superior plus puzzles

Everything about Sudoku that doesn't fit in one of the other sections

Postby ab » Sat Aug 26, 2006 12:20 pm

maybe inspired by daj95376, my solver threw up a puzzle with two swordfish and i think they're both required:
Code: Select all
 . 5 . | . 6 . | . 9 .
 . . . | . . . | . . 7
 . . 9 | 2 . 4 | 3 . .
 ------+-------+------
 . . 7 | . 1 3 | 8 . .
 4 . . | 6 . 2 | . . 1
 . . 5 | 8 4 . | 9 . .
 ------+-------+------
 . . 2 | 7 . 8 | 4 . .
 3 . . | . . . | . . .
 . 7 . | . 2 . | . 5 .
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Postby daj95376 » Sun Aug 27, 2006 1:07 am

ab, your double in swordfish seem necessary to my solver.

Here's my final contribution to this thread. I was never able to generate a triple like gsf. I guess that's not surprising.

Code: Select all
# Naked Quad + Swordfish
8..3..71.......4.57..6.4.3..5.7.....4...5...7.....1.8..4.5.6..22.3.......76..8..4

# Naked Quad + Jellyfish
# Naked Quad in box 6 is destroyed by Naked Quad in row 5 ... but not vice versa
24.9...35...5..28.5.6.1...9....45.63.........63.89....3...2.5.4.52..8...19...3.28

# Swordfish  + Swordfish
..5...3..9...2..87.....1...25..1.79.4...7...2.83.9..51...7.....39..4...8..4...2..
.328..69...9.5...1.8...9....5.2..7..9...6...2..7..3.5....5...3.8...2.5...25..716.
.7.1.29...563.....2......36.3...62..7...4...3..95...6.54......1.....537...36.4.5.
7.....8...6.8..2.9.9..4..714.26......1.7.5.9......46.265..7..4.1.7..9.2...9.....7
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Postby gsf » Sun Aug 27, 2006 7:53 am

this one requires 3 swordfish
Code: Select all
#15.3.12:C28.M/S2.h/F9.23/N8.28/B5.22.3.5/T12.38.6.6/H7.13.2.5/W5.14.3.3.2

. . 9 | . 5 . | . 8 .
. . 3 | . . 1 | 2 . .
7 . . | 2 . . | . . 1
------+-------+------
1 . . | 8 . . | 3 4 5
. . . | . . . | . . .
6 . . | 4 . . | 9 1 2
------+-------+------
8 . . | 6 . . | . . 4
. . 7 | . . 9 | 8 . .
. . 6 | . 4 . | . 2 .
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Postby gsf » Sun Aug 27, 2006 8:04 am

Ocean wrote:
gsf wrote:if the doubles are duals then my code (and brain) certainly missed that

Why are they not duals? (Every fish has a dual, which eliminates exactly the same candidates. Where are the duals here, if not the listed doubles?)

I missed the fish duality memo and was commenting on that
which means my code doesn't check for duals explicitly and ends up listing
the duals in the verbose trace before discovering by more general mechanisms
that two moves cover the same eliminations
i.e., by the time the second one is applied (with its eliminations already done)
any information leading to its dual is gone
thanks
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Postby Ocean » Sun Aug 27, 2006 10:49 am

gsf wrote:this one requires 3 swordfish

Congratulations! - first puzzle I have seen in this category!

Analysis
First: Swordfish (with Swordfish dual, both with cp 2+2+2 / ep 2+2+1) (one choice)
Second: Swordfish (with Jellyfish dual) (cp 2+2+2 / ep 1+1+1) (one choice)
Third: Swordfish (with Jellyfish dual) (cp 2+2+2 / ep 1+0+0) (one choice)
[cp: cell pattern / ep: elimination pattern]

No branch of the solution path (when non-splus techniques are treated as iterative group).

#
For classificaton, maybe it's relevant to distinguish between the various fish types (subtypes):
1. JF/5-F (Jellyfish with a 5-fish dual)
2. JF/JF (Jellyfish with a Jellyfish dual)
3. SF/6-F (Swordfish with a 6-fish dual)
4. SF/5-F (Swordfish with a 5-fish dual)
5. SF/JF (Swordfish with a Jellyfish dual)
6. SF/SF (Swordfish with a Swordfish dual)
#
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Postby ravel » Sun Aug 27, 2006 2:20 pm

Nice find, gsf.

