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PrintSouth African Mathematics Olympiad First Round
South Africa counting and probability
Problem
Devious Steve either lies for the whole day or tells the truth for the whole day. Which one of the following statements can he never say? (A) "Yesterday I told the truth" (B) "Yesterday I lied" (C) "Today I am telling the truth" (D) "Today I am lying" (E) "Tomorrow I shall lie"
Solution
Statements A, B and E can be made irrespective of whether Devious Steve is lying or telling the truth. Statement C can also be made whether he is telling the truth or lying. However, if statement D is true, then Steve is a liar, which contradicts the truth of statement D. Similarly if statement D is false, then Steve is a truth-teller, which contradicts the falsity of statement D.
Final answer
D
Techniques
Logic