Problema Solution
Sophie tells the truth only on Monday, Tuesday, Wednesday, and Thursday. She lies on all other days. Her sister Mary tells the truth only on Monday, Friday, Saturday, and Sunday. She lies on other days. If they both said to their mom, "Yesterday I lied", what day is it today?
Answer provided by our tutors
Lets assume it is Monday today thus yesterday was Sunday:
Sophie says "Yesterday I lied" - she is telling the truth fits with the fact for Sunday (she lies on Sundays) - so all is good.
Mary says "Yesterday I lied" - she is telling the truth but this contradicts with the fact that that on Sunday she is telling the truth.
Monday is not the solution
Lets assume it is Tuesday today thus yesterday was Monday:
Sophie says "Yesterday I lied" - she is telling the truth contradicts with the fact for Monday (she is telling the truth on Monday).
Tuesday is not the solution.
Lets assume it is Wednesday today thus yesterday was Tuesday:
Sophie says "Yesterday I lied" - she is telling the truth contradicts with the fact for Tuesday (she is telling the truth on Tuesday).
Wednesday is not the solution.
Lets assume it is Thursday today thus yesterday was Wednesday:
Sophie says "Yesterday I lied" - she is telling the truth contradicts with the fact for Wednesday (she is telling the truth on Wednesday).
Thursday is not the solution.
Lets assume it is Friday today thus yesterday was Thursday:
Sophie says "Yesterday I lied" - she lies on Fridays and that fits that fact that she is telling the truth on Thursday - so all is good.
Mary says "Yesterday I lied" - she is telling the truth on Fridays and that fits that fact that she lies on Thursdays.
Thus the solution is Fridays.