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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sat Dec 31, 2005 10:18 pm Post subject: A remarkable (and very difficult) one for New Year! |
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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 . |
+-------+-------+-------+
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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: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jan 01, 2006 4:16 am Post subject: A valid puzzle, and a "masterpiece" |
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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
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| Posted: Sun Jan 01, 2006 3:14 pm Post subject: |
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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
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| Posted: Sun Jan 01, 2006 3:49 pm Post subject: I don't think you need the forcing chains! |
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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: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jan 01, 2006 11:33 pm Post subject: |
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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
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| Posted: Fri Jan 06, 2006 10:03 pm Post subject: A more detailed explanation |
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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: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jan 07, 2006 12:08 am Post subject: |
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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
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| Posted: Sat Jan 07, 2006 9:59 am Post subject: Missing corners from a Swordfish, Jellyfish or Squirmbag |
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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 
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: 3355
Location: near Detroit, Michigan, USA
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someone_somewhere
Joined: 07 Aug 2005
Posts: 275
Location: Munich
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| Posted: Sun Jan 08, 2006 8:22 am Post subject: Fishy Cycles |
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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
Guest
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| Posted: Wed Jan 18, 2006 10:35 pm Post subject: |
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| This puzzle can be made slightly harder by removing the nine in the top left square - and still be solvable |
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