Single Hidden Single All Singles Puzzle

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

Single Hidden Single All Singles Puzzle

Postby udosuk » Tue May 13, 2008 7:05 am

This from JSudoku:
Code: Select all
..97814..
.........
7..9.5..8
6.......9
2.84.63.5
..3...2..
9.4...5.2
.........
8.12.39.4

... requires only singles to solve. And the shortest path I found (with pencilmark) is:

HS: r2c8=9 => HS: r1c8=5 => all naked singles

There are 29 given clues, and initially no naked single and only 2 hidden singles (r2c2=8, r2c8=9).

So I wonder if a puzzle with the following properties exists:

1. Only a small amount of given clues (20-25 preferably, and <20 even better).

2. No naked single to start with.

3. Only 1 hidden single to start with.

4. After this hidden single is placed, the rest can be solved by naked singles.

Any such puzzle?:?:
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Postby tarek » Tue May 13, 2008 8:16 am

When you ALL naked singles....

Unless last digit in grid or last digit in sector, does your naked singles mean naked singles but not hidden singles.

I have a collection of high stepper single onl;y puzzles puzzles with a very narrow startup path....... Not symmetric though:(

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Postby udosuk » Tue May 13, 2008 11:12 am

tarek wrote:When you said ALL naked singles....

Unless last digit in grid or last digit in sector, does your naked singles mean naked singles but not hidden singles?

All naked singles mean you can press F12 in Simple Sudoku and get the grid solved. It doesn't matter if there are other hidden singles, subsets, fishes, chains etc as long as in each step there is at least a naked single to choose from. And it doesn't have to be a narrow path, there can be heaps of naked singles and other moves to choose from in each step.

tarek wrote:I have a collection of high stepper single only puzzles, puzzles with a very narrow startup path....... Not symmetric though:(

I'm only looking for a narrow first step (1 HS+0 NS+other moves), and symmetry is not an issue. Thanks for looking!:)
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Postby tarek » Tue May 13, 2008 12:01 pm

I haven't used simple sudoku, I hope this is what you're after though
Code: Select all
 . 6 . | . 2 5 | . . . 
 . 9 . | . . . | . . 1 
 2 . . | 1 . . | 5 4 . 
-------+-------+------
 . . . | . 1 . | . . 5 
 . 8 . | . . 6 | . . . 
 3 2 6 | . . 8 | . . . 
-------+-------+------
 . . . | . . 2 | 4 . . 
 . . . | 4 . . | 8 . . 
 . . . | 7 . . | . 3 .
37 Steps: 01010101010101010101010101010102020101020102010202010201010102030304040401
 

 . . . | 1 . . | . . 4 
 . 7 . | . 4 . | 1 . . 
 . . 2 | . . . | . 9 3 
-------+-------+------
 . . 5 | . . . | . 8 . 
 . . . | . 9 . | . . . 
 8 9 . | . 1 . | . . 6 
-------+-------+------
 . 3 6 | 7 8 . | . . . 
 . . . | 4 . . | . . . 
 7 . 8 | 6 . 5 | . . . 
37 Steps: 01010101010101010101010101020101010201020101010101010102010203010205050501


 . . . | 7 . 6 | . . . 
 2 1 . | . 3 4 | . 8 . 
 . 3 4 | . . . | . 9 . 
-------+-------+------
 8 . 7 | . . . | . 5 . 
 . . . | . . . | . . . 
 . 5 . | . 7 . | . . 2 
-------+-------+------
 . . . | . . . | 9 . . 
 . 6 . | 2 4 . | . . . 
 4 . . | . 6 8 | . . 1
38 Steps: 0101010101010101030201010101010202010201010101010101010101010101020204050501
 

 . . 5 | . . 3 | . . . 
 . . . | . 4 8 | . . 2 
 . . . | . . . | 4 . . 
-------+-------+------
 5 . 1 | . . . | . . . 
 3 . . | . 9 . | . 1 . 
 . 9 . | . . . | 6 . . 
-------+-------+------
 7 1 . | 6 . . | 2 4 . 
 . . 2 | . . . | 7 . . 
 9 . 6 | . . 1 | . 3 . 
38 Steps: 0101010101010102010101010101020101010102020101010101040101010101010204050501



