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A remarkable (and very difficult) one for New Year!

 
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keith



Joined: 19 Sep 2005
Posts: 3175
Location: near Detroit, Michigan, USA

PostPosted: Sat Dec 31, 2005 10:18 pm    Post subject: A remarkable (and very difficult) one for New Year! Reply with quote

Try this one. It is a truly interesting puzzle!

To tell you why would spoil the surprise!

Code:


Puzzle: Scanraid Fiendish
+-------+-------+-------+
| . 2 . | . . . | . 7 . |
| 9 . . | 5 . 8 | . . 4 |
| . . . | . . . | . . . |
+-------+-------+-------+
| 4 . . | . 3 . | . . 8 |
| . 7 . | . 9 . | . 2 . |
| 6 . . | . 1 . | . . 5 |
+-------+-------+-------+
| . . . | . . . | . . . |
| 5 . . | 6 . 4 | . . 1 |
| . 3 . | . . . | . 9 . |
+-------+-------+-------+



and, a Happy New Year to all!

Keith


Last edited by keith on Sun Jan 01, 2006 4:20 am; edited 1 time in total
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keith



Joined: 19 Sep 2005
Posts: 3175
Location: near Detroit, Michigan, USA

PostPosted: Sun Jan 01, 2006 4:16 am    Post subject: A valid puzzle, and a "masterpiece" Reply with quote

A friend has confirmed this is a valid, unique puzzle, and calls it a "masterpiece".

Keith
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sun Jan 01, 2006 3:14 pm    Post subject: Reply with quote

Hi,

If it's a masterpice, than it looks good for me...

Starting from:
Code:
  . 2 . . . . . 7 .
  9 . . 5 . 8 . . 4
  . . . . . . . . .
  4 . . . 3 . . . 8
  . 7 . . 9 . . 2 .
  6 . . . 1 . . . 5
  . . . . . . . . .
  5 . . 6 . 4 . . 1
  . 3 . . . . . 9 .

