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carl
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 Posted: Wed May 24, 2006 8:45 pm Post subject: may 9 puzzle |
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| can anybody in laymans langauge explain how to resolve may 9 puzzle |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed May 24, 2006 10:23 pm Post subject: Re: may 9 puzzle |
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| carl wrote: | | can anybody in laymans langauge explain how to resolve may 9 puzzle |
I don't know what constitutes laymans language. But after filling in the cells with their candidates and scanning for obvious moves, I reached a point where four key moves were made.
1) In c9, the only possibilities for 2 are in box 6, so other 2s are removed from elsewhere in that box, which solves a cell or two.
2) In box 8, there is a 179 triple. After eliminating 179 from other cells in the box, a naked 45 pair is exposed. After eliminating 45 from other cells in c6, a 28 pair is exposed and that solves r3c6=1.
3) There is a type 4 unique rectangle of 45 in r8-9 and c6-8. After taking the action there (remove the 5s), a 47 pair is left in box 9, c8, which allows you to eliminate some candidates. See Keith's discussion of rectangles at:
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=744
4) There is a 567 triple in c3. After eliminating those numbers from other cells in that column, very basic techniques will solve the rest of the puzzle.
Hope this helps. |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Wed May 24, 2006 10:57 pm Post subject: Here's a step by step procedure |
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Hi, Carl!
Since you didn't specify where you got stuck, I've reconstructed my solution from the very beginning. If any of the terminology seems unclear, please ask.
1. r2c9 = 1; r7c9 = 8 (unique horizontal)
2. The "4" in column 2 must lie in the top left 3x3 box.
3. The triplet {2, 3, 8} lies in r1c4, 5, & 6.
4. r3c6 = 1 (sole candidate); naked pair {7, 9} in r2c4 & r3c5, also in r2c4 & r9c4.
5. r7c4 = 6 (sole candidate); naked pair {2, 3} in r1c4 & r6c4.
6. Naked pair {4, 5} in r8c6 & r9c6;
7. The "2" in column 9 must lie in the middle right 3x3 box.
8. r6c7 = 4; r2c7 = 3 (sole candidate); naked pair {2, 5} in r3c7&8.
9. r1c9 = 4; r1c2 = 6; r1c1 = 5; r5c2 = 1; r7c2 = 7; r4c2 = 8; r3c2 = 3; r2c2 = 4 (sole candidate).
10. r7c3 = 5; r8c3 = 6; r6c3 = 7; r3c3 = 9; r4c3 = 4; r2c1 = 7; r3c1 = 8 (sole candidate).
11. r8c1 = 3; r9c1 = 1; r2c4 = 9; r3c5 = 7; r4c5 = 6; r5c5 = 4; r9c5 = 9; r8c5 = 1 (sole candidate).
12. r9c4 = 7; r4c6 = 2; r1c6 = 8; r1c5 = 3; r1c4 = 2; r6c4 = 3; r6c5 = 8; r6c9 = 2 (sole candidate).
13. r6c1 = 6; r6c8 = 1; r5c9 = 9; r5c8 = 6; r5c1 = 2; r4c1 = 9; r4c7 = 5; r4c9 = 7 (sole candidate).
14. r3c7 = 2; r3c8 = 5; r7c8 = 2; r7c7 = 9; r8c9 = 5; r9c9 = 3; r9c8 = 4; r9c6 = 5 (sole candidate).
15. r8c6 = 4; r8c8 = 7 (sole candidate -- puzzle completed).
So I guess the "tough" moves were spotting the naked triplet {2, 3, 8} and the pair {2, 5}. dcb |
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carl
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| Posted: Thu May 25, 2006 3:38 pm Post subject: may 9 puzzle |
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thanks for your help
regards, carl |
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