There are phrases that seem innocent until you examine who says them and when. If someone lies on some days and tells the truth on others, a single statement about yesterday can reveal—or rule out—almost every day of the week.
Monday's lie
Riddle statement
A person says:
—Yesterday I lied.
You know that this person always lies on Mondays, Tuesdays and Wednesdays, and always tells the truth on other days.
What day of the week could today be?
Show solution
Solution
Answer: today could be Monday or Thursday.
The person says: "Yesterday I lied."
Case 1: today is a truth-telling day. The statement is true, so yesterday was a day when the person lied. The truth-telling days are Thursday, Friday, Saturday and Sunday. The previous days are Wednesday, Thursday, Friday and Saturday respectively. Only Wednesday is a lying day, so this case works only if today is Thursday.
Case 2: today is a lying day. The statement is false, so yesterday was not a day when the person lied; yesterday was a truth-telling day. The lying days are Monday, Tuesday and Wednesday. The previous days are Sunday, Monday and Tuesday respectively. Only Sunday is a truth-telling day, so this case works only if today is Monday.
Every other day leads to a contradiction. On Tuesday or Wednesday the person lies, but yesterday would also have been a lying day, so "Yesterday I lied" would be true — impossible on a lying day. On Friday, Saturday or Sunday the person tells the truth, but yesterday would not have been a lying day, so the statement would be false — impossible on a truth-telling day.
The only possible days are:
- Monday;
- Thursday.