Pencil mark notation

Advanced methods and approaches for solving Sudoku puzzles

Pencil mark notation

Postby kayjay40 » Wed Oct 05, 2005 4:58 am

Pencil mark notation: I've done a couple of things to help myself. First I drew a 9 x 9 table in MS Word obtaining 1/2 inch squares. I print up a dozen copies or so. I then copy the puzzle to the printed form, using a large colored pen.
After finding the obvious numbers, I set pencil marks in the following way: I visualize each square having nine positions , upper left, upper center, upper right, middle left, middle center, middle right, lower left, lower center, lower right.
I then work the grid for each square, marking a pencil dot (or small dash) in the nine positions for each number that might go into that square. For example, the left most column might have blank blank 2 blank 3 blank 7 blank 9 and the top row might hold blank 3 blank blank blank 1 blank 6 blank. So between the row and the grid, we accounted for 2, 3, 7, 9 vertically and 3, 1, 6 horizontally. We've accounted for 1, 2, 3, 6, 7, 9. The only numbers that might fit in the upper left blank, r1c1, are 4,5 and 8. I'd then put a dot in middle left, middle center and lower center.
This does take a bit of time to work through, but once you start to solve using forcing chains, the dots are easy to see and easy to erase as you fill in the puzzle. They are much quicker to place than writing little numbers, the standard pencil mark.
Yes, it would be a stinker on the 16 x 16 puzzles. kayjay40
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Postby sonovapreechaman » Wed Oct 05, 2005 7:26 am

I use a similar system that evolved from what you do. however I don't have an eraser on my pencils and often resort to using a pen so I found that if I had a cell with 2,4,6 and 9 as possibilities and was able to deduce that 6 and 9 were no longer elligible I was left with a cell that had 2,4 as options and squiggles that took up enough space to make it diffcult to write the numbers - it was a good system but prone to getting messy
I decided to only pencil mark the numbers that it couldn't be
eg. for a cell with 2,4,6 and 9 possibilities I had dots at 1,3,5,7 and 8; when I was able to eliminate 6 and 9 I inserted dots there and could easily see that only 2 and 4 were now candidates
It all sounds a bit backwards, I know but it works for me ;-)
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Postby kayjay40 » Fri Oct 07, 2005 12:37 am

I like your system too. When I copy the core numbers to the larger grid I've printed out, the issue of "too many dots" doesn't get in the way. I only use a pen to record the core or given numbers on the larger grid. The one and two stars work well, the three star and higher need more help. Thanks for responding. Ken
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Postby PhatFingers » Sun Oct 09, 2005 6:17 am

I use a similar dot notation when solving newspaper puzzles, where position of a dot represents a candidate value, and I mark that position right on the puzzle itself. That would normally get messy, except I only place a dot when I've narrowed a candidate value to two positions within a box and then I place a dot in the appropriate position of both cells. I've also tended over time to place each dot close to the edge of a cell, so there's always lots of white-space for the number.

It's a fun and fast technique, and will allow you to see some patterns early and easily with very few pencilmarks. In many cases, you can solve even a hard puzzle with these pencilmarks alone, but for the other cases, it will at least help you preprocess the board before you start the more labor-intensive task of pencilmarking every available remaining candidate (which is often necessary-- I'm not knocking that technique, but offering a way to narrow the playing field before applying it).

Some of the things this technique exposes:

* The dots always represent a locked candidate pair inside a box.
* When in the same row or column, they represent a locked candidate pair for that row or column.
* If any two cells share any of the same two dots, it represents a naked pair, and you can immediately eliminate any additional dots in the same cells as candidates.
* If you eliminate any dot in any way within a cell (other than writing in its own value) then you can immediately write in the value in its companion cell, which can always be found in the same box.
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