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Glassman
Joined: 21 Oct 2005 Posts: 50 Location: England

Posted: Sat Feb 04, 2006 1:30 am Post subject: The Times Killer Su Doku book strategies and notation 


Having completed about three quarters of the puzzles, I felt members might find it useful to consider the notation I use for the special strategy required by this type of puzzle.
It is obvious that each row, column, and 3x3 box must add up to 45. Once you have completed the early, easy puzzles, you have to consider combinations of rows, columns and boxes. So box 1, 2 and 3 plus row 4 must add up to 4 x 45, or 180. Of course, these combinations do not necessarily have to be exclusive, so box 1, 2 and 3 plus column 1 would also have to add up to 180, where cells r1c1, r2c1 and r3c1 are counted twice towards the total.
Of couse, the joined cells that are counted into the totals printed on the puzzle do not follow row, column and box lines. So you find yourself looking for combinations of rows, columns and boxes that could be productive.
Let's say you have found that row 1 plus cell r2c1 adds up to 51. You then know that r2c1 must be 6, as the rest must add up to 45. The opposite is also equally productive. If all of row 1 except r1c1 adds up to 42, then r1c1 must be 3.
Combinations can be equally or even more productive. If you have found that row 1 plus cell r2c1 but not including cell r1c9 adds up to 53, you know that 53  r2c1 + r1c9 = 45, or r1c9 + 8 = r2c1, so r1c9 must be 1 and r2c1 9, the only two possible numbers with a difference of 8.
As I have a poor memory for numbers, I needed an efficient shorthand for this strategy. Take puzzle 78, for example. Here columns 3 and 4, excluding cell r4c4 and including cell r1c5 add up to 96. So I have a note on the page:
C34±=+6
I do not need to note the identity of the "plus" cell, r1c5, or the "minus" cell r4c4, as it is obvious, looking at the grid. My shorthand tells me that there are cells included and excluded, and that the pair r1c5:r4c4 must be one and only one of 7:1, 8:2 or 9:3.
Sometimes I include the number of cells, where it is not trivial. In that form the above would be written:
C34+(1)(1)=+6
Here I have used brackets to distinguish clearly between numbers placed in cells and numbers of cells.
Another variant is the more explicit:
C34+r1c5r4c4=+6
So my shorthand:
B123C5(3)=4
would indicate that the three cells not included in the totals for boxes 1, 2 and 3 and column 5 would have to be 1, 1 and 2.
I hope that is useful, and that I have not just confused everyone!
What shorthand do you use?
Glassman 

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