On the questioners’ planet (where everyone can only ask questions. Cricks can only ask questions to which the answer is yes, and Goops can only ask questions to which the answer is no), you meet 4 alien mathematicians.
They’re called Alexander Grothendieck, Nicolas Bourbaki, Henri Cartan and Daniel Kan (you may like to shorten their names to \(A\), \(B\), \(C\) and \(D\)).
Alexander asks the following question “Am I the kind who could ask whether Bourbaki could ask whether Cartan could ask whether Daniel is a Goop?"
Amongst the final three (that is, Bourbaki, Cartan and Daniel), are there an even or an odd number of Goops?
Let \(n\ge r\) be positive integers. What is \(F_n^2-F_{n-r}F_{n+r}\) in terms of \(F_r\)?