I am just working up for the new year marathon:
3 not in r7c7, it is in r8c7 or r8c8 (Row on 3x3 Block interaction)
3 not in r7c8, it is in r8c7 or r8c8 (Row on 3x3 Block interaction)
3 not in r7c9, it is in r8c7 or r8c8 (Row on 3x3 Block interaction)
9 not in r7c2, it is in r8c2 or r8c3 (Row on 3x3 Block interaction)
9 not in r7c3, it is in r8c2 or r8c3 (Row on 3x3 Block interaction)
2 not in r7c3, it is in r7c1 or r9c1 (Column on 3x3 Block interaction)
2 not in r8c3, it is in r7c1 or r9c1 (Column on 3x3 Block interaction)
2 not in r9c3, it is in r7c1 or r9c1 (Column on 3x3 Block interaction)
4 not in r1c4, it is in r1c5 or r3c5 (Column on 3x3 Block interaction)
4 not in r3c4, it is in r1c5 or r3c5 (Column on 3x3 Block interaction)
5 not in r7c6, it is in r7c5 or r9c5 (Column on 3x3 Block interaction)
5 not in r9c6, it is in r7c5 or r9c5 (Column on 3x3 Block interaction)
6 not in r1c6, it is in r1c5 or r2c5 or r3c5 (Column on 3x3 Block interaction)
6 not in r3c6, it is in r1c5 or r2c5 or r3c5 (Column on 3x3 Block interaction)
8 not in r7c4, it is in r7c5 or r8c5 or r9c5 (Column on 3x3 Block interaction)
8 not in r9c4, it is in r7c5 or r8c5 or r9c5 (Column on 3x3 Block interaction)
7 not in r7c7, it is in r7c9 or r9c9 (Column on 3x3 Block interaction)
7 not in r8c7, it is in r7c9 or r9c9 (Column on 3x3 Block interaction)
7 not in r9c7, it is in r7c9 or r9c9 (Column on 3x3 Block interaction)
9 not in r1c7, it is in r1c9 or r3c9 (Column on 3x3 Block interaction)
9 not in r3c7, it is in r1c9 or r3c9 (Column on 3x3 Block interaction)
1 not in r7c4, Hidden Pair 3 9 in r7c4 and r7c6 (in Row)
1 not in r7c6, Hidden Pair 3 9 in r7c4 and r7c6 (in Row)
2 not in r7c4, Hidden Pair 3 9 in r7c4 and r7c6 (in Row)
2 not in r7c6, Hidden Pair 3 9 in r7c4 and r7c6 (in Row)
7 not in r7c4, Hidden Pair 3 9 in r7c4 and r7c6 (in Row)
7 not in r7c6, Hidden Pair 3 9 in r7c4 and r7c6 (in Row)
1 not in r9c1, it is in r7c1 or r7c2 or r7c3 (Row on 3x3 Block interaction)
1 not in r9c3, it is in r7c1 or r7c2 or r7c3 (Row on 3x3 Block interaction)
8 not in r3c2, Nacked Pair 8 9 in r6c2 and r8c2 (same Column)
9 not in r4c2, Nacked Pair 8 9 in r6c2 and r8c2 (same Column)
8 not in r7c2, Nacked Pair 8 9 in r6c2 and r8c2 (same Column)
2 not in r6c4, Hidden Pair 4 8 in r5c4 and r6c4 (in Column)
7 not in r6c4, Hidden Pair 4 8 in r5c4 and r6c4 (in Column)
2 not in r4c6, Hidden Pair 5 6 in r4c6 and r5c6 (in Column)
7 not in r4c6, Hidden Pair 5 6 in r4c6 and r5c6 (in Column)
1 not in r4c7, Hidden Pair 7 9 in r4c7 and r6c7 (in Column)
3 not in r6c7, Hidden Pair 7 9 in r4c7 and r6c7 (in Column)
4 not in r6c7, Hidden Pair 7 9 in r4c7 and r6c7 (in Column)
6 not in r4c7, Hidden Pair 7 9 in r4c7 and r6c7 (in Column)
2 not in r3c5, it is in r2c5 r2c7 r8c5 r8c7 (X-Wing on Column)
2 not in r3c7, it is in r2c5 r2c7 r8c5 r8c7 (X-Wing on Column)
2 not in r7c5, it is in r2c5 r2c7 r8c5 r8c7 (X-Wing on Column)
2 not in r7c7, it is in r2c5 r2c7 r8c5 r8c7 (X-Wing on Column)
2 not in r9c5, it is in r2c5 r2c7 r8c5 r8c7 (X-Wing on Column)
2 not in r9c7, it is in r2c5 r2c7 r8c5 r8c7 (X-Wing on Column)
7 not in r3c3, it is in r2c3 r2c5 r8c3 r8c5 (X-Wing on Column)
7 not in r3c5, it is in r2c3 r2c5 r8c3 r8c5 (X-Wing on Column)
7 not in r7c3, it is in r2c3 r2c5 r8c3 r8c5 (X-Wing on Column)
7 not in r7c5, it is in r2c3 r2c5 r8c3 r8c5 (X-Wing on Column)
7 not in r9c3, it is in r2c3 r2c5 r8c3 r8c5 (X-Wing on Column)
7 not in r9c5, it is in r2c3 r2c5 r8c3 r8c5 (X-Wing on Column)
1 not in r7c1, Hidden Pair 2 7 in r7c1 and r7c9 (in Row)
6 not in r7c9, Hidden Pair 2 7 in r7c1 and r7c9 (in Row)
8 not in r7c1, Hidden Pair 2 7 in r7c1 and r7c9 (in Row)
6 not in r2c5, Hidden Pair 2 7 in r2c5 and r8c5 (in Column)
8 not in r8c5, Hidden Pair 2 7 in r2c5 and r8c5 (in Column)
8 not in r7c3, Hidden Triple 4 1 6 in r7c2 r7c3 r9c3
8 not in r9c3, Hidden Triple 4 1 6 in r7c2 r7c3 r9c3
1 not in r4c3, Hidden Triple 1 5 6 in r4c2 r4c6 r4c8
5 not in r4c3, Hidden Triple 1 5 6 in r4c2 r4c6 r4c8
Now a forcing chain:
assuming 7 in r7c1, than r8c3 <> 7, r8c5 = 7, r8c5 <> 2
7 in r7c1, than r7c9 <> 7, r7c9 = 2, r8c8 <> 2
and we can't put digit 2 in row 8 any more. This means:
7 not in r7c1