But it should be mentioned, that a simple xy-chain also solves the puzzle:
7-r2c4-9-r2c9=9=r9c9-9-r9c4-7 => r1c4<>7
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Postby gsf » Sun Aug 27, 2006 2:38 pm

ravel wrote:But it should be mentioned, that a simple xy-chain also solves the puzzle:
7-r2c4-9-r2c9=9=r9c9-9-r9c4-7 => r1c4<>7

thanks, but xy-cycles are not in scope in this thread
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Postby ravel » Sun Aug 27, 2006 3:54 pm

gsf wrote:thanks, but xy-cycles are not in scope in this thread

Yes, i know, i just wanted to point out a problem, that i still generally have with this - though already sophisticated - classification of sudokus.

I know that this xy-chain pattern has no name:
Code: Select all
 #
 #
12 --------- 2X
 #            |
 #            |
 #           (2)
 #            |
 #            |
1Y ---(1)--- 12Z
 #

(X,Y,Z are arbitrary numbers, (n) is a strong link for n, 1 can be eliminated in cells marked #.)
But for a manual solver it is easier to spot than a swordfish - it already can be seen with pencilmarks for the cell with candidates 12 and the 2 strong links only, whereas i never found a swordfish without having filled out almost all candidates.
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Postby udosuk » Sun Aug 27, 2006 5:40 pm

ravel wrote:I know that this xy-chain pattern has no name:
Code: Select all
 #
 #
12 --------- 2X
 #            |
 #            |
 #           (2)
 #            |
 #            |
1Y ---(1)--- 12Z
 #

(X,Y,Z are arbitrary numbers, (n) is a strong link for n, 1 can be eliminated in cells marked #.)

Very cool technique... If I have a choice I'll call it a boomerang for the shape of the strong links and also movement - either the bottom left corner=1, or the 1 would "boomerang" curve all the way to the top left corner...
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Postby daj95376 » Sun Aug 27, 2006 6:43 pm

It reminds me of a Double Implication Chain on <2> in the right column. Whichever cell contains the <2> forces the corresponding cell in the left column to be <1>. The result is that the remaining cells in the left column are forced not to be <1>. Right/Wrong?
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Postby udosuk » Sun Aug 27, 2006 7:36 pm

Right! Very clear reasoning too...

If top right cell = 2, then top left cell = 1 (naked single)
If bottom right cell = 2, then bottom left cell = 1 (hidden single)

Since exactly one of the two right cells must be 2, exactly one of the two left cells must be 1...
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re: classification of quartets

Postby Pat » Thu Aug 31, 2006 10:13 am

classification of quartets:

Ocean (2006.Aug.24) wrote:1. NQ/HQ (row/col): Naked quad in row or column, with hidden quad counterpart.
2. NQ/HQ (box): Naked quad in box, with hidden quad counterpart.

3. NQ/HV (row/col): Naked quad in row or column, with hidden quint counterpart.
4. NQ/HV (box): Naked quad in box, with hidden quint counterpart.

5. HQ/NV (row/col): Hidden quad in row or column, with naked quint counterpart.
6. HQ/NV (box): Hidden quad in box, with naked quint counterpart.



9 empty cells in a unit:
    A. 4+5 (quartet with quintet)
      A.1 "hidden" quartet with "naked" quintet
      A.2 "naked" quartet with "hidden" quintet
    B. 4+4+1 (2 quartets - find either of them and you're left with a "single")
8 empty cells in a unit:
    C. 4+4 (2 quartets)
( if desired, may further sub-classify by type of unit i.e. box or line )


it would be nice to find an example of each type,
perhaps Ruud would add such examples in the Benchmark Sudoku List
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re: classification of Jellyfish

Postby Pat » Thu Aug 31, 2006 10:14 am

classification of Jellyfish:

Ocean (2006.Aug.27) wrote:1. JF/5-F (Jellyfish with a 5-fish dual)