This not what you're after, but this is the the longest solution path for a singles puzzle:
Code: Select all
 . . 5 | 7 . . | . . . 
 . 1 . | 9 3 . | 7 . . 
 . . 6 | . . . | . . 4 
-------+-------+------
 . . 8 | . . . | . 5 . 
 . . . | . 9 . | . . . 
 . 5 . | . 7 . | . . 2 
-------+-------+------
 . 3 . | . . . | . 4 . 
 . 8 7 | . . . | . . . 
 . 4 . | . 6 8 | 3 1 .
39 Steps: 030101010101010201010101010201020101010102010101010101010101010101020203030504
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Postby Pat » Tue May 13, 2008 12:14 pm

sorry, tarek, but in those 4 puzzles, after the initial "hidden single", the puzzle cannot be solved by "naked singles"
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Postby gsf » Tue May 13, 2008 2:39 pm

Pat wrote:sorry, tarek, but in those 4 puzzles, after the initial "hidden single", the puzzle cannot be solved by "naked singles"

found these with symmetry, symmetric minimal, but not minimal
Code: Select all
# C27.M/S2.a NFFFFFFFFFFF N1F3F3F4F2F1F1F1F10F15F9F4

. . . | 4 8 . | . . .
3 1 . | 6 9 . | 5 . .
6 . . | . . 1 | . 7 .
------+-------+------
4 . . | . . . | 7 . .
. 7 2 | . . . | . 3 5
. 5 . | . . . | . 8 2
------+-------+------
. . . | . 5 . | . . .
. . . | 9 4 . | . 6 .
2 . . | . . 3 | 1 5 .

# C27.M/S2.d NFFFFFFFFF N1F2F2F4F8F6F12F7F11F1

. . . | . . 4 | . . .
. 9 5 | . . . | 2 6 .
. 7 . | 3 . . | 5 . 1
------+-------+------
. . 8 | . . . | . . 6
. . . | . . 2 | 4 8 .
5 . . | . 6 . | . 2 9
------+-------+------
. 1 4 | . 9 . | . . .
. 5 . | . 7 8 | . . .
. . 9 | 1 . 5 | . . .

# C28.M/S2.d NFFFFFFFFFFFF N1F1F4F2F3F6F2F2F5F6F8F10F3

. . . | . . . | . 2 .
. . 8 | . . . | 3 5 6
. 4 6 | . . . | 8 . .
------+-------+------
. . . | . . 3 | 5 . .
. . . | . 9 5 | 2 1 .
. . . | 1 7 . | 9 . 4
------+-------+------
. 2 5 | 8 3 1 | . . .
1 3 . | . 6 . | . . .
. 8 . | . . 4 | . . .

my solver options
Code: Select all
-f'# %(CSM)#c#/q %#qP %#SP%:%#pg'

for udosuk's request %#qP must match the RE ^NF*$ and %#SP must match ^N1F
so the above puzzles were generated by this pipeline
Code: Select all
sudoku -gp -sg -m -qFN-G -e V -f'%#0v # %G %#qP %#SP' | grep ' NF* N1F'

now running with -sg omitted (no symmetry ok), but those will be tougher (if not impossible?) to find
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Postby udosuk » Tue May 13, 2008 2:43 pm

Yep sorry tarek your grids are not what I'm looking for.

Let's pretend you have a program which knows only 2 techniques to solve a Sudoku: the so-called "naked singles" and "hidden singles". So you have to find a puzzle that on first sight, it can't see any "naked single" and sees one and only one "hidden single". After applying this "hidden single" it will disable any further application of that technique (i.e. have "naked singles" as the one and only one trick in its arsenal). Then still it can solve the rest of the puzzle. I'm looking for such a puzzle.:idea:

Added later:

Thanks gsf! Yours match my conditions except they have too many clues (27 at least). If not symmetric would it be possible to be with fewer clues?

Also a side question: how few given clues can you make for an "all naked singles" puzzle? Is 17-given possible? (This might have been discussed already but sorry not motivated enough to dig up the old posts.)

