most influential book in the thought-life of your puzzle-master is a small volume entitled How to Solve It by Hungarian mathematician George Pólya.  The work is framed on four principles…

1.     Understand the problem (puzzle).

2.     Devise a plan.

3.     Carry out the plan.

4.     Review / Extend.

The most important – and creative! – is signified by the word “Extend,” which I have colloquialized for my students: “Here is a solution to a problem what other problems can I now solve.”  That will be seen as the heuristic concept selected for emphasis in Discovering Assumptions. 

Let us apply the fourth principle by generalizing the problem/puzzle with the parameter X as a replacement for the fixed integer 15...

Original Puzzle... parametric replacement... rearranging... squaring both members... rearranging...   algebraic simplification... squaring both members...

Simple: Just multiply both members of the equation by the expression X – 1, et voilà: X = 1.  Here again we will review our solution by substituting X = 1 into the original equation, et voilà: 1 / 0 = 1 / 0.  Oh, but wait: 1 / 0 = ...

 ...which reminds solvers of the mischief revealed in Double Integrity.