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Hungvuong
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 Posted: Sat Dec 31, 2005 4:44 am Post subject: Please help on this tough one. |
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Hi Sudoku Friends,
I got this puzzle off the internet. The level it claims was "Extreme". Well I guess it is extreme for me. I was able to solve so far, but then I got stuck there and wasn't able to figure it out for 2 days already. I would not feel OK until I see the technique for my next move. So would someone out there give me a clue for my next move, and I am greatly appreciate. Thanks. Here is the puzzle, and I will put the 0's where there were empty spaces.
| Code: | 000 583 000
500 916 003
039 742 150
976 020 534
213 654 987
458 379 612
004 035 200
300 490 005
005 267 340
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scorpio56xxl
Joined: 16 Oct 2005
Posts: 7
Location: Bonn, Germany
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| Posted: Sat Dec 31, 2005 10:50 am Post subject: Help for the really tough one |
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Hi Huongvong,
I found a solution for your puzzle. It's not the shortest one. Maybe some others found a faster but anyway I solved it for you. In this sense I wish you a Happy New Year. Here is my solution.
First I expanded the grid with the candidate list. It looks like followed:
| Code: | 167 2468 127 47 2679 69
5 248 27 9 1 6 478 27 3
68 3 9 7 4 2 1 5 68
9 7 6 18 2 18 5 3 4
2 1 3 6 5 4 9 8 7
4 5 8 3 7 9 6 1 2
167 689 4 18 3 5 2 679 1689
3 268 127 4 9 18 78 67 5
18 89 5 2 6 7 3 4 189 |
First of all you have a naked pair 27 in r2c3/c8. Therefore you can remove the "2" and the "7" of r2c2 respectively r2c7. Then you got another naked pair "48". Then you have an x-wing with "1" in r4c4/c6 u. r8c3/c6. But this is not very helpful. Therefore I build the following chain:
r9c2=8 => r2c2=4 => r2c7=8 => r3c9=6 => r3c1=8 => r9c1=1 =>
r9rc9=9 => r1c9=6 ! this is a contradiction to r3c9 with two "6" in the same column!
Therefore r9c2=9! and you can remove all "9's" in the last row and in the 7th block. The next step is also a forced chain which leads to a contradiction:
r8c7=8 => r2c7=4 => r2c2=8 => r3c1=6 => r3c9=8 => r9c9=1 => r9c1=8 => r7c2=6 => r8c2=2 => r1c2=4 => r1c7=7 => r2c8=2 =>
r2c3=7 => r1c1=1 => r1c3=2 => r8c3=1 => r8c6=8 which gives two "8's" in r8c6/c7! Therefore r8c7 must be "7" and you can remove all "7's" from block 9 and row 8 and so you get a "6" in r8c8 and a "9" in r7c8. This gives a naked pair "18" in r7c9 and r9c9.
Now it goes like follows:
r8c7=7 => r1c7=4 => r2c7=8 respectively r2c2=4(naked pair!) => r3c9=6 => r1c9=9 This gives a naked pair "27" in r1c8 and r2c8 and you can go on with r3c1=8; r9c1=1 this gives a "2" in r8c3 and a "7" in r2c3 and thus a "1" in r1c3 and a "6" in r1c1; and now you can solve the x-wing set: r8c6=1 and r4c4=1 respectively r4c6=8 and r7c4=8
Now you can complete block 7 with the remaining digits in r7c1 (7) and r7c2 (must be 6 sole candidate) and r8c2 (must be 8 sole candiate)
And last not least you can complete the block one with the remaining "2".
I hope this helps. Any questions please shout! Here is the complete puzzle:
| Code: | 621 583 479
547 916 823
839 742 156
976 128 534
213 654 987
458 379 612
764 835 291
382 491 765
195 267 348 |
[/code]
Many greetings from Bonn /Germany!
JB alias scorpio56xxl |
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someone_somewhere
Joined: 07 Aug 2005
Posts: 275
Location: Munich
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| Posted: Sat Dec 31, 2005 11:45 am Post subject: |
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Hi,
| Quote: | | So would someone out there give me a clue for my next move, and I am greatly appreciate. |
You called for me, here I am!
| Code: | Initial SuDoku Table
. . . 5 8 3 . . .
5 . . 9 1 6 . . 3
. 3 9 7 4 2 1 5 .
9 7 6 . 2 . 5 3 4
2 1 3 6 5 4 9 8 7
4 5 8 3 7 9 6 1 2
. . 4 . 3 5 2 . .
3 . . 4 9 . . . 5
. . 5 2 6 7 3 4 . |
2 not in r2c2, Hidden Pair 4 8 in r2c2 and r2c7 (in Row)
7 not in r2c7, Hidden Pair 4 8 in r2c2 and r2c7 (in Row)
| Code: | 167 246 127 5 8 3 47 2679 69
... ... ... . . . Aa .... ..
..a ... ..a . . . aA .... ..