2 in r7c1 - Sole Candidate
7 in r7c9 - Sole Candidate
And from here on, I had to use the DIC (Double Implication Chains).
Code:
138   2     134568 139   46    139   13568  7     369     

9     16    1367   5     27    8     1236   136   4     

1378  1456  134568 12379 46    12379 13568  13568 2369     

4     15    29     27    3     56    79     16    8     

138   7     1358   48    9     56    1346   2     36     

6     89    2389   48    1     27    79     34    5     
.     ..    bBbb   ..    .     ..    ..     aB    .     
.     Bb    ..b.   ..    .     ..    ..     ..    .
              *       
2     146   146    39    58    39    4568   4568  7     

5     89    789    6     27    4     238    38    1     
.     ..    ...    .     ..    .     ...    Aa    .     
.     aB    ...    .     ..    .     ...    aA    .
                                            ==
78    3     46     127   58    127   4568   9     26     

1. path: r8c8 = 3, r6c8 <> 3, r6c3 = 3, r6c3 <> 8
2. path: r8c8 = 8, r8c2 <> 8, r6c2 = 8, r6c2 <> 8
and from 1. and 2. we deduce:
8 not in r6c3

Code:
138   2     134568 139   46    139   13568  7     369     
.a.   .     aAaaaa .a.   Bb    .a.   baBbb  .     aC.
             =                                     *       
9     16    1367   5     27    8     1236   136   4     
     
1378  1456  134568 12379 46    12379 13568  13568 2369     
.a..     
4     15    29     27    3     56    79     16    8     
.     ..    ..     ..    .     ..    ..     ..    .     
138   7     1358   48    9     56    1346   2     36     
bBb   .     ....   ..    .     ..    ....   .     bC
                                                   *     
6     89    239    48    1     27    79     34    5     
     
2     146   146    39    58    39    4568   4568  7     
     
5     89    789    6     27    4     238    38    1     
     
78    3     46     127   58    127   4568   9     26

1. path r1c3 = 3, r1c3 <> 6,
r1c3 <> 4, r1c5 = 4, r1c5 <> 6,
r1c3 <> 5, r1c7 = 5, r1c7 <> 6,
and this leads to r1c9 = 6
2. path r1c3 = 3, r1c1 <> 3 and r3c1 <> 3, r5c1 = 3, r5c9 <> 3, r5c9 = 6
and the 2 pathes leads us to a double digit 6 in column 9, so:
3 not in r1c3
Code:
138   2     14568  139   46    139   13568  7     369     

9     16    1367   5     27    8     1236   136   4     
.     aB    a.bC   .     Bb    .     Aaaa   aCb   .
                                     =       *
1378  1456  134568 12379 46    12379 13568  13568 2369     

4     15    29     27    3     56    79     16    8     

138   7     1358   48    9     56    1346   2     36     

6     89    239    48    1     27    79     34    5     

2     146   146    39    58    39    4568   4568  7     

5     89    789    6     27    4     238    38    1     
.     ..    ...    .     ..    .     Bbb    C.    .
                                            *
78    3     46     127   58    127   4568   9     26     

1. path r2c7 = 1, r2c8 <> 1,
r2c2 <> 1, r2c2 = 6, r2c8 <> 6,
and this leads to r2c8 = 3
2. path r2c7 = 1, r2c7 <> 2, r8c7 = 2, r8c7 <> 3, r8c8 = 3
and the 2 pathes leads us to a double digit 3 in column 8, so:
3 not in r1c3
Code:
138   2    14568  139   46  139   13568 7      369         
         
9     16   1367   5     27  8     236   136    4         
.     Ba   b.aC   .     Bb  .     aaA   bCa    .
                                    =    *
1378  1456 134568 12379 46  12379 13568 13568  2369         
         
4     15   29     27    3   56    79    16     8         
         
138   7    1358   48    9   56    1346  2      36         
         
6     89   239    48    1   27    79    34     5         

2     146  146    39    58  39    4568  4568   7         
         
5     89   789    6     27  4     238   38     1         
.     ..   ...    .     bC  .     Bbb   C.     .
                                        *     
78    3    46     127   58  127   4568  9      26         

