Puzzles needing lots of locked candidates

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

Re: ISS #1-13

Postby gsf » Wed May 30, 2007 8:00 am

Pat wrote:
Code: Select all
13,...1.2....3.....4...1.5.6..5.......7..2.3.8..9.......5..6.8.3...1.....8....7.4...,21,-,-

does the compilation only consider box-line types independently?
otherwise #13 does solve when both box-line types are enabled
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Postby ravel » Wed May 30, 2007 9:37 am

Mauricio wrote:This puzzle seems to use many instances of locked candidates 1 and 2
Yes, there are a lot of possible box-lines. But how would you solve it manually ?
Code: Select all
. . 2|. . .|. . 1
. . .|. . .|. . 2
. . 3|2 4 5|. 6 .
-----+-----+-----
. 3 .|. . .|. 1 4
. 5 .|. . 7|. . .
. 2 .|8 . .|. 5 .
-----+-----+-----
3 8 .|. 1 .|6 . 7
6 9 7|. . .|1 . .
2 . .|. 7 6|. 3 .
None of the boxlines give you a number directly.
But the hidden pair 35 in r12c7 leaves only r9c7 for the 4.
Or you spot the x-wing for 7 in r12c48, which together with the boxline in column 1 gives r3c2=7, r3c1=1. And then the UR 89 in r39c79. Since 8 cannot be in the rest of row 9, the 9 must be outside the rectangle, and the only place in box 9 is r7c8.

So counting boxlines for me is more of theoretical interest.
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re: #13 - ISS.D

Postby Pat » Wed May 30, 2007 11:48 am

gsf wrote:
Pat wrote:
Code: Select all
13,...1.2....3.....4...1.5.6..5.......7..2.3.8..9.......5..6.8.3...1.....8....7.4...,21,-,-


does the compilation only consider box-line types independently?
otherwise #13 does solve when both box-line types are enabled


exactly, "-,-" means that neither type on its own can solve the puzzle,
but the puzzle is on the list because using both types does solve it ( D in my May.8 post above )

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re: #14

Postby Pat » Wed May 30, 2007 1:51 pm

#14
Mauricio (2007.May.30) wrote:
      [ 22 clues ]
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 .



thanks, Mauricio!

i've run it through gsf's software
and have thus learnt that it can be solved by l\b (B3) in 2 steps.
    #13 remains the only one on the list which
    requires both types -- b\l (B2) and l\b (B3).
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Re: re: #13 - ISS.D

Postby gsf » Wed May 30, 2007 1:58 pm

Pat wrote:
gsf wrote:does the compilation only consider box-line types independently?
otherwise #13 does solve when both box-line types are enabled


exactly, "-,-" means that neither type on its own can solve the puzzle,
but the puzzle is on the list because using both types does solve it

thanks
I would suggest one field instead of 2 for lazy readers like me
and also to differentiate "requires both" and "not solvable with constraints in scope"
something like: 1:type-1-only, 2:type-2-only, e:either-types-1-or-2-not-both, b:both-types-1-2, 0:not-solvable
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ISS #1-17 summary

Postby Pat » Wed May 30, 2007 2:15 pm


    1. puzzle # ( 1-17 ) [ edited to add #15-17 ]
    2. the puzzle
    3. number of clues

      steps reported by gsf's software --
    4. steps as ISS.1 ( or "-" )
    5. steps as ISS.2 ( or "-" )
    6. steps as ISS
    note: in all examples so far, min(d,e) = f
    -- still waiting for an example of min(d,e) > f

