Can someone simplify Sue de Cog for me?

Advanced methods and approaches for solving Sudoku puzzles

Can someone simplify Sue de Cog for me?

Postby stumble » Thu Jan 15, 2009 4:38 am

Yesterday I was working the BrainBasher 1-13-09SuperHard puzzle.
On coming to a dead end I referred to my solver's (SudoCue)
Solvers Log and encountered my first Sue de Cog. Rather than
trying to figure out the brief explanation, I went directly to

Alas, I am still too dumb to figure the example out even with the
beautiful colored picture. For this reason I'm not even posting
my BrainBasher puzzle, at least at this time. So explanations of
two puzzles don't get confused in this thread.

Could someone explain what the letter N equals in this Sudopedia
example. (I believe it MUST be 9, since there is 9 cells in a row
and 9 cells in a box) I believe the first subset (A) is r3, and
2nd subset (B) is box 3. The 'intersection' r3c7,r3c8,r3c9, has
candidates 1,2,5,8,9.

"Candidates can be eliminated from the cells in the line that are
not in A, and the cells in the box that are not it B."

If 'the line' is row 3 and is subset A, this doesn't make any
sense to me.

I figure maybe someone who DOES understand this technique could
put this another way, possibly? In other wording? So that it'll
sink into my recalcitrant brain.
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Postby hobiwan » Thu Jan 15, 2009 5:09 am

Hello stumble,

I didn't get the explanation in Sudopedia either. I suggest you have a look at the explanation given by DonM here or visit the original thread here for further info.

If this doesnt make things clearer please dont hesitate to ask again.
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Postby aran » Thu Jan 15, 2009 10:49 am

You're right to be confused because the definition isn't right.
But forget about that for the time being.
In the example the N cells in the row are r3c2789 (ie N=4), and in the box the cells are r3c789+r1c7.
The candidates are 12589 ie 5 candidates.
Think about it like this :
- the five cells in total (r3c789+r3c2+r1c7) must be filled by 12589 and only by those candidates
- furthermore and this is the crucial part each candidate can appear only once.
Consequently each candidate must appear exactly once.
And therefore any candidate anywhere which reduces ie prevents that situation must be false.
Take for example : 1r2c8.
If true, this removes 1 completely from the 5 cells (r3c789+r3c2+r1c7).
So there would now only be 4 candidates (2589), each of which can appear only once, for 5 cells. An impossible position, so 1r2c8 is false.
If you do follow that, then you can in fact by-pass sue de coq which is a particular case of a more general rule : when N cells can be filled only by N candidates, and where each candidate can appear at most once (ie exactly once) then anything which prevents that is false.
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