1. path r2c7 = 6, r2c8 <> 6,
r2c2 <> 6, r2c2 = 1, r2c8 <> 1,
and this leads to r2c8 = 3
2. path r2c7 = 6, r2c7 <> 2, r8c7 = 2, r8c7 <> 3, r8c8 = 3
and the 2 pathes leads us to a double digit 3 in column 8, so:
6 not in r2c7
And now the final sprint:
Code:
138  2    14568  139   46   139   13568 7     369     
     
9    16   1367   5     27   8     23    136   4     
.    ..   .a..   .     bC   .     Ba    aAa   .
                                         =     
1378 1456 134568 12379 46   12379 13568 13568 2369     
     
4    15   29     27    3    56    79    16    8     
     
138  7    1358   48    9    56    1346  2     36     
     
6    89   239    48    1    27    79    34    5     
.    C.   bBb    bC    .    C.    ..    aB    .
     *            *
2    146  146    39    58   39    4568  4568  7     
     
5    89   789    6     27   4     238   38    1     
.    b.   ...    .     ..   .     ...   aB    .
     
78   3    46     127   58   127   4568  9     26     

1. path r2c8 = 3, r8c8 <> 3, r8c8 = 8, r8c2 <> 8, r6c2 = 8
2. path r2c8 = 3, r6c8 <> 3, r6c8 = 4, r6c4 <> 4, r6c4 = 8
and the 2 pathes leads us to a double digit 8 in row 6, so:
3 not in r2c8

1 not in r2c3, Nacked Pair 1 6 in r2c2 and r2c8 (same Row)
6 not in r2c3, Nacked Pair 1 6 in r2c2 and r2c8 (same Row)
1 not in r3c8, Nacked Pair 1 6 in r2c8 and r4c8 (same Column)
6 not in r3c8, Nacked Pair 1 6 in r2c8 and r4c8 (same Column)
6 not in r7c8, Nacked Pair 1 6 in r2c8 and r4c8 (same Column)
1 not in r3c2, it is in r2c2 r2c8 r4c2 r4c8 (X-Wing on Column)
1 not in r7c2, it is in r2c2 r2c8 r4c2 r4c8 (X-Wing on Column)
1 in r7c3 - Unique Horizontal
3 not in r1c7, it is in r2c3 r2c7 r6c3 r6c8 r8c7 r8c8 (Swordfish on Row)
3 not in r3c3, it is in r2c3 r2c7 r6c3 r6c8 r8c7 r8c8 (Swordfish on Row)
3 not in r3c7, it is in r2c3 r2c7 r6c3 r6c8 r8c7 r8c8 (Swordfish on Row)
3 not in r3c8, it is in r2c3 r2c7 r6c3 r6c8 r8c7 r8c8 (Swordfish on Row)
3 not in r5c3, it is in r2c3 r2c7 r6c3 r6c8 r8c7 r8c8 (Swordfish on Row)
3 not in r5c7, it is in r2c3 r2c7 r6c3 r6c8 r8c7 r8c8 (Swordfish on Row)
8 not in r8c7, Hidden Pair 2 3 in r2c7 and r8c7 (in Column)
6 not in r1c9, Hidden Triple 3 2 9 in r1c9 r2c7 r3c9
6 not in r3c9, Hidden Triple 3 2 9 in r1c9 r2c7 r3c9
1 not in r1c1, Naked Triple 1 3 9 in Row 1 Columns 4 6 9
3 not in r1c1, Naked Triple 1 3 9 in Row 1 Columns 4 6 9
1 not in r1c7, Naked Triple 1 3 9 in Row 1 Columns 4 6 9
8 in r1c1 - Sole Candidate
7 in r9c1 - Sole Candidate
7 in r8c5 - Unique Horizontal
7 in r2c3 2 in r8c7 - Unique Horizontal
2 in r2c5 3 in r2c7 2 in r3c9 3 in r8c8 - Unique Horizontal
3 in r6c3 - Unique Horizontal
3 in r5c9 2 in r6c6 2 in r9c4 - Unique Horizontal
2 in r4c3 7 in r6c7 1 in r9c6 - Unique Horizontal
1 in r1c4 7 in r4c4 9 in r4c7 9 in r6c2 9 in r8c3 - Unique Horizontal
3 in r1c6 3 in r3c1 7 in r3c6 8 in r6c4 3 in r7c4 8 in r8c2 - Unique Horizontal
9 in r1c9 1 in r3c7 9 in r3c4 1 in r5c1 8 in r5c3 4 in r6c8 9 in r7c6 - Unique Horizontal
1 in r2c2 8 in r3c8 1 in r4c8 4 in r5c4 5 in r5c6 - Unique Horizontal
6 in r2c8 5 in r4c2 6 in r4c6 6 in r5c7 6 in r7c2 6 in r9c9 - Unique Horizontal
5 in r3c3 4 in r7c7 4 in r9c3 - Unique Horizontal
4 in r1c5 5 in r1c7 4 in r3c2 6 in r3c5 8 in r7c5 5 in r9c5 8 in r9c7 - Unique Horizontal
6 in r1c3 5 in r7c8 - Unique Horizontal

