udosuk wrote: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}

- gsf
- 2014 Supporter
**Posts:**7306**Joined:**21 September 2005**Location:**NJ USA

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...

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...

- udosuk
**Posts:**2698**Joined:**17 July 2005

udosuk wrote: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

- gsf
- 2014 Supporter
**Posts:**7306**Joined:**21 September 2005**Location:**NJ USA

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)...

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

- udosuk
**Posts:**2698**Joined:**17 July 2005

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

great

udosuk wrote: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 . .

- gsf
- 2014 Supporter
**Posts:**7306**Joined:**21 September 2005**Location:**NJ USA

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

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

So which is true?

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

From this thread you wrote:

- 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

But then above you wrote: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?

- udosuk
**Posts:**2698**Joined:**17 July 2005

udosuk wrote:From this thread you wrote:

- 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 99650But then above you wrote: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
- 2014 Supporter
**Posts:**7306**Joined:**21 September 2005**Location:**NJ USA

udosuk wrote: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

- gsf
- 2014 Supporter
**Posts:**7306**Joined:**21 September 2005**Location:**NJ USA

gsf wrote: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!

- udosuk
**Posts:**2698**Joined:**17 July 2005

udosuk wrote: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"<>"`

log wrote:

[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}

- gsf
- 2014 Supporter
**Posts:**7306**Joined:**21 September 2005**Location:**NJ USA

gsf wrote: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 ...

- 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?

- ronk
- 2012 Supporter
**Posts:**4764**Joined:**02 November 2005**Location:**Southeastern USA

ronk wrote:

- 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

- gsf
- 2014 Supporter
**Posts:**7306**Joined:**21 September 2005**Location:**NJ USA

gsf wrote: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.

- ronk
- 2012 Supporter
**Posts:**4764**Joined:**02 November 2005**Location:**Southeastern USA