Solving without pencilmarks

Advanced methods and approaches for solving Sudoku puzzles

Re: Solving without pencilmarks

Postby eleven » Wed Dec 25, 2013 11:36 pm

gearss wrote:Can Mr. RW solve the following puzzle step by step in detail? Please donot use the word like "easy to know".
If you can solve it without pencilmark, I beleive millions of player in the world must study your article as textbook.

it is out of question for me, that RW can solve this puzzle without pencilmarks. But why do you think, he should ? As i see it, it is just one of myriads uninteresting puzzles, which require a lot of time to solve manually, with or without pencilmarks. RW has already shown, that he is worth to be read by millions of players.
eleven
 
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Making easy puzzles harder

Postby Noumenon » Fri Sep 23, 2016 5:25 pm

I found a new constraint I impose on myself while solving without pencil marks. I only allow myself to fill in the grid while maintaining rotational symmetry. Here's what I do:

Stage 1 -- If the puzzle is one which contains some asymmetry, I must first only allow myself to bring the puzzle back to a symmetric state one asymmetric cell at a time. For example if there is a clue in r1c2 but not in r9c8, I must find r9c8. (Of course if there's another asymmetry in the puzzle, I have a choice on which to find first.) For example r2c2 and r8c8, or r5c1 and r5c9.
Finally I reach a state where every clue cell has its rotationally symmetric "antipode" filled; it's now a symmetric puzzle.

Stage 2 -- Next, I only allow myself to fill in two cells at a time, they must be proven and antipodes. There is one exception; the center square (which is its own antipode), if unfilled -- r5c5. Note I am not allowed to fill it until stage one is complete.

This makes many of the duller puzzles more fun and reveals much about their construction.
Noumenon
 
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