Code: Select all

01,97..483163681.7.4.14..367.82193758648364192577548621395.76.34814837.16..6.1.84.73,65,1,-,1
02,74.3.9.51.2.....8.5...2...32..6.3..7.........1..2.5..66...3...2.3.....7.95.1.7.38,30,2,-,2
03,..4......9..86.3.......91..4...5..76.5.9.4.1.32..8...9..92.......6.47..8......4..,26,1,-,1
04,91..3..284....7..3...8.5....43...8..6.......5..9...47....2.9...1..3....483..4..69,28,2,1,1
05,.6...491...4......3..5.8.......4...35.......72...9.......7.2..5......8...138...6.,22,1,-,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,-,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,-,1
08,...1.9.....1...3...2.....5.3...7...44...5...85...2...3.6.....2...7...6.....5.3...,21,3,2,2
09,..6....8.43..1..7....2....5....9.1...2.8.7.4...7.3....2....1....9..8..34.6....5..,24,-,1,1
10,...916.....3...1...4.....9.1...8...75..3.9..16...2...5.9.....4...8...2.....458...,24,-,2,2
11,...6.9.....1...7...2.....9.8...5...77...4...64...2...8.3.....2...5...3.....4.8...,21,-,5,5
12,..1....2.3.4....5.....63......5...1...2...6...7...8......31.....3....8.5.9....7..,20,4,-,4
13,...1.2....3.....4...1.5.6..5.......7..2.3.8..9.......5..6.8.3...1.....8....7.4...,21,-,-,4
14,........1........2..3.45.6........14.5...7....2.8...5..8..1...769.......2...76.3.,22,-,2,2
15,................12..3.45......6....7.71....8.9...28.....98.4.5..58...1..16...7.9.,24,-,-,2
16,............456.....17.92....2.1.3...5.....9.7.......4..3.8.1...4.....6.5.......9,21,-,4,4
17,5..3.6.....9.1.4.....5...7.37....6..8.......9..1....87.6...8.....8.4.1.....7.9..3,24,-,-,5

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re(2): #14

Postby Pat » Thu May 31, 2007 4:16 pm

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

Yes, there are a lot of possible box-lines. But how would you solve it manually ?

None of the boxlines give you a number directly.
But the hidden pair 35 in r12c7 leaves only r9c7 for the 4.
Or you spot the x-wing for 7 in r12c48, which together with the boxline in column 1 gives r3c2=7, r3c1=1. And then the UR 89 in r39c79. Since 8 cannot be in the rest of row 9, the 9 must be outside the rectangle, and the only place in box 9 is r7c8.

So counting boxlines for me is more of theoretical interest.


i solved #14 (on paper) with 5 line-to-box exclusions

this does include situations where i used 2 of them together to solve a cell

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Postby Mauricio » Fri Jun 01, 2007 12:31 am

A new one
Code: Select all
. . .|. . .|. . .
. . .|. . .|. 1 2
. . 3|. 4 5|. . .
-----+-----+-----
. . .|6 . .|. . 7
. 7 1|. . .|. 8 .
9 . .|. 2 8|. . .
-----+-----+-----
. . 9|8 . 4|. 5 .
. 5 8|. . .|1 . .
1 6 .|. . 7|. 9 .
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Postby daj95376 » Fri Jun 01, 2007 5:59 am

I don't recall gsf's use of steps, but here's some maximum possible counts.

Code: Select all
a. Puzzle #
b. Max box-to-line when ISS.1 applied first \ max line-to-box when ISS.2 applied second
c. Max line-to-box when ISS.2 applied first \ max box-to-line when ISS.1 applied second

Group counts for a technique are separated by (+).

#   ISS.1  \ISS.2    ISS.2     \ISS.1
01 ,2      \0       ,0         \2
02 ,1+1    \0       ,0         \1+1
03 ,5      \0       ,2+1       \3
04 ,4+1    \0       ,4         \0
05 ,6      \0       ,6         \2
06 ,5      \0       ,3         \2
07 ,7      \0       ,4         \3
08 ,10+1+1 \0       ,8+2       \0
09 ,2      \1       ,3         \0
10 ,8      \3       ,8+2       \0
11 ,12     \2+2+1+1 ,12+2+2+1+1\0
12 ,6+1+2+1\0       ,6+2+2     \1
13 ,5+4+1  \2       ,5+2+2+1   \3
14 ,9+1+1  \2       ,9+3       \0
15 ,4      \4       ,2+1+3     \2

