You meet another alien, whose name is Teddy. He asks you “Am I the kind who could ask whether I am a Goop?"
Can anything be deduced about Teddy?
You meet a couple, Dan and Daisy. Dan asks Daisy “Are you the kind who could ask me whether I am a Crick?"
What can be deduced about Dan and Daisy?
You meet an alien called Bobby. He asks you “Am I the kind who could ask whether the wizard is the kind who could ask whether I am the wizard?"
Do you now know for sure who the wizard is?
You then meet a strange alien who asks you “Am I the kind who could ask you the question I am now asking?"
What can be said about her?
You meet three friends: Alex, Bernie and Carol. Alex asked Bernie “Are you the kind who could ask Carol whether she is the kind who could ask you whether you two are of different kinds?".
You might realise that it is only possible to deduce the kind of one of the three friends. Which one and are they a Crick or a Goop?
You meet an alien called Charlie. He asks you “Are the wizard and I the same kind?"
Who is the wizard?
What is logically the opposite of the statement “every \(n\) is odd or \(p<q\)"?
Four different digits are given. We use each of them exactly once to construct the largest possible four-digit number, and use each of them exactly once to construct the smallest possible four-digit number which does not start with 0. If the sum of these two numbers is 10477, what are the given digits?
Today we will solve some logic problems. This time, we are visiting a strange planet. This planet is inhabited by two kinds of aliens, Cricks and Goops. The physical differences between them are not enough for a human being to distinguish them, but they have another remarkable feature. They can only ask questions. Cricks can only ask questions whose answer is yes, while Goops can only ask questions whose answer is no.
Label the vertices of a cube with \(1,2,3,\dots,8\) so that the sum of the labels of the four vertices of each of the six faces is the same.