The New Sudoku Players' Forum

[udosuk]

Thanks ronk! I suppose if we expand to naked singles + hidden singles + locked candidates + naked pairs + 1-level T&E then all puzzles could be solved...

[gsf]

Thanks ronk! I suppose if we expand to naked singles + hidden singles + locked candidates + naked pairs + 1-level T&E then all puzzles could be solved...

interesting, I just posted info related to this here
the question can be rephrased (in my old terminology): are there any
(naked single + hidden single)-2-constrained (FN-2-constrained) puzzles? yes
ocean posted 49 in the hardest sudoku thread

are there any FN-3-constrained puzzles? my conjecture says no

are there any (up to and including multi-coloring)-2-constrained puzzles? yes
this is the only known one, posted by ocean in the hardest sudoku thread

Code: Select all

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


with these backdoors of size 2 (pairs of cells)

Code: Select all

[11]4*{[36]8[46]2[56]3[57]2[87]1}
[12]9*{[36]8}
[13]8*{[29]1}
[14]5*{[29]1[46]2[56]3[79]8[95]2}
[15]7*{[36]8[54]6[69]6}
[21]7*{[36]8[87]1}
[24]9*{[69]6}
[26]6*{[99]9}
[27]8*{[44]4[56]3[62]4[64]7[84]8[92]8}
[38]9*{[64]7[69]6[87]1}
[48]1*{[64]7[69]6}
[65]1*{[69]6}


[udosuk]

No, but gsf, we're talking about different things here... I just don't want to repeat the saga between bennys and several members in this thread ...

What you're talking about (constrained puzzles, backdoors etc) only concerns if there is a cell/group of cells that when fixed on the correct value(s), the rest of the puzzle could be solved using a certain technique set...

The puzzles I (and bennys) talked about we could apply an extra step: if we find a candidate leading to a contradiction (under a certain technique set), we could eliminate it, and start over in a new puzzle state. This is what I meant by 1-level T&E...

Of course the puzzle you showed could still be unsolvable with 1-level T&E under the technique set singles+pairs+locked candidates... We need a program to verify that...

I wonder if we use the whole SSTS (up to multi-colors & xy-wing) would the puzzle be still unsolvable using 1-level T&E...

[gsf]

The puzzles I (and bennys) talked about we could apply an extra step: if we find a candidate leading to a contradiction (under a certain technique set), we could eliminate it, and start over in a new puzzle state. This is what I meant by 1-level T&E...

Of course the puzzle you showed could still be unsolvable with 1-level T&E under the technique set singles+pairs+locked candidates... We need a program to verify that...

I wonder if we use the whole SSTS (up to multi-colors & xy-wing) would the puzzle be still unsolvable using 1-level T&E...

aha
I think this thread is what you're after

in particular, my solver with these options on ocean's 55 hardest lists 27
puzzles unsolvable when the base and proposition (T&E) constraints are restricted
to naked/hidden singles

Code: Select all

-q'FNP(FN)-G' -e !V -F%a

add box/line to the proposition constraints and there's only 4 unsolvable
(this cracks the ocean puzzle I posted above)

Code: Select all

-q'FNP(FNB)-G' -e !V -F%a

add naked pairs and there's only 1

Code: Select all

-q'FNP(FNBT2)-G' -e !V -F%a

finally, adding in hidden pairs cracks the last one

Code: Select all

-q'FNP(FNBT2H2)-G' -e !V -F%a

strengthening the base constraints does not have much effect on ocean's hardest

[udosuk]

Thank you! That's exactly what I (& bennys) were looking for... (If I haven't mistaken...)

Could you post the puzzle where you need "hidden pairs on propositions" to solve?

Or better yet, post all 4 puzzles where "singles+locked candidates on propositions" couldn't solve...

Just out of curiosity, do these puzzles all have a backdoor-size of 2 themselves?

Thanks again!


PS: Checked out your thread, I think this is the (unique) one you said needed "propositional hidden pairs" to solve (3rd puzzle of ocean-02)...

Code: Select all

1.......2
.3..4..5.
..6...7..
...1.3...
.8..7..4.
...4.6...
..2...6..
.5..3..8.
9.......1

It seems there are another 6 puzzles which are exclusively solvable to "propositional singles+naked pairs+locked candidates" (labelled V(6) by you)...

