The questions I want to give something to ponder, something that is not immediately straightforward, and some cool and rational thought will be required to answer the question.
Admittedly, I've touched a modicum bit in this regard at this slideshow (http://masteringolympiadmathematics.blogspot.com/2015/06/slideshow-9-creative-teaching.html), you could, if you want to refer it and answer the following quiz questions.
Question 1: What is the next square number after $(x-6)^4$?
$((x-6)^2)^2+1$
$((x-6+1)^2)^2$
$((x-6)^2+1)^2$
Answer: