The New Sudoku Players' Forum

[denis_berthier]

Hi Paquita

-the braids for BxB, do they include bivalue chains and whips?

Both bivalue-chains and whips (and z-chains and t-whips) are special cases of braids of same length. Whether you decide to include them or not in a resolution path may change the path, but it can't change the final B rating.
Of course, the same applies to B-braids, i.e. braids with inner braids as right-linking objects. They may have inner whips, BC...

-there is some order as you indicated in PBC, what goes first, a longer bivalue or a shorter braid?

The priority order mentioned in [PBCS] is for a fixed length: bivalue-chain > z-chain > t-whip > whip
Between any two chains (or patterns) of different lengths (or sizes), the shorter one comes first.
This is the basis of the simplest-first strategy.

So what is the BxB number based on then?

Same answer as 1.
Of course, in the SHC, where speed is the goal, only braids are present.

-braids as oppposed to whips seem to have more than one assumption.

There is no assumption, neither in whips nor in braids. The word "assumption" was used by people who reasoned in terms of "inference steps"; all my approach is formulated in terms of patterns. Resolution isn't doing inferences; resolution is finding patterns and applying the theorems.
For whips or braids and for each fixed length, there is a pattern well defined in pure logic terms and there is a universal theorem (valid in any CSP) saying: if this pattern is present in the grid, then the target cannot be true.
The "continuity condition" in the braid[n] pattern is different from that in the whip[n] pattern, but that's all.

I wonder if that is a relation between the T&E level and the number of assumptions in a braid? It seems right that T&E(2) corresponds to 2 assumptions

Again, there are no assumptions in braids. But I've proven the following theorems long ago in [PBCS]:
- Solvable by braids (i.e. finite B rating) <==> in T&E(1)
- Solvable by Bp-braids (i.e. finite BpB rating) for some p <==> in T&E(2)
When you're reasoning in terms of T&E instead of braids, the T&E-depth is indeed the minimum number of simultaneous assumptions one must make at one point or another.
.

[coloin]

These 3 twin BxB6 puzzles are the only tridagon puzzles in my BxB6 file with gsf -q2 rating "M3"

Code: Select all

1.3...7...5678....7...........87.9.6.6.9.5.7..7..62.58...62...76.75.8.92..2.97... 97788 FNBP C33/M3.1351.393
1.3....8945..8.....8.........81.369....97..18..1..83.7...8...616.....87.81.6.79.3 97788 FNBP C33/M3.1351.393
1.3....8945..8.....8.........89.361....17..98..1..83.7...8...616.....87.81.6.79.3 97788 FNBP C33/M3.1351.393

Code: Select all

1.3...7...5678....7...........87.9.6.6.9.5.7..7..62.58...62...76.75.8.92..2.97... ED=11.7/10.5/4.0

+---+---+---+
|1.3|...|7..|
|.56|78.|...|
|7..|...|...|
+---+---+---+
|...|87.|9.6|
|.6.|9.5|.7.|
|.7.|.62|.58|
+---+---+---+
|...|62.|..7|
|6.7|5.8|.92|
|..2|.97|...|
+---+---+---+ 

The tridagon maybe doesnt look that complicated... but the M3 label { no double backdoor clues ?] might mean something ?

[denis_berthier]

These 3 twin BxB6 puzzles are the only tridagon puzzles in my BxB6 file with gsf -q2 rating "M3"

Code: Select all

1.3...7...5678....7...........87.9.6.6.9.5.7..7..62.58...62...76.75.8.92..2.97... ED=11.7/10.5/4.0
The tridagon maybe doesnt look that complicated...

There are 3 guardians, easily reducible to 2.
It's easily solved with digit replacement. Otherwise, it doesn't look so easy.

but the M3 label { no double backdoor clues ?] might mean something ?

No idea about that.

[coloin]

I guess it was just a hunch ... being the only puzzle with M3 ...and there are not that many with coresponding high ED

explained by eleven some time ago

Mladen has posted the first known puzzles with singles backdoor size 4, which means you have to guess (add) at least 4 correct numbers to make it a singles puzzle.

and from One flew over the backdoors

Backdoors and T&E are indeed very different.
As i understood it (without having checked it with Denis' definitions), T&E(1) corresponds to solving with singles chains, i.e. you can try each candidate - put it in - then solve all singles, and eliminate the candidate, if a contradiction arises (e.g. empty cell, missing digit for a unit). A puzzle is not solvable with singles chains, if you arrive at a grid, where no candidate can be eliminated that way.
T&E(2) then corresponds to nested singles chains (of depth 2), i.e. when you are stuck with the singles chain for a candidate, you can copy the grid, try to eliminate each candidate with singles chains - if so, eliminate it from the original grid (with the candidate tried), and then look if it leads to a contradiction there now. If so, you can eliminate the original candidate. If no progress can be achieved any more this way in the original puzzle, the candidate cannot be eliminated. Of course this is a very strong, but also elaborate method.
If a puzzle is not unique, this cannot be found with T&E - when no candidate can be eliminated, you don't know, if it has multiple solutions or the method is too weak.

If a solution is accepted, when it "happens" from trying a candidate, is a matter of taste. A solution is a solution. So it sounds strange, when in using T&E the solution is an Error But of course then T&E and pure guessing would be mixed.
I think that gsf's opinion, that (otherwise) extremely hard puzzles should be rated easier, if they have a single backdoor, has to be accepted (though i think different).
On the other side many solvers don't want to allow any T&E based solutions, only "pattern based" ones, where "pattern" refers to a predefined set of more or less easy-to-spot situations. What this set contains, differs between players, but those who allow chains too, are in a minority....

[denis_berthier]

.
No need to complicate something very simple: there's no relation between T&E and backdoors.
.

[Paquita]

I still don't fully understand braids and the rating. From PBC, I thought that a BxB 14 means there is a braid with length 14. This is the detailed output for a B14B puzzle

Hidden Text: Show

SHC version 6.2 will run under the following conditions:
*******************************************************
Rating category: BxB
max-length = 30
buffer-size = 1000000

Rating only this sudoku:
......7.9456....31......56..1......863.8.4..58..1.....34..18...5..64.......3.5.1.
|--------------------------------------------------------------------|
| 12 28 1238 | 245 23568 1236 | 7 248 9 |
| 4 5 6 | 279 2789 279 | 28 3 1 |
| 1279 2789 123789 | 2479 23789 12379 | 5 6 24 |
|--------------------------------------------------------------------|
| 279 1 24579 | 2579 235679 23679 | 23469 2479 8 |
| 6 3 279 | 8 279 4 | 129 279 5 |
| 8 279 24579 | 1 235679 23679 | 23469 2479 23467 |
|--------------------------------------------------------------------|
| 3 4 279 | 279 1 8 | 269 2579 267 |
| 5 2789 12789 | 6 4 279 | 2389 2789 237 |
| 279 26789 2789 | 3 279 5 | 24689 1 2467 |
|--------------------------------------------------------------------|