Code: Select all
Grouping for puzzle #15 with ISS.2\ISS.1 order

 r7  b9  -  6     Locked Candidate 2   concurrent
   c3b1  -  7     Locked Candidate 2        "

 r3  b3  -  7     Locked Candidate 2

 r8  b8  -  2     Locked Candidate 1   concurrent
   c5b5  -  9     Locked Candidate 1        "

   c9b9  -  3     Locked Candidate 2   concurrent
   c9b9  -  4     Locked Candidate 2        "
   c8b3  -  6     Locked Candidate 2        "
Last edited by daj95376 on Mon Jun 04, 2007 4:53 pm, edited 1 time in total.
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re: #15

Postby Pat » Fri Jun 01, 2007 7:32 am

#15
Mauricio (2007.Jun.1) wrote:
      [ 24 clues ]
Code: Select all
 . . . | . . . | . . .
 . . . | . . . | . 1 2
 . . 3 | . 4 5 | . . .
-------+-------+------
 . . . | 6 . . | . . 7
 . 7 1 | . . . | . 8 .
 9 . . | . 2 8 | . . .
-------+-------+------
 . . 9 | 8 . 4 | . 5 .
 . 5 8 | . . . | 1 . .
 1 6 . | . . 7 | . 9 .



thanks, Mauricio!!

i've run it through gsf's software
and have thus learnt that it can be solved in 2 steps.

so i went ahead and solved it --
turns out i needed 3 box-line interactions (in 2 steps).
    like #13,
    this puzzle requires both types -- b\l (B2) and l\b (B3).
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re: steps

Postby Pat » Mon Jun 04, 2007 7:52 am

daj95376 wrote:I don't recall gsf's use of steps


in an earlier topic, i had tried to define steps --
  • solve by "singles" as far as possible (not using box-line interaction at all)
  • when stuck, use all box-line interactions available at that point;
    then revert to using only "singles" until stuck again
( even that does not really get me what i'd like to know, which is:
how many box-line interactions were actually needed for solving the puzzle.
)


i got the steps in 3 passes through gsf's software --
    sudoku -B -q{NF}B2-G -f%(clues)x,%(valid*I2)x < puzzles.TXT
    sudoku -B -q{NF}B3-G -f%(clues)x,%(valid*I2)x < puzzles.TXT
    sudoku -B -q{NF}B-G -f%(clues)x,%(valid*I2)x < puzzles.TXT
-- the 3 only differ in the red parameter.
( then changed "0" to "-". )

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Postby daj95376 » Mon Jun 04, 2007 4:30 pm

Aaaaah! In that case, my concurrent all happen at one step. Unfortunately, it doesn't answer your required criteria. What an interesting search tree puzzle #11 must create -- starting with 12 initial box-line choices!

[Correction: changed 24 to 12]
Last edited by daj95376 on Tue Jun 05, 2007 8:05 am, edited 1 time in total.
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re: #11

Postby Pat » Tue Jun 05, 2007 11:00 am

daj95376 wrote:my concurrent all happen at one step.
Unfortunately, it doesn't answer your required criteria.

What an interesting search tree puzzle #11 must create -- starting with 24 initial box-line choices!

      re: #11

      solving on paper,
      i don't actually know how many box-line interactions are available.

      i solved it with a total of 15
      -- no idea how many are required.
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Postby daj95376 » Tue Jun 05, 2007 12:12 pm

Correction to my above statement. There are only 12 initial choices. There is a one-to-one correspondence between the first 12 Locked Candidate 1s and the first 12 Locked Candidate 2s. After that, only Locked Candidate 2 choices exist. Interesting!!!
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Re: re(2): #7

Postby ronk » Sun Nov 04, 2007 1:53 pm

gsf wrote:first determine the cyclic permutation from the "minimal" puzzle (isomorphic to the original)
Code: Select all
g -p ...6..3.7...12.6.5.........2.7.4.9.......3.1.5.4...........9.4.6.5......8.2.7....

which produces
Code: Select all
r(149)(267)(358)c(168259347)

Does that mean r1 is replaced by r4, etc. ... or is r4 replaced by r1, etc.:?: Given that mathematical assignment is almost unversally expressed ... assign right-side-value to left-side-variable, I would hope it's ...

tmp = r1; r1 = r4; r4 = r9; r9 = tmp;

... not that it makes any difference if your program is the only one to "read" the output.:)
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