture of Veselinov and Marinov. We also disprove another conjecture of theirs by showing that $m_{3,11}(2,2)>m_{3,11}(1,1)$. 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