*** Test in T&E(1)

Single(s): 1r5c7, 5r7c8, 1r8c3, 6r9c2
Candidate leading to a T&E contradiction => -8r1c3
Candidate leading to a T&E contradiction => -2r1c4
Candidate leading to a T&E contradiction => -2r1c5
Candidate leading to a T&E contradiction => -2r1c6
Candidate leading to a T&E contradiction => -2r1c8
Candidate leading to a T&E contradiction => -2r3c1
Candidate leading to a T&E contradiction => -2r3c2
Candidate leading to a T&E contradiction => -2r3c3
Candidate leading to a T&E contradiction => -8r3c3
Single(s): 8r9c3
Candidate leading to a T&E contradiction => -7r3c4
Candidate leading to a T&E contradiction => -9r3c4
Candidate leading to a T&E contradiction => -2r3c5
Candidate leading to a T&E contradiction => -7r3c5
Candidate leading to a T&E contradiction => -9r3c5
Candidate leading to a T&E contradiction => -2r3c6
Candidate leading to a T&E contradiction => -7r3c6
Candidate leading to a T&E contradiction => -9r3c6
Candidate leading to a T&E contradiction => -2r4c3
Candidate leading to a T&E contradiction => -7r4c3
Candidate leading to a T&E contradiction => -9r4c3
Candidate leading to a T&E contradiction => -2r4c7
Candidate leading to a T&E contradiction => -4r4c8
Candidate leading to a T&E contradiction => -2r6c3
Candidate leading to a T&E contradiction => -7r6c3
Candidate leading to a T&E contradiction => -9r6c3
Candidate leading to a T&E contradiction => -6r6c6
Candidate leading to a T&E contradiction => -2r6c7
Candidate leading to a T&E contradiction => -9r6c7
Candidate leading to a T&E contradiction => -2r6c9
Candidate leading to a T&E contradiction => -7r6c9
Candidate leading to a T&E contradiction => -2r7c9
Candidate leading to a T&E contradiction => -2r8c8
Candidate leading to a T&E contradiction => -7r8c8
Candidate leading to a T&E contradiction => -2r8c9
Candidate leading to a T&E contradiction => -2r4c6
Candidate leading to a T&E contradiction => -7r4c6
Candidate leading to a T&E contradiction => -9r4c6
Candidate leading to a T&E contradiction => -3r6c6
|--------------------------------------------------------------------|
| 12 28 23 | 45 3568 136 | 7 48 9 |
| 4 5 6 | 279 2789 279 | 28 3 1 |
| 179 789 379 | 24 38 13 | 5 6 24 |
|--------------------------------------------------------------------|
| 279 1 45 | 2579 235679 36 | 3469 279 8 |
| 6 3 279 | 8 279 4 | 1 279 5 |
| 8 279 45 | 1 235679 279 | 346 2479 346 |
|--------------------------------------------------------------------|
| 3 4 279 | 279 1 8 | 269 5 67 |
| 5 279 1 | 6 4 279 | 2389 89 37 |
| 279 6 8 | 3 279 5 | 249 1 247 |
|--------------------------------------------------------------------|

*** Test in T&E(B1,1)

Candidate leading to a T&E contradiction => -9r4c5
Candidate leading to a T&E contradiction => -7r6c5
Candidate leading to a T&E contradiction => -9r6c5
|-----------------------------------------------------------|
| 12 28 23 | 45 3568 136 | 7 48 9 |
| 4 5 6 | 279 2789 279 | 28 3 1 |
| 179 789 379 | 24 38 13 | 5 6 24 |
|-----------------------------------------------------------|
| 279 1 45 | 2579 23567 36 | 3469 279 8 |
| 6 3 279 | 8 279 4 | 1 279 5 |
| 8 279 45 | 1 2356 279 | 346 2479 346 |
|-----------------------------------------------------------|
| 3 4 279 | 279 1 8 | 269 5 67 |
| 5 279 1 | 6 4 279 | 2389 89 37 |
| 279 6 8 | 3 279 5 | 249 1 247 |
|-----------------------------------------------------------|

*** Test in T&E(B2,1)

Candidate leading to a T&E contradiction => -2r4c5
Candidate leading to a T&E contradiction => -7r4c5
|--------------------------------------------------|
| 12 28 23 | 45 3568 136 | 7 48 9 |
| 4 5 6 | 279 2789 279 | 28 3 1 |
| 179 789 379 | 24 38 13 | 5 6 24 |
|--------------------------------------------------|
| 279 1 45 | 2579 356 36 | 3469 279 8 |
| 6 3 279 | 8 279 4 | 1 279 5 |
| 8 279 45 | 1 2356 279 | 346 2479 346 |
|--------------------------------------------------|
| 3 4 279 | 279 1 8 | 269 5 67 |
| 5 279 1 | 6 4 279 | 2389 89 37 |
| 279 6 8 | 3 279 5 | 249 1 247 |
|--------------------------------------------------|

