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Interesting fact:

The answer to our question goes something like this: If Peter said the statement on a truth day, then he would also be telling the truth the next day. However, there are no two truth days in a row, so he must be saying it on a lying day. Since the statement was made on a lying day, then the next day must also be a lying day. The only two lying days in a row are Saturday and Sunday, so he made the statement on Saturday! Phew, did you get that all?