Possible error in "simple sudoku" conjugate logic

OJO-Oregon · Last edited by OJO-Oregon on Sun Aug 26, 2007 8:48 pm; edited 1 time in total

Hi. I'm fairly new to the world of sudoku, and apologize if this topic is stale. (I would send this post to Angus Johnson directly, but the simple solutions site says to address issues here.)

In his Solving Sudoku section, under the solving with colors section, the second example applying the conjugate chain rule, it states, "whenever a candidate outside the chain relates by column, row or box to two alternately colored cells in a conjugate chain, that 'non-chain' candidate can be excluded.

I seem to have found a puzzle that disproves the rule. The puzzle, at its beginning is this:

. 9 . l . . . l . 2 .
3 5 6 l . . . l . . 1
. . . l . 6 . l . . 8
________________

. . 4 l 6 . . l . . .
8 . . l 5 3 7 l . . 9
. . . l . . 1 l 5 . .
__________________

7 . . l . 9 . l . . .
2 . . l . . . l 3 6 4
. 4 . l . . . l . 9 .

The first few obvious moves got me to:

. 9 8 l . . . l 6 2 .
3 5 6 l . . . l . . 1
. . . l . 6 . l . . 8
________________

. . 4 l 6 . . l . . .
8 . . l 5 3 7 l . . 9
. . . l . . 1 l 5 . .
__________________

7 . . l . 9 . l . . .
2 . . l . . . l 3 6 4
. 4 . l . . . l . 9 .

This is where the problem seems to appear. Filtering for 7 shows the bottom right and upper right squares each have only two 7s. Assigning r9c9 the color blue, and r9c7 green, then r2c7 would be blue and r2c8 green. Applying the rule stated above, r4c7 relates to two alternating colors in the same column, and therefore 7 should be able to be eliminated, but the 7 actually belongs there, and can't be eliminated. In completing the puzzle, it turns out that 7 also goes at r9c9, a green square and r2c8 a blue square, which seems to undermine the whole conjugate chain logic rule. I suspect that I am misinterpreting this rule, but if so, I don't see how.

Any ideas?

daj95376 · Posted: Sun Aug 26, 2007 8:32 pm Post subject:

Your original puzzle and later position ... for those who may have an answer to your question.

OJO-Oregon · Posted: Sun Aug 26, 2007 8:47 pm Post subject:

Thanks! That looks better.

Ruud · Site Admin

Hi,

you missed a few singles in the puzzle. after those and:
- locked pair (1,4) in box 1, column 1
- locked pair (2,7) in box 1, row 3
- locked candidates 2 in row 9, box 8
- locked candidates 3 in row 9, box 8
- locked candidates 7 in row 9, box 9
- locked candidates 5 in row 8, box 8
- hidden pair (3,5) in box 3
- locked candidates 7 in row 2, box 3
- naked pair (2,8) in column 5
the puzzle solves with singles only.

Regarding your colors argument:

There is also a candidate for digit 7 in r4c7. You can only color r2c7 and r9c7 with opposite colors when there are no other candidates in that column.

Ruud
_________________
Meet me at sudocue.net

NewUrbanBlues · Posted: Sat Sep 01, 2007 1:02 pm Post subject:

Using Isanaki 2.0, solution uses mainly pointing-pair reduction and box-line reduction techniques ...

Board Solving Log

001 Single in a Box Given 8 solved at r1c3
002 Single in a Box Given 5 solved at r4c1
003 Single in a Box Given 9 solved at r8c3
004 Single in a Box Given 9 solved at r6c1
005 Single in a Box Given 9 solved at r4c6
006 Hidden Single in a Column Given 6 solved at r9c1
007 Single in a Box Given 6 solved at r7c6
008 Single in a Box Given 4 solved at r7c4
009 Single in a Box Given 4 solved at r6c5
010 Pointing Pair Reduction in a Row Candidate 2 removed in Cells r3c4 & r3c6
011 Pointing Pair Reduction in a Row Candidate 7 removed in Cells r3c4, r3c7 & r3c8
012 Pointing Pair Reduction in a Row Candidate 2 removed in Cells r9c7 & r9c9
013 Pointing Pair Reduction in a Row Candidate 3 removed in Cell r9c3
014 Pointing Pair Reduction in a Row Candidate 7 removed in Cells r9c4 & r9c5
015 Box Line Reduction in a Row Candidate 5 removed in Cells r9c5 & r9c6
016 Box Line Reduction in a Col Candidate 1 removed in Cells r3c2 & r3c3
017 Hidden Pair in a Box Candidates other than 3 and 5 removed in Cells r3c8 & r1c9
018 Hidden Single in a Row Given 6 solved at r1c7
019 Single in a Box Given 6 solved at r6c9
020 Single in a Box Given 6 solved at r5c2
021 Pointing Pair Reduction in a Row Candidate 7 removed in Cells r2c4 & r2c5
022 Naked Pair in a Column Candidates 2 and/or 8 removed in Cells r8c5 & r9c5
023 Naked Single in a Box, a Row or a Column Given 1 solved at r9c5
024 Hidden Single in a Row Given 1 solved at r8c2
025 Single in a Box Given 1 solved at r5c3
..... and Single in a Box up to the end