IMC 2006 Q7
7. The Queen of Spades always lies for the whole day or always tells the truth for the whole day. Which of these statements can she never say?
- A “Yesterday, I told the truth.”
- B “Yesterday, I lied.”
- C “Today, I tell the truth.”
- D “Today, I lie.”
- E “Tomorrow, I shall tell the truth.”
Intermediate Mathematical Challenge 2006, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D “Today, I lie.”
Statements A, B, and E may be made by the Queen of Spades, whether it is a day on which she is telling the truth or a day on which she is lying. She may also make statement C providing she is telling the truth that day. However, if she is telling the truth on a particular day then she could not make statement D since that would be a lie. Also, if she is not telling the truth on that day then she could not make statement D either, since that would then be a true statement. So she cannot make statement D.
Solution © UK Mathematics Trust, from the IMC 2006 solutions.