(Typo edited)
Last edited by udosuk on Tue May 13, 2008 12:06 pm, edited 1 time in total.
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Postby Pat » Tue May 13, 2008 3:06 pm

udosuk wrote:
a side question: how few given clues can you make for an "all naked singles" puzzle?



it was once reported that the collection of 17-clue puzzles has none
    this should be re-tested as the collection grows



18 clues -- plenty

gsf (2006.Sep.24) wrote:Gordon's collection of 18-clue puzzles (22 million)
has 307 solved by "naked singles"

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Postby Pat » Tue May 13, 2008 3:13 pm

    and he posted these 66
      ( the rarest type -- they can be solved by "naked singles" and cannot be solved by "hidden singles" )
Code: Select all
1...32.8.6.97..1...........3..9..6...2..4...3..........5.....2....6......7.......
1...32.8.6.97..1...........3..9..6...2..4...5..........5.....2....6......7.......
1...32.8.6.97..1...........3..9..6...2..4...8..........5.....2....6......7.......
1...3..47.3..658...........9.72...........61....8.....4..7......6....5...........
1..3..7...52.4.............3..7..6.........45......1...4..52.8.7.....3...........
1...3..97.3..658...........9.72...........61....8.....4..7......6....5...........
.1.4..3......2..8.....7....9.4....7....15.2.....3.....7...6..2....5..1...........
1...5.3.7.5..28.............2...6.8.....7.9.....4.....9..6..4.........2....3.....
1...5.3.9.5..27.............2...6.7.....1.8.....4.....8..6..4.........2....3.....
.1..5..7....8....9.........2..6..8.....3......7.........6.71.4.8.5.4.2...........
1....5.79.5..438...........7..9...6..3..1.4...........9..2...........3.....8.....
.174...5..5..236...........23..8.......7...1.......2..4.....8.....1.....9........
1...7.......8..4........9....2.6..1..8.3......4..5....6...1..5....4..8.....9.....
1...7.......8..9........4....2.6..1..8.3......4..5....6...1..5....4..8.....9.....
.184...5..5..726...........27..3.......8...1.......3..9.....2.....1.....4........
.18.5.4...5.6...72...............81.2..3......7.......4..2....3......1..9........
.185...6..6..237...........23..4.......8...1.......4..5.....2.....1.....9........
.23.6.5...6.7...18.........18.....4......23.....4.....5..1...........2..9........
.23.6.5...6.7...18.........81.....4......23.....4.....5..8...........2..9........
2..4.1.......3.7...........4..2...6.......3..8.........37.5...2.5.6...41.........
...2..4.51...........3......54.9.6...7..18.9..........8....2.1.6...........5.....
...2..4.51...........3......54.9.6...7..18.9..........8....3.1.6...........5.....
.246...7..7..35..8...........84...2.3...9.5...........1.....3.....2.....6........
24.7........9...3..1......83.8.2..5.....146...........7..3...........1..5........
.2..56..34..1..7............65.3....1..7...........4.......2.6.7..4.....8........
.2..56..34..1..8............65.3....1..8...........4.......2.6.7..4.....8........
.2...6.453..9..1...............4..2.9.....3..8.....9...45.....6...3.....1........
..2.6..718..5...........4...1.....265..3..............3..4..5......21...4........
.3.....1....2..4.............1.3..6.4..7..5........2...6..81.3.2.....7..5........
..3.2..5....6..7..4.....8.....7..4...2.....3...........5..31.2.7.....6..8........
3...4.8...9.7...2...........275...6..6..83..4.........1.....3.....2.....5........
3...4.9...8.7...2...........275...6..6..83..4.........1.....3.....2.....5........
3...4.9...8.7...2...........275...8..6..93..4.........1.....3.....2.....5........
.......35...1........8.....6..2..4..1.....8..2.........7..3...9.4..9..2..8....1..
3..5..1.........42......8..5..1..3...4..62.............62.4..7....3..5...........
3...5.7...8.2.................8...3.7.....9........4..1...37..6.6.4...28.........
3...5.7...8.2.................8...3.7.....9........4..1...73..6.6.4...28.........
3...8..4..7....6...1..........1..7...6....5..4......8.8.2.4...3...7..1...........
.385...4...4.216...........7.....1..52..........8.....1...9...2...3...8..........
....41....2....9..63.......5......4.......2...6.......1.87...5....2..7..4...6....
4.1.5..3.2......68...3.........4.1..36.............2...8.6......7.5...........4..
.41..7.......2.3..5.....8.....1...4.3.....2............7.6.4.1.2...3..........5..
.4.2....89.....1..............6..8.....5...2.1........6...197...82.7..3..........
.4.6..1..8...2...............2.7...3....9..........4...5.4.1.7.3..5...62.........
4.....6.5...3.....9.........37.8..9.....562...1.........97...3....2.....5........
.49.5..3..3.6.27...........5..8..2..1............4....2.....8.....49.....6.......
5......1...63........4..7...2..18.....7...3.....6.....18..2...5...7..6...........
.5.2...3.....6.4..1.........3.5.8..2......6..4........6...4.1.....3...5.......7..
5..3..2.........1....9......1.....84...5.....3.........6..185..2...6.3.7.........
.5.3...8.1...7.4............832...5..6..417...........9.......1...8.....2........
.5.3...9.1...7.4............932...5..6..817...........4.......1...9.....2........
...57..2.84..1...........6....2...9.1...................7.3.1....26..5...3....8..
.......57...4........3.....3..2..4..1.....6..2.........8..5...9.6..9..2..4....3..
6...2.....3....7.....8..4...1.3.7.6.5..1...29.........2...9..........3......4....
6...3.1...8.7...2...........274...5..5..19..8.........1.....3.....2.....4........
6...3.1...9.7...2...........274...5..5..81..9.........1.....3.....2.....4........
.63..7.1.2..4..5...........4..5..2......1...78.........1.....73...2.....5........
.6.3...8.1...7.4............832...5..5..417...........9.......1...8.....2........
.6.3...8.1...7.4............832...5..5..617...........4.......1...8.....2........
.6.3...8.1...7.4............832...5..5..617...........9.......1...8.....2........
.6.3...8.1...9.4............832...5..5..617...........4.......1...8.....2........
.6.3...9.1...7.4............932...5..5..817...........4.......1...9.....2........
6....5.9..8....3...4.......1..8...5..7.4...........8.....62.4..51.......9........
6...7..4..2.3..5............5.2..3..4.......7......8..7.1.4..6....5..2...........
.7....2..4...8.......1.....5...6..8..1.3......2..........2..9.56...7....84.......
.8..7..147...95.6..........2.....5.....6..3.....1......1.4...8.5.....9...........

