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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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 Posted: Mon Feb 27, 2006 7:32 pm Post subject: Another "coloring" example |
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| Keith wrote: | | Thank you. These colors, chains and cycles are coming into focus for me. |
Today's "Nightmare" puzzle (27 Feb 2006) offers an excellent opportunity for "coloring" logic.
| Code: | .1....6..
.8.2.4...
6...3...8
.5......1
..6.9.2..
7......8.
4...1...3
...8.3.5.
..9....7. |
1. Naked pair {3, 4} in row 5.
2. Hidden pair {5, 8} in r7c3 & r9c1; r9c2 = 3.
3. Naked pair resolved -- r5c3 = 4, r5c8 = 3.
4. r9c7 = 1 (unique horizontal)
5. r9c1 = 8 (unique horizontal); r7c3 = 5 (sole candidate)
6. r5c1 = 1 (sole candidate); r7c1 = 2 (sole candidate); r7c3 = 1 (sole candidate)
7. {6, 7} pair in r7c2 & r8c2.
8. r4c3 = 8 (unique vertical); r7c7 = 8 (unique horizontal)
9. r1c5 = 8 (unique vertical); r5c6 = 8 (unique vertical)
10. r2c8 = 1 (unique horizontal)
11. The "2" in row 6 lies in middle left 3x3 box.
12. r2c7 = 3 (unique horizontal); r2c3 = 7 (sole candidate); r2c5 = 6 (sole candidate)
13. Naked triplet {2, 4, 9} in row 3.
14. The "9" in row 1 lies in top center 3x3 box.
15. Coloring on "5" in row 5 and column 7 reveals r3c4 <> 5
16. X-Wing on "9" in columns 4 & 6 -- r7c8 <> 9.
At this point we're ready for the final push -- the grid looks like this.
| Code: | 35 1 234 579 8 579 6 24 2457
59+ 8 7 2 6 4 3 1 59-
6 29- 24 17 3 157 57 249+ 8
39- 5 8 3467 247 276 479 469- 1
1 4 6 57 9 8 2 3 57
7 29+ 23 13456 45 156 459(-) 8 4569*
4 67 5 679 1 2679 8 26 3
2 67 1 8 47 3 49(-) 5 469(+)
8 3 9 456 245 256 1 7 246 |
We have a binary chain in the "9"s, marked +/- above. First we observe that the "9" at r6c9 can be eliminated because there's a "+" at r6c2 and a "-" at r2c9. With that "9" out of the way we can mark another "+" at r8c9, and two more "-9"s, at r6c7 and r8c7.
But now we have two "-9"s in the same column (7), and also two "-9"s in the same row (4). We conclude that "-" is not 9, and "+" is, solving for ten cells simultaneously and breaking the puzzle wide open. dcb |
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