Solution
The Weekday Liar
Show the problem again
Marlow lies on Tuesdays, Thursdays and Saturdays, and tells the truth on every other day of the week. One day he says "I will lie tomorrow", and on that same day he also says "I will lie the day after tomorrow." What day of the week was it? Answer with the weekday.
Worked solution
On a truth-telling day (Mon, Wed, Fri, Sun) both statements would have to be true, so both of the next two days would be lying days. Mon is followed by Tue and Wed, Wed by Thu and Fri, Fri by Sat and Sun, and Sun by Mon and Tue; none of these has two consecutive lying days. On a lying day (Tue, Thu, Sat) both statements must be false, so neither of the next two days is a lying day. Tue is followed by Wed and Thu (Thu lies), Thu by Fri and Sat (Sat lies), but Sat is followed by Sun and Mon, both truthful days. So only Saturday works, as a check of all seven days confirms. Answer: Saturday.
Source: Original puzzle in the tradition of Lewis Carroll's Lion and Unicorn weekday puzzles. Statement written for AxiomIQ.