and I got to the finish:
Code:
  8 2 6 1 4 3 5 7 9
  9 1 7 5 2 8 3 6 4
  3 4 5 9 6 7 1 8 2
  4 5 2 7 3 6 9 1 8
  1 7 8 4 9 5 6 2 3
  6 9 3 8 1 2 7 4 5
  2 6 1 3 8 9 4 5 7
  5 8 9 6 7 4 2 3 1
  7 3 4 2 5 1 8 9 6


It's full winter here, but this one made me sweat!

see u all this year,
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun Jan 01, 2006 3:49 pm    Post subject: I don't think you need the forcing chains! Reply with quote

I agree that this is one tough puzzle. Here's how I solved it.

1. Hidden pair {4, 8} in r5c4 & r6c4.
2. Hidden pair {5, 6} in r4c6 & r5c6.
3. Another pair, {2, 7}, lies in r4c4 & r6c6.
4. Naked pair {8, 9} in r6c2 & r8c2.
5. Naked triplet {1, 5, 6} in r4c2, r4c6, & r4c8, allows us to uncover the hidden triplet {2, 7, 9} in r4c3, r4c4, & r4c7.
6. The "2" in column 1 lies in bottom left 3x3 box. Eliminate "2" from r7c3, r8c3, & r9c3.
7. The "3" in row 8 lies in bottom right 3x3 box. Eliminate "3" from r7c7, r7c8, & r7c9.
8. Jellyfish (on column) in columns 1, 4, 6, & 9 -- in rows 1, 3, 5, & 7. Eliminate "3" from r1c3, r1c7, r3c3, r3c7, r3c8, r5c3, & r5c7.
9. The "7" in column 9 lies in bottom right 3x3 box. Eliminate "7" at r7c7, r8c7, & r9c7.
10. X-Wing on "7" in rows 2 & 8. Eliminate "7" at r3c3, r7c3, r9c3, r3c5, r7c5, & r9c5.
11. The "9" in row 8 lies in bottom left 3x3 box. Eliminate "9" at r7c3.
12. The "9" in column 7 lies in middle right 3x3 box. Eliminate "9" at r1c7 & r3c7.
13. Hidden pair {7, 9} in r4c7 & r6c7. Eliminate "3" & "4" at r6c7.
14. X-Wing on "2" in rows 2 & 8. Eliminate "2" at r3c5, r7c5, r9c5, r3c7, r7c7, & r9c7.
15. Pairs (4, 6} in r1c5 & r3c5 and {5, 8} in r7c5 & r9c5 are now apparent, revealing {2, 7} in r2c5 & r8c5.
16. Hidden pair {2, 3} lies in r2c7 & r8c7.
17. Naked triplet {1, 2, 7} in r8c5, r9c4, & r9c6 reveals hidden pair {3, 9} in r7c4 & r7c6.
18. The "1" in row 7 lies in bottom left 3x3 box. Eliminate "1" at r9c1 & r9c3.
19. Hidden pair {2, 7} lies in r7c1 & r7c9.
20. Hidden triplet {1, 4, 6} lies in r7c2, r7c3, & r9c3.
21. Swordfish (on rows) in the "1"s, rows 2, 4, & 7. Eliminate "1" at r3c2, r3c3, & r3c8.
22. Naked quad {4, 5, 6, 8} in r3c2, r3c3, r3c5, & r3c8. So r3c7 = 1.

