Kennedy is a bizarre fabricator. He lies on just 6 days of the week, but on the 7th day, he tells just the truth. Following are the three statements made by him on three consecutive days.
Day 1: "I lie on Monday and Tuesday."
Day 2: "Today, it's Thursday, Saturday, or Sunday."
Day 3: "I lie on Wednesday and Friday."
Can you find out the day on which Kennedy speaks truth only?
Solution:
Now from the question, we only know one thing for sure i.e. Kennedy tells truth on just a single day of the week. Now let us take the statements one by one.
If the first statement is false, it will mean that Kennedy speaks truth on either Monday or Tuesday. If the statement made by him on day 3 is false, it will mean that he speaks truth on either Wednesday or Friday. But we know that Kennedy speaks truth just on one day, we can safely say that these statements can't both be false. Thus only one of these must be true and then the statement made on day 2 must be false.
If we assume that the statement Kennedy made on the first day is true, then what he said on day 3 must be false according to which he speaks truth on Wednesday or Friday. Subsequently, day 1 is either Wednesday or Friday. Thus, day 2 is either a Thursday or a Saturday. Nonetheless, it will conclude that the day 2 statement is true but that is impossible. From all this, we can say that the day 1 statement must be false.
We can conclude from all the above that Kennedy spoke truth on the third day and then the day was either a Monday or a Tuesday. Hence, day 2 is either Sunday or Monday. But we know that the statement on day 2 must be false, we can say that day 2 in a Monday.
Therefore, day 3 is definitely a Tuesday. Thus Kennedy speaks truth on Tuesday.