[gsf]

Thank you! That's exactly what I (& bennys) were looking for... (If I haven't mistaken...)

great

Just out of curiosity, do these puzzles all have a backdoor-size of 2 themselves?

(up to and including multi-coloring) backdoor size is 1 for all ocean's hardest but
this one with size 2:

Code: Select all

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


[udosuk]

Not necessary techniques "up to and including multi-coloring"...

How about "up to and including hidden pairs" or "up to and including naked pairs"?

Code: Select all

ocean-02  3 7  2 99729
ocean-01  1 6 10 99706
ocean-01  2 6  9 99699
ocean-01  8 6  9 99697
ocean-02 12 6  6 99667
ocean-01  3 6  5 99660
ocean-01  5 6  4 99650

in particular, my solver with these options on ocean's 55 hardest lists 27
puzzles unsolvable when the base and proposition (T&E) constraints are restricted
to naked/hidden singles

Code: Select all

-q'FNP(FN)-G' -e !V -F%a

add box/line to the proposition constraints and there's only 4 unsolvable
(this cracks the ocean puzzle I posted above)

Code: Select all

-q'FNP(FNB)-G' -e !V -F%a

add naked pairs and there's only 1

Code: Select all

-q'FNP(FNBT2)-G' -e !V -F%a

finally, adding in hidden pairs cracks the last one

Code: Select all

-q'FNP(FNBT2H2)-G' -e !V -F%a

strengthening the base constraints does not have much effect on ocean's hardest

So which is true?

[gsf]

Code: Select all

ocean-02  3 7  2 99729
ocean-01  1 6 10 99706
ocean-01  2 6  9 99699
ocean-01  8 6  9 99697
ocean-02 12 6  6 99667
ocean-01  3 6  5 99660
ocean-01  5 6  4 99650

in particular, my solver with these options on ocean's 55 hardest lists 27
puzzles unsolvable when the base and proposition (T&E) constraints are restricted
to naked/hidden singles

Code: Select all

-q'FNP(FN)-G' -e !V -F%a

add box/line to the proposition constraints and there's only 4 unsolvable
(this cracks the ocean puzzle I posted above)

Code: Select all

-q'FNP(FNB)-G' -e !V -F%a

add naked pairs and there's only 1

Code: Select all

-q'FNP(FNBT2)-G' -e !V -F%a

finally, adding in hidden pairs cracks the last one

Code: Select all

-q'FNP(FNBT2H2)-G' -e !V -F%a

strengthening the base constraints does not have much effect on ocean's hardest

So which is true?

both

the former was done with batching on (-B) -- this identifies all moves at a
position and then applies them in a batch, better for puzzle comparison
(e.g., via ratings), not so for finding shorter solution(s)

the latter were done without -B -- moves applied as they are found, which
usually results in fewer and easier moves

thanks for catching the difference
I was concerned that posted data was bad
instead it was "just" insufficiently labelled

[gsf]

No, but gsf, we're talking about different things here... I just don't want to repeat the saga between bennys and several members in this thread ...

ha
I just reread the entire thread and saw a bunch of gsf posts
6 months to sink in, hmm

the reread did confirm that the recent proposition formulation is almost
equivalent to a forward check search -- almost because forward
checking includes some learning outside of the proposition candidates
which can lead to more eliminations

the learning is: pick a proposition cell A and for all of the candidates that
don't lead to a contradiction inclusive-or the candidate values for all of the
other candidate cells and use the inclusive-or'd values as the new
candidate values

so the forward checking equivalents for the proposition technique posted
above on ocean's hardest are:

29 solved (26 unsolved vs 27 proposition)

Code: Select all

-q FN -e 'depth==1' -f- -F%a

51 solved (4 unsolved vs 4 proposition)

Code: Select all

-q FNB -e 'depth==1' -f- -F%a

54 solved (1 unsolved vs 1 proposition)

Code: Select all

-q FNBT2 -e 'depth==1' -f- -F%a

55 solved (0 unsolved vs 0 proposition)

Code: Select all

-q FNBT2H2 -e 'depth==1' -f- -F%a

so the forward check learning only paid when the proposition techniques
were limited to naked/hidden singles

[udosuk]

both

the former was done with batching on (-B) -- this identifies all moves at a
position and then applies them in a batch, better for puzzle comparison
(e.g., via ratings), not so for finding shorter solution(s)

the latter were done without -B -- moves applied as they are found, which
usually results in fewer and easier moves

thanks for catching the difference
I was concerned that posted data was bad
instead it was "just" insufficiently labelled

Fair enough...