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Postby m_b_metcalf » Tue May 13, 2008 3:18 pm

These (25 clues) solve in SS with F11 followed by F12:


Code: Select all
   . . . . 5 3 1 . .
 . . . . . . . 3 2
 . 7 3 . 9 . 8 . .
 6 . 5 7 . . . . .
 . . . . . 2 . . .
 . . . . . 8 6 7 5
 4 . . 9 . . . . .
 . . . . . 7 9 . 3
 . . 8 . . . 5 4 .

Code: Select all
 . . . . . 2 1 . .
 . . 5 3 . . 4 . .
 . 8 . . . 7 . . .
 7 . 8 . 2 . . 1 .
 . 5 . 7 . . . . 4
 . 1 . 4 . . 6 . .
 . . . . . . . . .
 . 2 . . . 6 . 4 5
 3 . 6 . . . 7 . 2

Regards,

Mike Metcalf
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Postby m_b_metcalf » Tue May 13, 2008 4:08 pm

This one doesn't solve with F11 then F12 because there are several options and SS takes the 'wrong' one. However, there is a clear hidden single in r3c9 and if that's forced in, F12 does the rest.

Code: Select all
 . 2 . 1 . . 6 . .
 . . . . . 8 . . 1
 . . . . 7 . 4 3 .
 . . . 2 . . . . 9
 4 . . 6 . . 3 . 7
 . . 8 . . 5 . . .
 . . 9 3 . . . 1 .
 2 5 . . . . . . .
 . . . 7 . 2 . . 6  24 clues

Regards,

Mike Metcalf
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Postby udosuk » Tue May 13, 2008 4:11 pm

m_b_metcalf wrote:These (25 clues) solve in SS with F11 followed by F12:

Thanks Mike but unfortunately these 2 don't match my requirements:

The first one has 6 initial HS's and the second one 4. I only allow one initial hidden single.