And with this one additional value placed, the rest of the puzzle is fairly simple. dcb
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keith



Joined: 19 Sep 2005
Posts: 3175
Location: near Detroit, Michigan, USA

PostPosted: Sun Jan 01, 2006 11:33 pm    Post subject: Reply with quote

You guys are good! (Better than me.)

The remarkable thing is that all the logic eliminates possibilities, it does not actually solve any squares, until ... Boom! One square is solved and all the other values are forced.

Here is an outline of my path to the solution:

Pair <89> in C2.
Pair <27> in B5.
Pair <48> in C4.
Pair <56> in C6.
Hidden pair <39> in B8.
Pair <39> in R7.
Hidden pair <79> in B6.
Pair <79> in C7.
Intersection <1> in R7 and B7.
Intersection <2> in C1 and B7.
Hidden triplet <279> in R4.
Unique rectangle <39> in R1, R7, C4, C6. (R1C4 or R1C6 must be <1>, so R1C1, R1C3, R3C4, R1C7, R3C6 are not <1>.)
X-Wing <2> in R2C5,7 and R8C5,7.
X-Wing <7> in R2C3,5 and R8C3,5.
Pair <46> in C5.
Pair <58> in C5.
Hidden pair <27> in R7.
Hidden triplet <146> in B7.
Swordfish <3> in R2C3,7,8, R6C3,8, R8C7,8. (R1C3, R1C7, R3C3, R3C7, R3C8, R5C3, R5C7 are not <3>.)
Hidden pair <23> in C7.
Quintet <14568> in R3.
R5C1 must be <1>

and all the other squares' values are immediately forced!!
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Fri Jan 06, 2006 10:03 pm    Post subject: A more detailed explanation Reply with quote

This is an expansion of my earlier explanation of this puzzle, posted here. I'm offering it because a few of the moves (jellyfish, swordfish) may not be familiar to all the participants in this forum. The puzzle starts from this initial position.
Code:
 . 2 .  . . .  . 7 .
 9 . .  5 . 8  . . 4
 . . .  . . .  . . .

 4 . .  . 3 .  . . 8
 . 7 .  . 9 .  . 2 .
 6 . .  . 1 .  . . 5

 . . .  . . .  . . .
 5 . .  6 . 4  . . 1
 . 3 .  . . .  . 9 .

The first seven moves from my original post were described as follows.

1. Hidden pair {4, 8} in r5c4 & r6c4. Notice the {4, 8} in row 4, and also in column 6.
2. Hidden pair {5, 6} in r4c6 & r5c6. Notice the {5, 6} in row 6, and also in column 4.
3. Another pair, {2, 7}, lies in r4c4 & r6c6. These are the only values left for the middle center 3x3 box.
4. Naked pair {8, 9} in r6c2 & r8c2. You can find these by simple counting.
5. Naked triplet {1, 5, 6} in r4c2, r4c6, & r4c8, allows us to uncover the hidden triplet {2, 7, 9} in r4c3, r4c4, & r4c7. Again, you can find the first triplet by simple counting.
6. The "2" in column 1 lies in bottom left 3x3 box (notice the "2"s at r1c2 & at r5c8). Eliminate "2" from r7c3, r8c3, & r9c3.
7. The "3" in row 8 lies in bottom right 3x3 box (notice the "3"s at r9c2 & at r4c5). Eliminate "3" from r7c7, r7c8, & r7c9.

After these seven moves the table of candidates looks like this.
Code:
*138    2  134568    *139   46   *139    135689    7   *369
   9   16   1367       5    267    8      1236    136    4
*1378 1456 1345678  *12379 2467 *12379   1235689 13568 *2369

   4   15    29       27     3    56       79     16     8
 *138   7   1358      48     9    56      1346     2   *36
   6   89   2389      48     1    27      3479    34     5

 1278  146 146789   *12379 2578 *12379   245678  4568   267
   5   89    789       6    278    4      2378    38     1
 1278   3   14678     127  2578   127    245678    9    267


Now we're ready for the big "jellyfish" move! The jellyfish (like the somewhat simpler swordfish) is just a generalization of the relatively familiar "X-Wing" pattern. An X-Wing (on rows) occurs when a particular value is constrained to appear in only two spots in each of two rows, and these two spots happen to fall in the same columns. You'll find two examples of the X-Wing later in this discussion, at moves 10 and 14.