For this puzzle (propositional hidden pairs):

Code: Select all

1.......2
.3..4..5.
..6...7..
...1.3...
.8..7..4.
...4.6...
..2...6..
.5..3..8.
9.......1

Is it possible to show us a solving log of how the 1-level T&E with hidden pairs is performed? Or, using naked singles+hidden singles, is it possible to show us a list of backdoor pairs? Thanks!

[gsf]

For this puzzle (propositional hidden pairs):

Code: Select all

1.......2
.3..4..5.
..6...7..
...1.3...
.8..7..4.
...4.6...
..2...6..
.5..3..8.
9.......1

Is it possible to show us a solving log of how the 1-level T&E with hidden pairs is performed? Or, using naked singles+hidden singles, is it possible to show us a list of backdoor pairs? Thanks!

unlike car commercials, you can try this at home

Code: Select all

-v2 -q"FNP(FNBT2H2)V(7)" -f%Q puzzle.dat

if you like r1c2 cell notation then throw in

Code: Select all

-Pr%rc%c -Le= -Ln"<>"

[2] P [98]?2
B4 [15][35][75][95]^8
H2 [71][93]={38}
P [98]?3
N2 [71]=3 [93]=8
B6 [15][35][75]^8 [47][57][67]^2
H2 [17][39]={34}
B5 [21][24][26][34][36]^8
N2 [31]=8 [13]=5
B3 [42][72][92]^4
B3 [86][87][89]^4
T5 [14][12][16]^{69} [79][87]^{79}
F1 [87]=2
P [98]?7
B7 [15][35][75][95]^8 [47][57][67]^2
H2 [71][93]={38}
P [92]?4
N6 [42][18][59][24][81][95]=6
B3 [15][35][75]^8
T2 [71][93]^{17}
H2 [31][13]={45}
B3 [26][27][29]^8
F1 [29]=9
F2 [27]=1 [38]=3
N8 [14]=3 [53][68][86][72][35]=1 [76]=4 [83]=7
F3 [23]=8 [89]=4 [93]=3
F2 [39][71]=8
F1 [17]=4
F5 [13][75]=5 [15][63]=9 [31]=4
F11 [12][26][98]=7 [16][65]=8 [21][62][96]=2 [32]=9 [43]=4 [97]=5
D [78]
P [92]?6
N5 [84][15][48][29][51]=6
B3 [35][75][95]^8
H2 [71][93]={38}
P [92]?7
N6 [42][18][59][24][81][95]=6
B3 [15][35][75]^8
T2 [71][93]^{14}
P [89]?4
N1 [17]=4
B4 [15][35][75][95]^8
T4 [71][72][83][93]^{67}
F1 [83]=1
F1 [72]=4
N9 [31][43][96]=4 [57][62][38][26][75]=1 [13]=5
B5 [24][27][29][34][36]^8
F3 [27]=9 [29]=6 [87]=2
F3 [18]=3 [39]=8 [98]=7
F2 [78]=9 [92]=6
F3 [68]=2 [81]=7 [86]=9
F2 [48][84]=6
N3 [15][51]=6 [34]=3
B2 [42]^9 [45]^2
T1 [76]^{25}
P [89]?7
B4 [15][35][75][95]^8
H2 [71][93]={38}
B3 [12][42][62]^7
P [89]?9
B4 [15][35][75][95]^8
H2 [71][93]={38}
P [87]?2
B4 [15][35][75][95]^8
H2 [71][93]={38}
P [87]?4
N1 [39]=4
B7 [15][35][75][95]^8 [94][95][96]^2
T4 [71][72][83][93]^{67}
F1 [83]=1
F1 [72]=4
N9 [13][41][96]=4 [57][62][38][26][75]=1 [31]=5
N1 [34]=3
N1 [36]=8
N2 [17]=8 [18]=3
F2 [27]=9 [29]=6
N7 [51][84][92][15][48]=6 [81]=7 [86]=2
F2 [89]=9 [95]=5
F2 [78]=7 [98]=2
F3 [68][76]=9 [97]=3
F6 [56][79]=5 [59]=3 [74][93]=8 [94]=7
D [54]
P [87]?9
