Taken from Brillant.org.
On a particular island live humans and vampires. The normal humans always tell the truth and the normal vampires always lie. However, there are abnormal varieties of each. Abnormal humans always lie and abnormal vampires always tell the truth.
An islander makes the statement “If I am a vampire, then I am normal.”
What are they?
My thought process:
If the islander is a normal vampire, then they told the truth and cannot do that. That eliminates this possibility.
If the islander is an abnormal vampire then they lied and cannot do that. Another elimination.
Now the islander must be human. But the IF statement precludes me going further logically. They are not lying nor telling the truth with this IF statement. We’re stuck here. I chose an answer Imposible to tell from the given information. They claim this is wrong and that the answer is Normal Human.
Looking at their explanation, they agree with me on the first two points, but then include the following:
If the islander is a human, the hypothesis of the if-then statement is false, so the if-then statement as a whole is true. The only humans that can tell the truth are normal ones, so the islander must be a normal human.
I contend this isn’t right. The statement as a whole is not true nor false. It’s unknown, null, nil, nothing. Where am I going wrong here?