Puzzles needing lots of locked candidates

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

Postby ravel » Sat Apr 28, 2007 3:31 pm

gsf wrote:so, e.g., anyone who prefers hidden pair before box-line can use
Code: Select all
-qT1H1H2B...
to analyze puzzles with my solver

what this really means is that problem statements like "how many x constraint (method/technique) steps"
must be qualified by a constraint order
I agree. What is different in SE is, that it distinguishs between hidden pairs/box lines and direct hidden pairs/box lines, which directly give you a number (not only eliminations) and therefore will be easier to use, when working without full pencilmarks.
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Postby gsf » Sat Apr 28, 2007 3:36 pm

ravel wrote:I agree. What is different in SE is, that it distinguishs between hidden pairs/box lines and direct hidden pairs/box lines, which directly give you a number (not only eliminations) and therefore will be easier to use, when working without full pencilmarks.

thanks for clarifying the difference
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Postby 999_Springs » Sat Apr 28, 2007 7:19 pm

The solver I use to solve my puzzles is not "my" solver but Sudoku Assistant/Solver. I pressed the "Solve" button and count the locked candidate steps and get 17. It takes each cell in turn starting from r1c1 and finds the locked candidates type 1 which eliminate candidate(s) from the cell. That is probably why it finds so many.

(The solver doesn't do locked candidates type 2. It finds those as Medusa strong chains. I don't know why.)

(50th post!!!)
Hidden Text: Show
Once upon a time I was a teenager who was active on here 2007-2011
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re(3): #7

Postby Pat » Sun Apr 29, 2007 7:29 am

gsf wrote:are you sorry you asked about someone's solver?


it is not every day that i visit the forum,
can't even guarantee once a week.
so it's nice to post a provocation
and read all the responses when i return.
    thus i'm not at all sorry i asked about the software,
    actually very happy with all the comments.
of course my result for #7 wasn't the best,
i'm not a computer and i do sometimes miss a "single"!
    i am stubborn, though, and did eventually solve #7 with just 4.
    then i went and read rep'nA's comment,
    and discovered that my solution-path differs ( 4 box-to-line exclusions all affecting c5 ) --
    i.e., the puzzle has (at least) 2 different solution-paths using 4 box-to-line exclusions.
        edit: since rep'nA's posts have now vanished,
        here's the missing post --

        rep'nA (2007.Apr.27 at 11:23) wrote:

        The best I could do was 4 LC steps ( At the start use LC 3 times on row 5, candidates 1,3,4. Then place all available singles. An LC in box 5 for 9 then leaves only singles. )
and thanks to gsf, we know there is probably no solution-path with fewer than 4.
( there seems to be no software to search the tree of solution-paths. )


999_Springs wrote:The solver I use to solve my puzzles is not "my" solver but Sudoku Assistant/Solver.
I pressed the "Solve" button and count the locked candidate steps and get 17.

The solver doesn't do locked candidates type 2.
It finds those as Medusa strong chains.
I don't know why.

i haven't tried Bob Hanson's software,
however, from his explanation it appears that he does use both types of "Locked Candidates"
( although his numbering of the 2 types is the reverse of angusj's ).

~ Pat
Last edited by Pat on Fri Jun 01, 2007 4:15 am, edited 1 time in total.
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#8

Postby Pat » Wed May 02, 2007 8:22 am

and the new challenge --


#8
Nemo (2007.Apr.21) wrote:
      [ 21 clues ]
Code: Select all
 . . . | 1 . 9 | . . .
 . . 1 | . . . | 3 . .
 . 2 . | . . . | . 5 .
-------+-------+------
 3 . . | . 7 . | . . 4
 4 . . | . 5 . | . . 8
 5 . . | . 2 . | . . 3
-------+-------+------
 . 6 . | . . . | . 2 .
 . . 7 | . . . | 6 . .
 . . . | 5 . 3 | . . .