B7 [15][35][75][95]^8 [94][95][96]^2
H2 [71][93]={38}
P [83]?1
N5 [57][62][38][26][75]=1
B3 [15][35][95]^8
H2 [71][93]={38}
P [83]?4
N6 [86][35][68][27][53][72]=1
B3 [15][75][95]^8
T2 [71][93]^{67}
H2 [97][79]={45}
B2 [18][38]^3
F1 [38]=9
F2 [18]=6 [29]=8
N7 [24][81][95][42][59]=6 [41]=4 [92]=7
B3 [84]^9 [54][56]^2
T4 [51][57][45][65]^{59}
H2 [31][13]={58}
B1 [26]^7
P [83]?7
F1 [92]=6
F2 [81]=4 [89]=9
F2 [72]=1 [87]=2
F2 [84]=6 [86]=1
N8 [27][35][53][68]=1 [29][51][15]=6 [48]=2
B7 [65]^2 [67][69]^3 [75][95]^8 [79]^7 [17]^9
N1 [95]=2
T8 [18][38][79][97]^{37} [78][98][17][39]^{39}
D [38]
P [81]?4
F1 [83]=1
F2 [72]=7 [92]=6
N10 [57][62][38][26][75]=1 [84][15][48][29][51]=6
B4 [35][95]^8 [45][65]^2
T2 [68][98]^{39}
H2 [97][79]={45}
N9 [93][61][17][78][59][34]=3 [39][97]=4 [71]=8
F3 [18]=9 [27]=8 [79]=5
F3 [12][76]=4 [74]=9
N15 [23][56][42][35]=9 [36][94][13]=8 [43]=4 [31]=5 [21][63][49][98]=7
[24][41]=2
D [54]
P [81]?6
F1 [92]=7
N5 [59][42][18][24][95]=6
B3 [15][35][75]^8
T2 [71][93]^{14}
P [81]?7
F1 [92]=6
N5 [84][15][48][29][51]=6
B3 [35][75][95]^8
T2 [71][93]^{14}
P [78]?3
N2 [93]=3 [71]=8
B3 [15][35][95]^8
T1 [72]^{67}
H2 [17][39]={34}
B5 [23][24][26][14][16]^8
N2 [13]=8 [31]=5
N4 [41][83]=4 [72][86]=1
N5 [27][35][53][68]=1 [29]=8
F1 [38]=9
F1 [18]=6
N6 [24][81][95][42][59]=6 [92]=7
F1 [98]=2
F3 [48][89]=7 [87]=9
F1 [84]=2
B4 [26]^7 [56]^2 [45][65]^9
T4 [45][47][57][65]^{59}
P [78]?7
B4 [15][35][75][95]^8
T3 [71][93]^{14} [93]^{67}
P [78]?9
F1 [87]=2
B4 [15][35][75][95]^8
T3 [71][72][93]^{67}
T2 [71][93]^{14}
P [72]?1
F1 [83]=4
N5 [86][35][68][27][53]=1
B3 [15][75][95]^8
T2 [71][93]^{67}
H2 [97][79]={45}
B2 [18][38]^3
F1 [38]=9
F2 [18]=6 [29]=8
N7 [24][81][95][42][59]=6 [41]=4 [92]=7
B3 [84]^9 [54][56]^2
T4 [51][57][45][65]^{59}
H2 [31][13]={58}
B1 [26]^7
P [72]?4
F1 [83]=1
N5 [57][62][38][26][75]=1
B3 [15][35][95]^8
T2 [71][93]^{67}
H2 [31][13]={45}
B3 [24][27][29]^8
F3 [27]=9 [29]=6 [87]=2
F2 [18]=3 [98]=7
F3 [78]=9 [89]=4 [92]=6
F4 [39]=8 [68]=2 [81]=7 [86]=9
F3 [17]=4 [48][84]=6
F2 [13]=5 [31]=4
N5 [15][51]=6 [34]=3 [43][96]=4
B2 [42]^9 [45]^2
T1 [76]^{25}
P [72]?7
D [92]
P [56]?2
B4 [15][35][75][95]^8
T4 [71][93]^{14} [71][93]^{67}
P [56]?5
B4 [15][35][75][95]^8
T4 [71][93]^{14} [71][93]^{67}
P [56]?9
B4 [15][35][75][95]^8
T4 [71][93]^{14} [71][93]^{67}
P [54]?2
B4 [15][35][75][95]^8
T4 [71][93]^{14} [71][93]^{67}
P [54]?5
B4 [15][35][75][95]^8
T4 [71][93]^{14} [71][93]^{67}
P [54]?9
B4 [15][35][75][95]^8
T4 [71][93]^{14} [71][93]^{67}
P [38]?1
N5 [26][83][62][75][57]=1
F1 [72]=4
B3 [15][35][95]^8
T2 [71][93]^{67}
