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Sometimes Liar - Answer

My neighbor tells the truth on Tuesdays.

Take them one at a time and assume he is telling the truth on each of the three days that he makes a statement. Then assume he is not telling the truth on any of the days that he makes a statement.

The only case that works is the one where he is telling the truth on the third day. On that third day, from the statements he made, he lies on Wednesdays and Fridays. He tells the truth on Mondays and Tuesdays. Yesterday was not Thursday, Saturday or Sunday. That means that he couldn't be telling the truth Monday because yesterday can't be Sunday and therefore, he must tell the truth on Tuesdays.

 

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