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Postby ravel » Wed May 02, 2007 10:27 am

Hidden singles bring you here:
Code: Select all
 +-------+-------+-------+
 | . 3 5 | 1 . 9 | . . 2 |
 | . . 1 | 2 . 5 | 3 . . |
 | . 2 . | . 3 . | . 5 . |
 +-------+-------+-------+
 | 3 . 2 | . 7 . | 5 . 4 |
 | 4 . . | 3 5 . | 2 . 8 |
 | 5 . . | . 2 . | . . 3 |
 +-------+-------+-------+
 | x 6 3 | . x . | . 2 5 |
 | x 5 7 | . x 2 | 6 3 . |
 | 2 . . | 5 6 3 | . . . |
 +-------+-------+-------+
Maybe the easiest is to find is the 4 in r7c7, because the 4 has to be in r9c23.
And the x-wing for 1 is easy to spot in columns 1 and 5. It leaves a naked single 9 in r8c9. Then singles to the end.
No (more) box-lines, no pairs, no pencilmarks ...
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Postby re'born » Wed May 02, 2007 7:10 pm

ravel wrote:Hidden singles bring you here:
Code: Select all
 +-------+-------+-------+
 | . 3 5 | 1 . 9 | . . 2 |
 | . . 1 | 2 . 5 | 3 . . |
 | . 2 . | . 3 . | . 5 . |
 +-------+-------+-------+
 | 3 . 2 | . 7 . | 5 . 4 |
 | 4 . . | 3 5 . | 2 . 8 |
 | 5 . . | . 2 . | . . 3 |
 +-------+-------+-------+
 | x 6 3 | . x . | . 2 5 |
 | x 5 7 | . x 2 | 6 3 . |
 | 2 . . | 5 6 3 | . . . |
 +-------+-------+-------+
Maybe the easiest is to find is the 4 in r7c7, because the 4 has to be in r9c23.
And the x-wing for 1 is easy to spot in columns 1 and 5. It leaves a naked single 9 in r8c9. Then singles to the end.
No (more) box-lines, no pairs, no pencilmarks ...


Actually, once singles are done, your x-wing for 1 solves the puzzle (singles) immediately.
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Infra-Sub-Superior

Postby Pat » Tue May 08, 2007 3:31 pm

999_Springs wrote:There are puzzles which cannot be solved with singles only,
but can be solved with singles and locked candidates type 1.


this class of puzzles needs a name — i call it: Infra-Sub-Superior 1
    the class of puzzles is defined as:
    those puzzles which can be solved by [ 1 ] + [ 2 ]
    but cannot be solved by [ 1 ] alone
ISS.1 wrote:
[ 1 ]
    "singles"
[ 2 ]
    box-to-line exclusions ("locked candidates type 1") ("pointing")


similarly we can define ISS.2

ISS.2 wrote:
[ 1 ]
    "singles"
[ 2 ]
    line-to-box exclusions ("locked candidates type 2") ("claiming")


and a broader class ISS

ISS wrote:
[ 1 ]
    "singles"
[ 2 ]
    box-to-line exclusions ("locked candidates type 1") ("pointing")
    line-to-box exclusions ("locked candidates type 2") ("claiming")


ISS is the union of 4 mutually-exclusive sets —
    edited 2007.May.10 to correctly classify the 13 examples

    A. ISS.1 ISS.2 (the intersection — puzzles which can be solved either way, e.g. puzzles #4,8 above)

    B. ISS.1 \ ISS.2 (e.g. puzzles #1–3,5–7 above, and Ocean's puzzle #12 below)
    C. ISS.2 \ ISS.1 (e.g. puzzles #9–11 below)

    D. ISS \ (ISS.1 union ISS.2) (e.g. Ocean's puzzle #13 below)


#9
Sudoku-San (2007.May.7) wrote:
      [ level 2: ] pernicious

      [ 24 clues ]
Code: Select all
 . . 6 | . . . | . 8 .
 4 3 . | . 1 . | . 7 .
 . . . | 2 . . | . . 5
-------+-------+------
 . . . | . 9 . | 1 . .
 . 2 . | 8 . 7 | . 4 .
 . . 7 | . 3 . | . . .
-------+-------+------
 2 . . | . . 1 | . . .
 . 9 . | . 8 . | . 3 4
 . 6 . | . . . | 5 . .




#10
Red Ed (2006.Mar.27) wrote:
Gakken Mook wrote:
      [ 24 clues ]
Code: Select all
 . . . | 9 1 6 | . . .
 . . 3 | . . . | 1 . .
 . 4 . | . . . | . 9 .
-------+-------+------
 1 . . | . 8 . | . . 7
 5 . . | 3 . 9 | . . 1
 6 . . | . 2 . | . . 5
-------+-------+------
 . 9 . | . . . | . 4 .
 . . 8 | . . . | 2 . .
 . . . | 4 5 8 | . . .