H2 [31][13]={45}
B3 [24][27][29]^8
F3 [27]=9 [29]=6 [87]=2
F2 [18]=3 [98]=7
F3 [78]=9 [89]=4 [92]=6
F4 [39]=8 [68]=2 [81]=7 [86]=9
F3 [17]=4 [48][84]=6
F2 [13]=5 [31]=4
N5 [15][51]=6 [34]=3 [43][96]=4
B2 [42]^9 [45]^2
T1 [76]^{25}
P [38]?3
N6 [14]=3 [68][27][53][72][86]=1
F1 [83]=4
N1 [35]=1
B3 [15][75][95]^8
T5 [71][93]^{67} [79][98][87]^{79}
D [98]
P [38]?9
N5 [68][27][53][72][86]=1
F1 [83]=4
N1 [35]=1
B3 [15][75][95]^8
T2 [71][93]^{67}
H2 [97][79]={45}
B2 [18]^3 [84]^9
F2 [18]=6 [29]=8
N7 [24][81][95][42][59]=6 [41]=4 [92]=7
B2 [54][56]^2
T4 [51][57][45][65]^{59}
H2 [31][13]={58}
B1 [26]^7
P [32]?2
B4 [15][35][75][95]^8
T4 [71][93]^{14} [71][93]^{67}
P [32]?4
F2 [72]=1 [83]=4
N10 [17][41][96][79]=4 [86][35][68][27][53]=1 [97]=5
F1 [38]=9
B11 [51][61]^2 [49][69][15][75][95]^8 [18][59][69]^3 [84]^9
F3 [18]=6 [29]=8 [39]=3
N7 [14]=3 [24][81][95][42][59]=6 [62]=2
F1 [92]=7
F4 [12][75]=9 [15]=5 [23]=7
F12 [13][65][71]=8 [16][61]=7 [21][98]=2 [26]=9 [31][76]=5 [51][93]=3
D [56]
P [32]?9
F1 [38]=1
N5 [26][83][62][75][57]=1
F1 [72]=4
F6 [12]=7 [23]=8 [27]=9 [29][92]=6 [87]=2
F7 [18][93]=3 [21][42]=2 [24][81][98]=7
F4 [71]=8 [78]=9 [89]=4 [97]=5
F9 [39][47]=8 [48]=6 [67][79]=3 [68]=2 [74]=5 [76]=7 [86]=9
F3 [17]=4 [61]=5 [84]=6
D [41]
P [29]?6
F1 [32]=2
N5 [51][84][92][15][48]=6
F1 [81]=7
F1 [21]=8
N2 [93]=8 [71]=3
B2 [35][75]^8
T3 [17][18][39]^{19}
F1 [18]=3
N6 [34][97]=3 [17][31]=4 [39]=8 [79]=5
N4 [96][89][72]=4 [13]=5
F1 [83]=1
N8 [43]=4 [57][62][38][26][75]=1 [27][78]=9
F4 [23][98]=7 [24][87]=2
F9 [12][49][86]=9 [42][69]=7 [59]=3 [68][95]=2 [94]=5
D [54]
P [29]?8
F1 [32]=2
F6 [21][92]=7 [23][38]=9 [27]=1 [81]=6
F7 [12][39][83]=4 [17]=3 [18]=6 [26]=2 [72]=1
F2 [24]=6 [62]=9
F1 [42]=6
N13 [34][69]=3 [41][76][97]=4 [53][68][86][35]=1 [59][95]=6 [16]=7
[79]=5
N22 [51][78][93]=3 [63][48][89][74]=7 [61][45][98][57][84]=2
[13][36][65][47][71][94]=8 [56][87]=9 [31][43]=5
F5 [49][75]=9 [54][67][96]=5
F2 [14]=9 [15]=5
S
propositions 38 solutions 1 contradictions 9 iterations 278 girth 17
[1] P10 [92][87][81][32]^4 [83][72]^7 [38]^3 [32]^9 [29]^6 [29]=8
F1 [32]=2
F6 [21][92]=7 [23][38]=9 [27]=1 [81]=6
F7 [12][39][83]=4 [17]=3 [18]=6 [26]=2 [72]=1
F2 [24]=6 [62]=9
F1 [42]=6
N13 [34][69]=3 [41][76][97]=4 [53][68][86][35]=1 [59][95]=6 [16]=7
[79]=5
N22 [51][78][93]=3 [63][48][89][74]=7 [61][45][98][57][84]=2
[13][36][65][47][71][94]=8 [56][87]=9 [31][43]=5
F5 [49][75]=9 [54][67][96]=5
F2 [14]=9 [15]=5
S
99718 FNBTHP C21.M/S8.f/F94.251/N53.322/B57.206.188.18/T34.105.52/H20.40.20/P1.10.38.1.9.278.17/M2.88.74/V7