Anyway, the jellyfish pattern (on rows) arises when a particular value is constrained to appear in no more than four spots in each of four separate rows, and these spots line up in exactly four columns (with at least two occurences lying in each of the four columns). No matter how that value is arranged, it cannot lie in any more than one of four possible spots in each of those four columns, and this fact may allow us to eliminate that value from one or more cells in those four columns.

A jellyfish on columns is the same pattern rotated by 90 degrees. The next move is a jellyfish on columns.

8. Jellyfish (on column) in columns 1, 4, 6, & 9 -- in rows 1, 3, 5, & 7. Eliminate "3" from r1c3, r1c7, r3c3, r3c7, r3c8, r5c3, & r5c7.

In column 1, "3" can only occur at r1c1, r3c1, or r5c1; in col 4 it can appear at r1c4, r3c4, or r7c4; in col 6 it can appear at r1c6, r3c6, or r7c6; and in col 9 "3" can only occur at r1c9, r3c9, or r5c9. This jellyfish doesn't occupy all 16 possible "corners" because four of those cells (r7c1, r5c4, r5c6, & r7c9) cannot possibly contain a "3" But we do have enough "corners" left to employ the jellyfish to make the indicated eliminations. I've marked the twelve corners of this jellyfish with an asterisk in the table above -- hopefully the picture will make all this a bit clearer.

After these eliminations the table of candidates looks like this.
Code:
*138    2   14568    *139   46   *139     15689    7   *369
   9   16   1367       5    267    8      1236    136    4
*1378 1456 145678   *12379 2467 *12379   125689  1568  *2369

   4   15    29       27     3    56       79     16     8
 *138   7    158      48     9    56       146     2   *36
   6   89   2389      48     1    27      3479    34     5

 1278  146 146789   *12379 2578 *12379   245678  4568   267
   5   89    789       6    278    4      2378    38     1
 1278   3   14678     127  2578   127    245678    9    267

The next 4 moves are much simpler.

9. The "7" in column 9 lies in bottom right 3x3 box (notice the "7"s at r1c8, and at r5c2). Eliminate "7" at r7c7, r8c7, & r9c7.
10. X-Wing on "7" in rows 2 & 8. Eliminate "7" at r3c3, r7c3, r9c3, r3c5, r7c5, & r9c5.
11. The "9" in row 8 lies in bottom left 3x3 box (notice "9"s at r5c5, and at r9c8). Eliminate "9" at r7c3.
12. The "9" in column 7 lies in middle right 3x3 box (notice "9"s at r5c5, and at r9c8). Eliminate "9" at r1c7 & r3c7.
13. Hidden pair {7, 9} in r4c7 & r6c7 (inspect candidates in middle right 3x3 box). Eliminate "3" & "4" at r6c7.

A note about move #10 -- after eliminating some "7"s from the bottom right 3x3 box, we can see that the only way a "7" can fit in row 2 is at r2c3, or else at r2c5. Similarly, the only way a "7" can then fit in row 8 is at r8c3, or else at r8c5. So there's either a "7" at r2c3 and a "7" at r8c5; or else there's a "7" at r2c5 and a "7" at r8c3 -- that's why we can make the indicated eliminations. This is just like the "jellyfish" described above, but simpler because it only involves two rows and two columns.

Now the table of candidates looks like this.
Code:
 138    2   14568     139   46   139     1568     7   369
   9   16   1367       5    267   8      1236    136   4
 1378 1456  14568    12379  246 12379    12568  1568  2369

   4   15    29       27     3   56       79     16    8
  138   7    158      48     9   56       146     2   36
   6   89   2389      48     1   27       79     34    5

 1278  146  1468     12379  258 12379    24568  4568  267
   5   89    789       6    278   4       238    38    1
 1278   3   14678     127   258  127     24568    9   267

The next 7 moves are again relatively simple.