#11
Pat (2007.May.2) wrote:
Deano (2007.Apr.20) wrote:
      [ 21 clues ]
Code: Select all
 . . . | 6 . 9 | . . .
 . . 1 | . . . | 7 . .
 . 2 . | . . . | . 9 .
-------+-------+------
 8 . . | . 5 . | . . 7
 7 . . | . 4 . | . . 6
 4 . . | . 2 . | . . 8
-------+-------+------
 . 3 . | . . . | . 2 .
 . . 5 | . . . | 3 . .
 . . . | 4 . 8 | . . .


Last edited by Pat on Thu May 10, 2007 8:35 am, edited 1 time in total.
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Postby Ocean » Tue May 08, 2007 11:44 pm

Did a search for LCs...
Code: Select all
# Locked candidates 1 "needed" at four different stages.
# (Simple Sudoku applies them 9 times, but not sure if all are necessary)
#
 . . 1 | . . . | . 2 .
 3 . 4 | . . . | . 5 .
 . . . | . 6 3 | . . .
-------+-------+------
 . . . | 5 . . | . 1 .
 . . 2 | . . . | 6 . .
 . 7 . | . . 8 | . . .
-------+-------+------
 . . . | 3 1 . | . . .
 . 3 . | . . . | 8 . 5
 . 9 . | . . . | 7 . .
Code: Select all
#
# Another one with more symmetry.
# Both type 1 and 2.
#
 . . . | 1 . 2 | . . .
 . 3 . | . . . | . 4 .
 . . 1 | . 5 . | 6 . .
-------+-------+------
 5 . . | . . . | . . 7
 . . 2 | . 3 . | 8 . .
 9 . . | . . . | . . 5
-------+-------+------
 . . 6 | . 8 . | 3 . .
 . 1 . | . . . | . 8 .
 . . . | 7 . 4 | . . .
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Postby re'born » Wed May 09, 2007 9:09 am

Ocean wrote:Did a search for LCs...
Code: Select all
# Locked candidates 1 "needed" at four different stages.
# (Simple Sudoku applies them 9 times, but not sure if all are necessary)
#
 . . 1 | . . . | . 2 .
 3 . 4 | . . . | . 5 .
 . . . | . 6 3 | . . .
-------+-------+------
 . . . | 5 . . | . 1 .
 . . 2 | . . . | 6 . .
 . 7 . | . . 8 | . . .
-------+-------+------
 . . . | 3 1 . | . . .
 . 3 . | . . . | 8 . 5
 . 9 . | . . . | 7 . .
[code]


I can do it with 5 LC's (I'm sorry, but I don't differentiate between the different types of LC's).

Singles, Box 5(2), Row 7(2), Single, Row 7(4), Singles, Column 3(6), Singles, Row 4(4), Singles.
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Postby gsf » Wed May 09, 2007 12:40 pm

Ocean wrote:Did a search for LCs...
Code: Select all
# Locked candidates 1 "needed" at four different stages.
# (Simple Sudoku applies them 9 times, but not sure if all are necessary)
#
 . . 1 | . . . | . 2 .
 3 . 4 | . . . | . 5 .
 . . . | . 6 3 | . . .
-------+-------+------
 . . . | 5 . . | . 1 .
 . . 2 | . . . | 6 . .
 . 7 . | . . 8 | . . .
-------+-------+------
 . . . | 3 1 . | . . .
 . 3 . | . . . | 8 . 5
 . 9 . | . . . | 7 . .

4 separate times if moves are batched (-B in my solver): collect all box-line at one ply and apply as batch
9 separate times if each move is applied when found and method application order rewound (-S in my solver)

background: batching is the consensus method of choice for step counting on this forum
(re: the inferior, superior, ulterior threads)
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Postby Ocean » Wed May 09, 2007 6:47 pm

rep'nA wrote:I can do it with 5 LC's (I'm sorry, but I don't differentiate between the different types of LC's).

