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.
This problem is taken from the UKMT Mathematical Challenges.