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Message: <blockquote data-quote="Nonentity" data-source="post: 2480548" data-attributes="member: 284324">1. At least one of these ten statements is false.This is true because even if more than one statement is false, then the least number that are false will be one. So at the very least one statement is false.BTW If the statements began with "At most" instead of "At least", then "At most nine of these ten statements is false" would be true. If all ten were false, then "At most ten of these ten statements is false" would have to be false. Since less than ten statements would have to be false, then "At most nine of these ten statements is false" would be the true statement.</blockquote>