Singles, Box 5(2), Row 7(2), Single, Row 7(4), Singles, Column 3(6), Singles, Row 4(4), Singles.


gsf wrote:4 separate times if moves are batched (-B in my solver): collect all box-line at one ply and apply as batch
9 separate times if each move is applied when found and method application order rewound (-S in my solver)

background: batching is the consensus method of choice for step counting on this forum
(re: the inferior, superior, ulterior threads)


Thanks to rep'nA and gsf for analyzing this puzzle. Confirming the expected number of 4 batches (this number should be rather stable/objective); if the number 9 is sum of all available LCs at each four batches, this should also be the same for all sudoku solvers, and for all isomorphic variations of the puzzle. The number 5 as minimum different LCs needed, is also an objective measure, provided all available ones are tried (one after another) as the first, second, third, fourth, (fifth).

[My own analyzer only reports the number of batches (and when they are applied).]
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Postby Pat » Thu May 10, 2007 10:35 am

#12
above, Ocean (2007.May.8) wrote:
      Locked candidates 1 "needed" at four different stages.
      (Simple Sudoku applies them 9 times, but not sure if all are necessary)

      [ 20 clues ]
Code: Select all
 . . 1 | . . . | . 2 .
 3 . 4 | . . . | . 5 .
 . . . | . 6 3 | . . .
-------+-------+------
 . . . | 5 . . | . 1 .
 . . 2 | . . . | 6 . .
 . 7 . | . . 8 | . . .
-------+-------+------
 . . . | 3 1 . | . . .
 . 3 . | . . . | 8 . 5
 . 9 . | . . . | 7 . .


    thanks!
    i confirm i've solved it by 4 box-to-line exclusions. ( b9 2: in r7 ; b7 4: in r7 ; b7 6: in c3 ; b4 4: in r4 )
#13
above, Ocean (2007.May.8) wrote:
      Another one with more symmetry.
      Both type 1 and 2.

      [ 21 clues ]
Code: Select all
 . . . | 1 . 2 | . . .
 . 3 . | . . . | . 4 .
 . . 1 | . 5 . | 6 . .
-------+-------+------
 5 . . | . . . | . . 7
 . . 2 | . 3 . | 8 . .
 9 . . | . . . | . . 5
-------+-------+------
 . . 6 | . 8 . | 3 . .
 . 1 . | . . . | . 8 .
 . . . | 7 . 4 | . . .


    nice!
    i've solved it by 6 box-line interactions. (yes, both types needed.)
    of course i can't tell if that's the minimum needed.
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ISS #1-13

Postby Pat » Thu May 10, 2007 12:50 pm


    1. puzzle # ( 1-13 )
    2. the puzzle
    3. number of clues
    4. is ISS.1 ( "1" or "-" )
    5. is ISS.2 ( "2" or "-" )

      i have now edited my earlier post to correctly classify the 13 examples
Code: Select all

01,97..483163681.7.4.14..367.82193758648364192577548621395.76.34814837.16..6.1.84.73,65,1,-
02,74.3.9.51.2.....8.5...2...32..6.3..7.........1..2.5..66...3...2.3.....7.95.1.7.38,30,1,-
03,..4......9..86.3.......91..4...5..76.5.9.4.1.32..8...9..92.......6.47..8......4..,26,1,-
04,91..3..284....7..3...8.5....43...8..6.......5..9...47....2.9...1..3....483..4..69,28,1,2
05,.6...491...4......3..5.8.......4...35.......72...9.......7.2..5......8...138...6.,22,1,-
06,7..1.5..3.9.....5....3.8...4.3...7.2.........8.2...9.4...7.6....3.....6.1..4.9...,23,1,-
07,...2.8..7.4.....9....5.6...3.7...6...........6.5...1.2...4.5....1.....3.9..7.2..4,22,1,-
08,...1.9.....1...3...2.....5.3...7...44...5...85...2...3.6.....2...7...6.....5.3...,21,1,2
09,..6....8.43..1..7....2....5....9.1...2.8.7.4...7.3....2....1....9..8..34.6....5..,24,-,2
10,...916.....3...1...4.....9.1...8...75..3.9..16...2...5.9.....4...8...2.....458...,24,-,2
11,...6.9.....1...7...2.....9.8...5...77...4...64...2...8.3.....2...5...3.....4.8...,21,-,2
12,..1....2.3.4....5.....63......5...1...2...6...7...8......31.....3....8.5.9....7..,20,1,-
13,...1.2....3.....4...1.5.6..5.......7..2.3.8..9.......5..6.8.3...1.....8....7.4...,21,-,-

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Postby Mauricio » Wed May 30, 2007 7:33 am

This puzzle seems to use many instances of locked candidates 1 and 2:

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