Perhaps a better tool to test is JSudoku: typing "h" initially shows how many hidden singles there are, then typing "Ctrl-Shift-n" solves all naked singles recursively.:idea:

(Added later)

No luck with your 24-clue one neither: it has 6 initial HS's.:(

BTW thanks heaps to Pat for the research on "all NS" puzzles. Please keep me informed if there're any discoveries in the 17-clue database!:)
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Postby gsf » Tue May 13, 2008 5:11 pm

udosuk wrote:BTW thanks heaps to Pat for the research on "all NS" puzzles. Please keep me informed if there're any discoveries in the 17-clue database!:)

this is the only 17 that starts with hidden and finishes with naked, but it has 13 initial hidden singles
Code: Select all
# C17.m NFFFFFFFFFFFF N13F2F3F3F3F6F4F6F4F4F4F7F5

. . . | . . . | . . .
. . . | . . . | . 1 2
. . 3 | . 4 5 | . . 6
------+-------+------
. . . | . . . | . . 7
. . 4 | . . . | 6 . .
. 8 . | 1 . . | . 2 .
------+-------+------
. . . | . 3 . | 5 . .
. . . | . 6 . | . . .
. 1 . | . . . | . 8 .
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Postby gsf » Tue May 13, 2008 5:42 pm

here are a few 21 clue minimal examples
Code: Select all
# C21.m NFFFFFFFFFFFFF N1F3F3F4F2F8F5F3F2F4F4F8F10F3

1 . . | 6 . . | . 3 .
. . . | . . 2 | 7 . .
9 . . | . . 5 | . . .
------+-------+------
. 5 . | 8 . 7 | . 1 .
. . . | . . . | . 9 .
. . . | . 4 . | . . .
------+-------+------
7 . . | 1 . . | . . 9
. . 4 | 3 . . | . . .
. 2 . | . . 4 | . . 8

# C21.m NFFFFFFFFFFF N1F3F3F4F2F3F2F9F5F9F11F8

1 . . | 6 . . | . 3 .
. . . | . . 2 | 7 . .
9 . . | . . 5 | . . .
------+-------+------
. 5 . | 8 . 7 | . 1 .
. . . | . . . | . 9 .
. . . | . 4 . | . . .
------+-------+------
. . . | 1 . . | . . 9
. . 4 | 3 . . | . 5 .
. 2 . | . . 4 | . . 8

# C21.m NFFFFFFFFFFF N1F6F2F2F5F6F8F8F6F6F9F1

1 . . | 6 . . | . 3 .
. . . | . . 2 | 7 . 8
9 . . | . . 5 | . . .
------+-------+------
. 5 . | 8 . . | . 6 .
. . . | . . . | . 9 .
. . . | . . 7 | . . .
------+-------+------
. . 7 | 1 . . | . . 9
. . 4 | 3 . . | . . .
. 2 . | . . 4 | 5 . .

# C21.m NFFFFFFFFFF N1F6F3F5F7F3F5F5F3F15F7

1 . . | 6 . . | . 3 .
. . . | . . 2 | 7 . .
9 . . | . . 5 | . . .
------+-------+------
. 5 . | 8 . 7 | . 1 .
. . . | . . . | . 9 .
. . . | . . . | 8 . .
------+-------+------
. . 7 | 1 . . | . . 9
. . 4 | 3 . . | . . .
. 2 . | . . 4 | 5 . .

# C21.m NFFFFFFFFFF N1F6F3F4F7F3F5F7F4F13F7

1 . . | 6 . . | . 3 .
. . . | . . 2 | 7 . .
9 . . | . . 5 | . . .
------+-------+------
. 5 . | 8 . 7 | . 1 .
. . . | . . . | . 9 .
. . . | . . . | . . .
------+-------+------
. . 7 | 1 . . | . . 9
. . 4 | 3 . . | . 7 .
. 2 . | . . 4 | 5 . .
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Postby Jean-Christophe » Tue May 13, 2008 7:16 pm

Here is one (difficult to compete with gsf...)

Initial HS: 1 Total HS: 1 Givens: 23
1.7..3.459...1.....8......1...4.7...2.3.....9....9.......8.1..3....6.5..5......72

Worst case:
Initial HS: 1 Total HS: 29 Givens: 23
9.3.67...........12.8..9...8.7.4..........32.3.9.....67...538..............2.6..4
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