Mixing my metaphors

If this were a book (and if anyone were reading it), I'd find myself on the horns of a dilemma about now.  I mean, I could go on with my method, and talk about how it's the Perfect Way to solve the Hardest Sudoku puzzles in the world.  Except for one thing.  I'm not sure it is.  You see, the more I play with sudokus, the more I realize that how easy a puzzle seems to solve is sometimes dependent on what angle you approached it from.  And sometimes, it seems, even the language you use affects what you see.

Take X-wings.  They used to drive me crazy, until I realized that they were just what I called "parallel pairs".  At that point I stopped trying to find them.  Bifurcation would reveal them, and their consequences, just as quickly as pattern hunting would.  It doesn't mean that I don't use them if they stand up and shout to be noticed though.

The simplest variation of parallel pairs happens within a zone, when a given symbol has pairs in two of the squares and the pairs happen to fall into the same two long sets which intersect the squares.   In fact, the principle applies even there aren't pairs, although you're less likely to notice it straight away.

So, if, for example, the only possible 2s in TL fall into Tt and Tb, and the only possible 2s in TC fall into Tt and Tb, then the 2s in TR must fall into TRm.

Parallel pairs, like knowns, have the power to eliminate sibs of the same symbol which are in the sets they share perpendicular to the pairs.

Confused yet?

Let's try a metaphor.  Instead of thinking about sibs as being symbols that might appear in each space, let's pretend that there are nine "bouncing balls" for each symbol array racketing around the grid.  Each ball can only bounce into spaces that are unoccupied by other symbol arrays.  In each of the remaining spaces is a folding chair that chimes when a ball bounces on it.

Now the game is musical chairs.  Whenever one of the bouncing balls settles into a chair and stays there, its presence folds up all the other chairs in its sets -- i.e,, the square, row, and column it occupies.  The remaining balls can't settle into those chairs, so they bounce around the spaces which still have chairs.  Each ball that settles removes more chairs, restricting the other balls into fewer and fewer spaces until all of the balls in the array are settled into nine chairs.

Which means, of course, that if there are only two spaces left in any set, a ball that falls into that set will bounce back and forth between them.

But if, by some chance, two balls start bouncing back and forth between matched chairs in parallel sets, hitting the same notes as it were, that sets up a vibration that will collapse the chairs between them.  The pattern will always be a rectangle or a square, and whether the balls are bouncing left to right or top to bottom, they will always create a pattern where when one is in the top left hand corner, the other is in the bottom right hand corner, and when one is in the top right hand corner the other is in the bottom left hand corner.

What metaphor makes sense to you?