2. JF/JF (Jellyfish with a Jellyfish dual)



digit missing 9 times:
    A. 4+5 (Jellyfish with Squirmbag)
    B. 4+4+1 (2 Jellyfish - find either of them and you're left with a "single")
digit missing 8 times:
    C. 4+4 (2 Jellyfish)
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Postby ab » Mon Sep 04, 2006 12:05 am

another swordfish puzzle;
Code: Select all
 . 3 7 | . 6 . | 9 1 .
 . . . | . . . | . . .
 . . 5 | 7 . 8 | 2 . .
 ------+-------+------
 . 9 . | 2 . 6 | . . .
 5 . . | . 8 . | . . 4
 . . . | 1 . 4 | . 3 .
 ------+-------+------
 . . 6 | 8 . 9 | 4 . .
 . . . | . . . | . . .
 . 2 9 | . 1 . | 8 6 .

however this one also requires locked candidates, naked pairs, a naked triple and an x-wing.
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Postby daj95376 » Mon Sep 04, 2006 5:21 am

ab: Are you looking for variety as well? My technique ordering may not match yours, but you might find these puzzles interesting anyway.

Code: Select all
# (3x)Naked Pair, (2x)X-Wing, Swordfish
....4.7...4.7..63...16.9..47..38.9...8.....6...3.96..74..5.83...37..4.5...8.1....

# (2x)Naked Pair, (3x)Naked Triple, (3x)Locked Candidate, Swordfish
..2.4....51..9..4.8....1...17.6.......6.7.2.......9.65...5....2.4..2..79....1.8..

# (4x)Naked Pair, (3x)Naked Triple, (3x)Locked Candidate, Swordfish
..4.1..8.2..6.....5.1.2....67...9.1....762....2.5...97....9.7.5.....6..8.1..8.9..

# (6x)Naked Pair, Hidden Pair, Naked Triple, Locked Candidate, X-Wing, Swordfish
..5...3..9...2...7...3..92..564...93....7....78...645..68..2...3...4...8..4...2..

# Naked Pair, (3x)Naked Triple, (3x)Locked Candidate, Swordfish
..5..94..64.5.........1..5.4....589...2.9.3...834....2.9..8.........1.83..62..9..

# (5x)Naked Pair, X-Wing, Swordfish
..85.94..4.9.1.....2.3.....1.5....8.28..9..45.3....2.1.....6.2.....5.3.4..32.86..

# Naked Pair, (3x)Naked Triple, (2x)Locked Candidate, Swordfish
..917...2.879.2....6.......41.5....9....9....9....4.27.......5....2.876.8...412..

# (2x)Naked Pair, Naked Triple, (3x)X-Wing, (3x)Locked Candidate, Swordfish
6.....54..1..64..2.92..5...9..84..6....5.9....4..12..9...2..67.7..45..8..84.....5

# (5x)Naked Pair, (3x)Naked Triple, X-Wing, (3x)Locked Candidate, Swordfish
7...46.5..13.......64.....3...6.2.9.9.6.7.2.1.2.1.9...3.....41.......57..5.91...6

# (3x)Naked Pair, (3x)Naked Triple, (3x)Locked Candidate, Swordfish
9.3.5...8.7.1.2.9...2.......8.2.49...95.7.41...79.5.3.......3...2.5.3.8.5...8.2.4

# Naked Pair, (2x)Naked Triple, (2x)Locked Candidate, Jellyfish
...2.17..2.35.....7.9.3...5.....62...5.....6...28.....8...2.5.9.....51.8..19.7...

# Naked Pair, Naked Triple, X-Wing, (3x)Locked Candidate, Jellyfish
..6..82...2.1....41.4....38...43.79.....6.....63.82...29....8.36....9.7...78..6..

# (5x)Naked Pair, Naked Triple, (4x)Locked Candidate, Jellyfish
.4....19.....42..7.....75....24....8.6.291.5.4....82....95.....8..67.....75....8.

# (2x)Naked Pair, (2x)Naked Triple, Locked Candidate, Jellyfish
1..86.3..34.7.2.....8.39.1..3.....79..4...6..79.....4..8.67.1.....9.1.27..7.23..8

# (4x)Naked Pair, Jellyfish
2...4...55987..3...4..589...3.8..4...7.....3...5..2.9...926..4...4..96736...8...9

# (this puzzle may have already been accepted as a multiple-solution puzzle)
# Naked Pair, Hidden Pair, X-Wing, (2x)Locked Candidate, Naked Quad, Jellyfish
24.9...35...5..28.5.6.1...9....45.63.........63.89....3...2.5.4.52..8...19...3.28

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