14. X-Wing on "2" in rows 2 & 8. Eliminate "2" at r3c5, r7c5, r9c5, r3c7, r7c7, & r9c7.
15. Pairs (4, 6} in r1c5 & r3c5 and {5, 8} in r7c5 & r9c5 are now apparent, revealing {2, 7} in r2c5 & r8c5.
16. Hidden pair {2, 3} lies in r2c7 & r8c7.
17. Naked triplet {1, 2, 7} in r8c5, r9c4, & r9c6 reveals hidden pair {3, 9} in r7c4 & r7c6.
18. The "1" in row 7 lies in bottom left 3x3 box. Eliminate "1" at r9c1 & r9c3.
19. Hidden pair {2, 7} lies in r7c1 & r7c9.
20. Hidden triplet {1, 4, 6} lies in r7c2, r7c3, & r9c3.

With all these preliminaries out of the way we're ready for the final push. The candidate matrix looks like this.
Code:
 138    2   14568     139   46   139     1568     7   369
   9  *16  *1367       5    27    8       23    *136   4
 1378 1456  14568    12379  46  12379    1568   1568  2369

   4  *15    29       27     3   56       79    *16    8
  138   7    158      48     9   56       146     2   36
   6   89   2389      48     1   27       79     34    5

  27  *146  *146      39    58   39      4568   4568  27
   5   89    789       6    27    4       23     38    1
  278   3    46       127   58   127     4568     9   267


21. Swordfish (on rows) in the "1"s, rows 2, 4, & 7. Eliminate "1" at r3c2, r3c3, & r3c8. (Although it's not essential for the next move, we can also eliminate "1" at r5c3.)

I've marked the seven corners of this swordfish with asterisks in the table above. Note that this is not the complete swordfish pattern, which has nine corners (intersection of 3 columns with 3 rows). In this case the value "1" has already been ruled out at r4c3 and at r7c8 -- these are the "missing" eighth and ninth corners. But there are still enough corners left for this swordfish to be valid.

22. Naked quad {4, 5, 6, 8} in r3c2, r3c3, r3c5, & r3c8. So r3c7 = 1.

With this single value placed, the rest of the puzzle falls apart rather quickly. dcb
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keith



Joined: 19 Sep 2005
Posts: 3175
Location: near Detroit, Michigan, USA

PostPosted: Sat Jan 07, 2006 12:08 am    Post subject: Reply with quote

David,

A good explanation! I think this is also a great teaching puzzle - each step is not trivial. But, each step is also not overly complex. (In my opinion.)

What I mean is, I can solve this puzzle, given enough time and concentration. At my level of understanding, I view long forcing chains and Nishio as guessing.

There is also the fact that this puzzle seems to have many paths to the solution. So, we can compare different approaches.

Keith
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sat Jan 07, 2006 9:59 am    Post subject: Missing corners from a Swordfish, Jellyfish or Squirmbag Reply with quote

Hi David, hi all of you,

Quote:
But we do have enough "corners" left to employ the jellyfish to make the indicated eliminations.

It did not cross my mind that there are also "incomplete" jellyfishs (and other see animals Wink
Did you already analyse (all) the possible patterns of such a fish, so that he is still a fish, and we can eliminate some bones from other cells?
If not, I will have to start doing it myself.

Open question for who is willing to look for an answer:

Q:How many and what corners can be missing from a Swordfish, Jellyfish or Squirmbag, so that they can be still used?

see u,
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keith



Joined: 19 Sep 2005
Posts: 3175
Location: near Detroit, Michigan, USA

PostPosted: Sat Jan 07, 2006 9:00 pm    Post subject: More on "Fishy Cycles" Reply with quote

Someone,

You may find this discussion relevant to your question about incomplete fishes.

http://www.setbb.com/phpbb/viewtopic.php?t=35&mforum=sudoku

Best wishes,

Keith
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sun Jan 08, 2006 8:22 am    Post subject: Fishy Cycles Reply with quote

Hi Keith,

Thank you for the link.
Now I got the information I was missing.

Fishy Cycles - very nice!

see u,
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Matt
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PostPosted: Wed Jan 18, 2006 10:35 pm    Post subject: Reply with quote

This puzzle can be made slightly harder by removing the nine in the top left square - and still be solvable
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