*** Test in T&E(B3,1)


*** Test in T&E(B4,1)


*** Test in T&E(B5,1)


*** Test in T&E(B6,1)


*** Test in T&E(B7,1)


*** Test in T&E(B8,1)


*** Test in T&E(B9,1)


*** Test in T&E(B10,1)


*** Test in T&E(B11,1)


*** Test in T&E(B12,1)


*** Test in T&E(B13,1)


*** Test in T&E(B14,1)

Candidate leading to a T&E contradiction => -7r5c5
Candidate leading to a T&E contradiction => -9r5c8
Candidate leading to a T&E contradiction => -2r6c2
braid[3]: r5c5{n9 n2}- r6n2{c5 c8}- b6n9{r6c8 .} => -9r4c4
braid[7]: r5n9{c5 c3}- r6c2{n9 n7}- r4c1{n7 n2}- r9c1{n2 n7}- r7c3{n7 n2}- r7c4{n2 n7}- b5n7{r4c4 .} => -9r9c5
braid[8]: r5c5{n9 n2}- r6c2{n9 n7}- r4c1{n7 n2}- r6c6{n7 n9}- r9c5{n2 n7}- r8c6{n7 n2}- r8c2{n2 n9}- r9c1{n9 .} => -9r5c3
Single(s): 9r5c5
braid[7]: r9c5{n7 n2}- b5n7{r4c4 r6c6}- r6n2{c6 c8}- r5n2{c8 c3}- r7c3{n2 n9}- r9c1{n9 n7}- b4n7{r4c1 .} => -7r7c4
braid[3]: r6c6{n2 n7}- r2n9{c6 c4}- c4n7{r2 .} => -2r2c6
braid[6]: r9c5{n7 n2}- r7c4{n2 n9}- r7c3{n9 n2}- r5c3{n2 n7}- r6c2{n7 n9}- r8c2{n9 .} => -7r9c1
braid[3]: r6c2{n9 n7}- c3n9{r3 r7}- b7n7{r7c3 .} => -9r3c2
braid[7]: r5c3{n7 n2}- r6c2{n7 n9}- b5n7{r4c4 r6c6}- c6n2{r6 r8}- r7c4{n2 n9}- r7c3{n9 n7}- r8c2{n7 .} => -7r4c1
Single(s): 7r3c1, 8r3c2, 2r1c2, 1r1c1, 3r1c3, 6r1c6, 9r3c3, 3r3c5, 1r3c6, 3r4c6
braid[3]: r5c8{n2 n7}- r6c6{n2 n7}- r4n7{c4 .} => -2r6c8
Box/line: 2r6b5 => -2r4c4
braid[3]: r9c1{n2 n9}- r8c2{n9 n7}- b8n7{r8c6 .} => -2r9c5
Single(s): 7r9c5
braid[2]: r2c5{n2 n8}- r2c7{n8 .} => -2r2c4
braid[2]: r3c9{n4 n2}- r9c9{n2 .} => -4r6c9
braid[2]: r2n2{c7 c5}- c4n2{r3 .} => -2r7c7
braid[4]: r8c9{n3 n7}- r8c2{n7 n9}- r9c1{n9 n2}- b9n2{r9c7 .} => -3r8c7
Single(s): 3r8c9, 6r6c9, 7r7c9, 2r7c3, 7r5c3, 2r5c8, 9r6c2, 2r4c1, 9r7c4, 7r2c4, 9r2c6, 5r4c4, 4r1c4, 8r1c8, 5r1c5, 2r2c7, 8r2c5, 2r3c4, 4r3c9, 4r4c3, 6r4c5, 9r4c7, 7r4c8, 5r6c3, 2r6c5, 7r6c6, 4r6c8, 3r6c7, 6r7c7, 7r8c2, 2r8c6, 8r8c7, 9r8c8, 9r9c1, 4r9c7, 2r9c9
|-----------------------|
| 1 2 3 | 4 5 6 | 7 8 9 |
| 4 5 6 | 7 8 9 | 2 3 1 |
| 7 8 9 | 2 3 1 | 5 6 4 |
|-----------------------|
| 2 1 4 | 5 6 3 | 9 7 8 |
| 6 3 7 | 8 9 4 | 1 2 5 |
| 8 9 5 | 1 2 7 | 3 4 6 |
|-----------------------|
| 3 4 2 | 9 1 8 | 6 5 7 |
| 5 7 1 | 6 4 2 | 8 9 3 |
| 9 6 8 | 3 7 5 | 4 1 2 |
|-----------------------|

Unique solution found.
BxB rating = 14
Max buffer filling: 53346 - 53346 /1000000
Run time = 5s

Execution finished.

This looks different from the procedure in PBC, the max braid = 8

i am trying to get a better understanding of what is a high BxB rating. Hoping it will help me to generate puzzles.

[denis_berthier]

.
Hi Paquita
You are confusing the B and the BxB classifications.
The B rating is for puzzles in T&E(1). It is indeed the length of the largest braid in the simplest solution.

