note merlyn <blockquote><i> Towers of Hanoi problems are good examples in that they are easy to visualize, and their relationship to sorting with stacks is obvious. </i></blockquote> However, if you are selecting problems for a syllabus, please be aware that "easy to visualize" can actually give an unfair disadvantage to some of your students. I've commented on my own affliction with regard to [id://32551|using GUIs] and [id://379335|learning to program]. <p> I completely understand the algorithm for Towers of Hanoi, and why it works, and have translated it into a few languages. But I understood it only by playing with physical disks or marks (and erasing) on a piece of paper. I could never have constructed it by "visualization", since my brain doesn't work that way. <p> So, beware when you pretend you know what skills are "universal" about thinking... you may have wrong thinking about that. {grin} <!-- Node text goes above. Div tags should contain sig only --> <div class="pmsig"><div class="pmsig-9073"> <p>-- [http://www.stonehenge.com/merlyn/|Randal L. Schwartz, Perl hacker] <br> Be sure to read [id://205373|my standard disclaimer] if this is a reply.</p> </div></div> 400359 400376