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may 9 puzzle

 
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carl
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PostPosted: Wed May 24, 2006 8:45 pm    Post subject: may 9 puzzle Reply with quote

can anybody in laymans langauge explain how to resolve may 9 puzzle
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Marty R.



Joined: 12 Feb 2006
Posts: 5128
Location: Rochester, NY, USA

PostPosted: Wed May 24, 2006 10:23 pm    Post subject: Re: may 9 puzzle Reply with quote

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

PostPosted: Wed May 24, 2006 10:57 pm    Post subject: Here's a step by step procedure Reply with quote

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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PostPosted: Thu May 25, 2006 3:38 pm    Post subject: may 9 puzzle Reply with quote

thanks for your help
regards, carl
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