The BxB classif is for puzzles in T&E(2), as in your example. It is the minimal length p necessary to solve a puzzle with Bp-braids of any length. In terms of T&E, it is the minimal length p necessary to solve a puzzle in T&E(Bp).
This is exactly what the SHC shows you:
it first tries to solve the puzzle in T&E(1) = T&E(Singles, 1) = T&E(B0, 1)
then it tries in T&E(B1, 1)
then in T&E(B2, 1)
...
finally it succeeds in T&E(B14, 1)
.

[Paquita]

I got a more detailed process for that B14B

Hidden Text: Show

*** Test in T&E(B7,1)

Assume 7r5c5 =>
braid[4]: r5n9{c8 c3}- c2n9{r6 r3}- c2n8{r3 r1}- c8n8{r1 .} => -9r8c8
Single(s): 8r8c8, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4
Box/line: 9c8b6 => -9r4c7
braid[2]: r2c5{n2 n9}- r9c5{n9 .} => -2r6c5

*** Test in T&E(B8,1)

Assume 7r5c5 =>
braid[4]: r5n9{c8 c3}- c2n9{r6 r3}- c2n8{r3 r1}- c8n8{r1 .} => -9r8c8
Single(s): 8r8c8, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4
Box/line: 9c8b6 => -9r4c7
braid[2]: r2c5{n2 n9}- r9c5{n9 .} => -2r6c5

*** Test in T&E(B9,1)

Assume 7r5c5 =>
braid[4]: r5n9{c8 c3}- c2n9{r6 r3}- c2n8{r3 r1}- c8n8{r1 .} => -9r8c8
Single(s): 8r8c8, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4
Box/line: 9c8b6 => -9r4c7
braid[2]: r2c5{n2 n9}- r9c5{n9 .} => -2r6c5

*** Test in T&E(B10,1)

Assume 7r5c5 =>
braid[4]: r5n9{c8 c3}- c2n9{r6 r3}- c2n8{r3 r1}- c8n8{r1 .} => -9r8c8
Single(s): 8r8c8, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4
Box/line: 9c8b6 => -9r4c7
braid[2]: r2c5{n2 n9}- r9c5{n9 .} => -2r6c5

*** Test in T&E(B11,1)

Assume 7r5c5 =>
braid[4]: r5n9{c8 c3}- c2n9{r6 r3}- c2n8{r3 r1}- c8n8{r1 .} => -9r8c8
Single(s): 8r8c8, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4
Box/line: 9c8b6 => -9r4c7
braid[2]: r2c5{n2 n9}- r9c5{n9 .} => -2r6c5

*** Test in T&E(B12,1)

Assume 7r5c5 =>
braid[4]: r5n9{c8 c3}- c2n9{r6 r3}- c2n8{r3 r1}- c8n8{r1 .} => -9r8c8
Single(s): 8r8c8, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4
Box/line: 9c8b6 => -9r4c7
braid[2]: r2c5{n2 n9}- r9c5{n9 .} => -2r6c5

*** Test in T&E(B13,1)

Assume 7r5c5 =>
braid[4]: r5n9{c8 c3}- c2n9{r6 r3}- c2n8{r3 r1}- c8n8{r1 .} => -9r8c8
Single(s): 8r8c8, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4
Box/line: 9c8b6 => -9r4c7
braid[2]: r2c5{n2 n9}- r9c5{n9 .} => -2r6c5