5 48 27 9 1 6 48 27 3
. .. .. . . . .. .. .
. .. bB . . . .. .. .
68 3 9 7 4 2 1 5 68
9 7 6 18 2 18 5 3 4
2 1 3 6 5 4 9 8 7
4 5 8 3 7 9 6 1 2
1678 689 4 18 3 5 2 679 1689
3 268 127 4 9 18 78 67 5
. ... ..b . . .. Bb .. .
. ... ..b . . .. .. .. .
18 89 5 2 6 7 3 4 189 |
starting from cell r1c7:
1. case: r1c7 = 4, r1c7 <> 7, r8c7 = 7, r8c3 <> 7
2. case: r1c7 = 7, r1c1 <> 7 and r1c3 <> 7, r2c3 = 7, r8c3 <> 7
and from 1. and 2. case we can exclude digit 7 from r8c3
7 in r7c1 - Unique in 3x3 block
6 not in r1c2, it is in r1c1 or r3c1 (Column on 3x3 Block interaction)
7 not in r2c8, XY-Wing X=4 Y=2 in r1c2 X=4 Z=7 in r1c7 Y=2 Z=7 in r2c3
2 in r2c8 - Sole Candidate
7 in r2c3 - Sole Candidate
| Code: | 16 24 12 5 8 3 47 679 69
Aa .. .. . . . .. ... ..
aA .. .. . . . .. a.. aB
5 48 7 9 1 6 48 2 3
. .. . . . . .. . .
. .. . . . . .. . .
68 3 9 7 4 2 1 5 68
.. . . . . . . . ..
.. . . . . . . . ..
9 7 6 18 2 18 5 3 4
. . . .. . .. . . .
. . . .. . .. . . .
2 1 3 6 5 4 9 8 7
. . . . . . . . .
. . . . . . . . .
4 5 8 3 7 9 6 1 2
. . . . . . . . .
. . . . . . . . .
7 689 4 18 3 5 2 69 1689
. ... . .. . . . .. ....
. ... . .. . . . .. ....
3 268 12 4 9 18 78 67 5
. ... .. . . .. .. .. .
. ... .. . . .. .. .. .
18 89 5 2 6 7 3 4 189
aB .. . . . . . . Bbb
.. .. . . . . . . ..b |
starting from cell r1c1:
1. case: r1c1 = 1, r9c1 <> 1, r9c9 = 1, r9c9 <> 9
2. case: r1c1 = 6, r1c9 <> 6 and r1c9 = 9, r9c9 <> 9
and from 1. and 2. case we can exclude digit 9 from r9c9
9 in r9c2 - Unique Horizontal
8 not in r7c9, it is in r3c1 r3c9 r9c1 r9c9 (X-Wing on Column)
| Code: | 16 24 12 5 8 3 47 679 69
.. .. b. . . . .. ... ..
5 48 7 9 1 6 48 2 3
. .b . . . . .. . .
68 3 9 7 4 2 1 5 68
.. . . . . . . . ..
9 7 6 18 2 18 5 3 4
. . . aB . Bb . . .
2 1 3 6 5 4 9 8 7
. . . . . . . . .
4 5 8 3 7 9 6 1 2
. . . . . . . . .
7 68 4 18 3 5 2 69 169
. bB . Aa . . . .. a..
3 268 12 4 9 18 78 67 5
. ..b Bb . . aB .. .. .
18 9 5 2 6 7 3 4 18
bb . . . . . . . B. |
starting from cell r7c4:
1. path: r7c4 = 1, r7c4 <> 8, r7c2 = 8, r9c1 <> 8
2. path: r7c4 = 1, r7c9 <> 1, r9c9 = 1, r9c1 <> 1
and from 1. and 2. we get to a contradiction because
in cell r9c1 we can't put any digit.
This means that we can exclude digit 1 from r7c4
and the rest is a pice of cake ... up to the solution:
| Code: | 6 2 1 5 8 3 4 7 9
5 4 7 9 1 6 8 2 3
8 3 9 7 4 2 1 5 6
9 7 6 1 2 8 5 3 4
2 1 3 6 5 4 9 8 7
4 5 8 3 7 9 6 1 2
7 6 4 8 3 5 2 9 1
3 8 2 4 9 1 7 6 5
1 9 5 2 6 7 3 4 8 |
hope I could help,
see u, |
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Hungvuong
Guest
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| Posted: Sun Jan 01, 2006 7:20 am Post subject: |
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Hi scorpio 56xxl and someone_somewhere,
Thank you very much for taking the time and explain my puzzle. I am now understand, and can sleep good as well. Like you have said Scorpio, I sure will have a Happy New Year. Scorpio, I like your forcing chain technique. I am kind of know how the forcing chain work, but have not been able to practice or apply it yet.
Someone_somewhere, your solving technique is very unique. I really like it. The combination of techniques using in this puzzle surely will improve my skill in the future puzzles.
Happy New Year to both of you. |
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