where F is naked single, N is hidden single, D is dead end, P is proposition, and S is solution

for the FN-backdoors (size 2 / pairs):

Code: Select all

-qFN -f%#Am puzzle.dat

Code: Select all

[12]4*{[15]5[18]6[24]6[29]8[42]6[47]8[48]7[51]3[57]2[59]6[81]6[84]2[92]7[95]6}
[13]8*{[26]2[61]2[69]3}
[14]9*{[45]2[57]2[92]7}
[17]3*{[26]2[27]1[35]1[38]9[53]1[57]2[62]9[68]1[72]1[75]9[83]4[86]1}
[21]7*{[29]8}
[34]3*{[57]2}
[49]9*{[63]7}
[76]4*{[92]7}


[udosuk]

Thanks gsf!

Sorry for too lazy to try out your program... I thought it requires Linux to run, but just found you've got a windows version...

The log looks scary... I'm sure Maria or Carcul could find a much shorter solution!

[ronk]

in particular, my solver with these options on ocean's 55 hardest lists 27
puzzles unsolvable when the base and proposition (T&E) constraints are restricted
to naked/hidden singles

Code: Select all

-q'FNP(FN)-G' -e !V -F%a

Using that option string, these two of Ocean's 55 puzzles ...

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1.......2.3..4..5...6...7.....1.3....8..7..3....5.8.....7...6...5..3..8.2.......1 # ER=9.8
1.......2.3..4..5...6...7.....1.3....4..6..8....4.5.....2...9...8..5..4.7.......1 # ER=9.6

... are considered solved, evidently because of backdoors [39]4 and [17]8, respectively.

Given the '-G' option, using the backdoors doesn't seem appropriate to me. Why do you think it is?

[gsf]

Code: Select all

-q'FNP(FN)-G' -e !V -F%a

Using that option string, these two of Ocean's 55 puzzles ...

Code: Select all

1.......2.3..4..5...6...7.....1.3....8..7..3....5.8.....7...6...5..3..8.2.......1 # ER=9.8
1.......2.3..4..5...6...7.....1.3....4..6..8....4.5.....2...9...8..5..4.7.......1 # ER=9.6

... are considered solved, evidently because of backdoors [39]4 and [17]8, respectively.

Given the '-G' option, using the backdoors doesn't seem appropriate to me. Why do you think it is?

first, the proposition constraint P(FN) is not considered guessing in this context
the FNP(FN)-G simply prevents backtrack guessing on puzzles where FNP(FN) does not produce a solution

about using backdoors, its a fallout from the definition of the P (proposition) constraint
each proposition can have 3 outcomes: contradiction, solution, inconclusive
P does not ignore solutions discovered during application of the constraints

when rating puzzles -B (batch moves) is on to wash out lucky propositions

[ronk]

first, the proposition constraint P(FN) is not considered guessing in this context
(...)
about using backdoors, its a fallout from the definition of the P (proposition) constraint
each proposition can have 3 outcomes: contradiction, solution, inconclusive

In this context the primary purpose of the proposition is to find a contradiction. If a secondary purpose of the proposition is to solve the puzzle, then it is guessing IMO.