The Last Round of Words -- I think...

If we were to create a "ghost map" of a sudoku puzzle grid, with all of the possible symbols represented in the eighty-one spaces, we'd have seven hundred and twenty-nine Possibilities.  In my notation a possibility is written as the space plus the symbol.  TLtl1, for example, means the 1 in the top left space of the Top Left square.  I frequently shorten the word down to Sibs, at least in my head, and I may end up doing it here too.

123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789

Each possibility has a cadre of what you can think of as "Anti-possibilities".  If the first possibility is true, all of its antis are false.  If any one of its antis is true, the first possibility is false.  So TLtl1, if true, will invalidate or eliminate TLtl2, TLtl3, TLtl4, TLtl5, TLtl6, TLtl7, TLtl8, and TLtl9 from that space, TLtc1, TLtr1, TLml1, TLmc1, TLmr1, TLbl1, TLbc1, and TLbr1 from the other spaces in that square, and reaching out along the row TCtl1, TCtc1, TCtr1, TRtl1, TRtc1, and TRtr1, as well as eliminating down the column MLtl1, MLml1, MLbl1, BLtl1, BLml1, and BLbl1.

123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789
123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789	123 456 789

If you look carefully, you'll notice that all of the Antis for a possibility share at least three of the letters or number in the notation.  With a great deal of stubbornness, you could actually do an easy sudoku using the notation without ever filling in the grid, and I may yet, but it would be a LOT more work.


In a given puzzle, the true sibs are Knowns.  Knowns can either be Givens, i.e., the symbols which were given to us by the puzzlemaker (or are visible through the sieve if you're using that analogy), or they can be Deductions or answers which the puzzle solver has filled in.  Each known eliminates its cadre of antis, but of course, the antis overlap, so while the first known on the map takes out twenty eight possibilities, later knowns don't provide as many clues.

As you work a puzzle, you'll not only write in deductions, you'll need to do some Marking.  Marks are simply little weenie numbers or other symbols you've put into the grid to represent something you've figured out about the remaining possibilities.  There are lots of systems of marking out there, and while I've got a distinct fondness for my own, it doesn't mean you can't come up with something that works better for you.  Just experiment until you can be consistent.  There is no One True Way to solve a sudoku puzzle.