Solution
Two Sisters, Alternating Lying Days
Show the problem again
Ada lies on Mondays, Wednesdays and Fridays and tells the truth on all other days. Bo lies on Tuesdays, Thursdays and Saturdays and tells the truth on all other days. On a certain day Ada says, "I lied yesterday," and Bo says, "Ada will lie tomorrow." What day of the week was it? Answer with the weekday.
Worked solution
Ada says "I lied yesterday", which is true exactly when today is Tue, Thu or Sat (yesterday was one of her lying days). She is truthful today on Tue, Thu, Sat and Sun, and lies on Mon, Wed, Fri. So the statement matches her honesty on Mon through Sat, but not on Sunday, when she is truthful and the statement is false. Today is not Sunday. Bo says "Ada will lie tomorrow", true exactly when today is Sun, Tue or Thu. Bo is truthful on Mon, Wed, Fri, Sun and lies on Tue, Thu, Sat. His statement is true on Sun (and he is truthful, a match), true on Tue and Thu (but he lies, a mismatch), and false on Mon, Wed, Fri (but he is truthful, a mismatch) and on Sat, when he lies and the statement is false, a match. So only Sunday and Saturday fit Bo, and Sunday is excluded by Ada. Answer: Saturday.
Source: Original puzzle in the tradition of Lewis Carroll's Lion and Unicorn weekday puzzles. Statement written for AxiomIQ.