Alan Schoenfeld suggests that this problem tends to provoke
immediate and widely divergent intuitive reactions (see some of the
possibilities listed in the Hint
He writes that he used this problem in a class where the
discussions "focused on what it means to have a compelling
mathematical argument. The general tenor of these discussions
followed the line of argumentation outlined in Mason, Burton and
Stacey's (1982) Thinking
: First, convince yourself; then, convince a
friend; finally, convince an enemy. (That is, first make a
plausible case and then buttress it against all possible
counterarguments.) In short, we focused on what it means to truly
understand, justify, and communicate mathematical ideas."
Teachers may want to use this problem in their classrooms to serve
the same purposes.