Last week’s introduction to the Heyawake puzzle I have decided was a bit hard as an introduction to the puzzle – although I’m now confident it wasn’t totally unfair having had this feedback from one of the best nikoli.com solvers out there:
"I liked it! The start was simple enough, and then you made some medium-level deductions to get some big sets of blocks, etc. I’d say the grand finale (I felt pretty sure there were two solutions or more…no, I was wrong) isn’t as bad as you claim. It probably shouldn’t be someone’s first Heyawake, but it’s not the pinnacle of difficulty. It’s a harder medium, how’s that for a/n non-/answer?"On the other hand, I’ve been having a little think about the nature of difficulty and the nature elegance within a puzzle. I think it’s fair to say that by no means are the two are correlated – see this entry for two examples of sudoku too hard to be elegant – well elegant for the pen and pencil solver anyway. To labour the point a little bit more, here is an example of a puzzle which is INSANELY difficult. If you solve it, the only logical deduction is that you used a computer:
Now, on the other hand, some easy puzzles can be extremely elegant. Not necessarily in the techniques required to solve them in isolation, but how the techniques come together to form a complete and satisfying solve. What this could mean for example, is a puzzle that has a definite starting point, which leads directly to another deduction and so on – inducing a “continuous flow” to the solving experience. It may be a repetition of a particular solving technique, or it may be a particular visual pattern that emerges as you solve the puzzle. I guess much like any art form, there isn’t really a satisfying way to define what makes a beautiful puzzle – but even a complete novice can spot it and enjoy it when they see it.
Anyhow, that’s an awful lot to aspire to. I’m not quite sure how much of that I’ve managed to achieve with this Heyawake (if any at all), but I’m running out of time to fiddle with it today…