1. Each half-liar alternates between lying and telling the truth every other day (if they lie today, they will tell the truth tomorrow, and vice versa). Exactly a week ago, one half-liar made two statements: "Yesterday was Wednesday"; "Tomorrow will be Thursday." Today he made two other statements: "Yesterday was Friday" and "Tomorrow will be a weekend." Can we determine what day of the week it is today? Justify your answer in detail.
Solution. The statements "Yesterday was Wednesday" and "Tomorrow will be Thursday" cannot both be true at the same time, so the half-liar was lying a week ago. Since there is an odd number of days in a week, today he is telling the truth. Therefore, yesterday was Friday, which means today is Saturday. Answer: yes, Saturday.