*** Test in T&E(B14,1)

Assume 7r5c5 =>
braid[4]: r5n9{c8 c3}- c2n9{r6 r3}- c2n8{r3 r1}- c8n8{r1 .} => -9r8c8
Single(s): 8r8c8, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4
Box/line: 9c8b6 => -9r4c7
braid[2]: r2c5{n2 n9}- r9c5{n9 .} => -2r6c5
braid[14]: r3c5{n3 n8}- r4c6{n3 n6}- r4c7{n6 n4}- r1n8{c5 c2}- r9n4{c7 c9}- r9n7{c9 c1}- b4n7{r4c1 r6c2}- c2n2{r6 r8}- r7c3{n2 n9}- r5n9{c3 c8}- r6n9{c8 c6}- r4c4{n9 n2}- r7c4{n2 n7}- r8c6{n7 .} => -3r4c5
braid[10]: r8c9{n3 n7}- r4n3{c7 c6}- r3c6{n3 n1}- r1n1{c6 c1}- r9n7{c9 c1}- c1n2{r9 r4}- r5c3{n2 n9}- b5n2{r4c4 r6c6}- r8c6{n2 n9}- b7n9{r8c2 .} => -3r6c9
Single(s): 3r8c9
braid[8]: r8c7{n2 n9}- r9c5{n2 n9}- r9c1{n9 n7}- r4n7{c1 c8}- r7n9{c4 c3}- r5c3{n9 n2}- r4n2{c1 c4}- r7n2{c4 .} => -2r9c7
braid[8]: r8c7{n9 n2}- r9c5{n9 n2}- r9c1{n2 n7}- r4n7{c1 c8}- r7n2{c4 c3}- r5c3{n2 n9}- r4n9{c1 c4}- r7n9{c4 .} => -9r9c7
Single(s): 4r9c7, 7r9c9, 6r7c9, 4r6c9, 5r6c3, 4r4c3, 5r4c5
braid[7]: r8c7{n2 n9}- r9c1{n2 n9}- r7n9{c3 c4}- r4c4{n9 n2}- r4c1{n2 n7}- r6c2{n7 n9}- r6c6{n9 .} => -2r8c2
braid[4]: r2c5{n2 n9}- r9n9{c5 c1}- r8c2{n9 n7}- c6n7{r8 .} => -2r2c6
braid[3]: r4c4{n9 n2}- r9c5{n9 n2}- r2n2{c5 .} => -9r7c4
braid[4]: r4c4{n9 n2}- r7c4{n2 n7}- r8n7{c6 c2}- b4n7{r6c2 .} => -9r4c1
braid[3]: r5c8{n2 n9}- r6c6{n2 n9}- r4n9{c4 .} => -2r6c8
braid[3]: r5c3{n9 n2}- c1n9{r3 r9}- b7n2{r9c1 .} => -9r3c3
braid[3]: r4c1{n7 n2}- c3n7{r3 r7}- b7n2{r7c3 .} => -7r3c1
Single(s): 7r4c1, 7r6c8
braid[4]: r8c7{n9 n2}- c3n9{r7 r5}- r6c2{n9 n2}- c6n2{r6 .} => -9r7c7
Single(s): 2r7c7, 7r7c4, 9r7c3, 2r5c3, 3r1c3, 7r3c3, 9r5c8, 2r4c8, 9r4c4, 2r2c4, 9r2c5
Candidate leading to a T&E contradiction => -7r5c5
Assume 9r5c8 =>
Single(s): 2r5c5, 7r5c3, 8r8c8, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4
braid[5]: r7c3{n2 n9}- r7c4{n9 n7}- r4c4{n7 n9}- r4c1{n9 n2}- r9n2{c1 .} => -2r7c7
braid[4]: r9c9{n4 n7}- r7n7{c9 c4}- r7n2{c4 c3}- r9n2{c1 .} => -4r9c7
Single(s): 4r9c9
braid[6]: r7c3{n9 n2}- r7c4{n2 n7}- r4c4{n7 n9}- r9c5{n7 n9}- r6n9{c6 c2}- r8n9{c2 .} => -9r7c7
Single(s): 6r7c7, 7r7c9, 3r8c9, 6r6c9
braid[3]: r2c5{n9 n7}- r6c6{n9 n7}- c4n7{r4 .} => -9r2c6
braid[2]: r4n9{c1 c4}- r7n9{c4 .} => -9r9c1
braid[5]: r9c7{n9 n2}- r9c1{n2 n7}- r8c2{n7 n2}- r6c2{n2 n9}- c6n9{r6 .} => -9r8c7
Single(s): 2r8c7, 9r9c7, 7r9c5, 9r2c5, 9r8c6, 7r6c6, 2r2c6, 7r2c4, 9r4c4, 2r4c1
Candidate leading to a T&E contradiction => -9r5c8
Assume 2r6c2 =>
Single(s): 8r1c2, 4r1c8, 5r1c4, 2r3c9, 8r2c7, 4r3c4, 8r3c5, 8r8c8
Box/line: 9c8b6 => -9r4c7
braid[3]: r4c1{n7 n9}- r6c6{n7 n9}- r5n9{c5 .} => -7r4c4
Single(s): 7r6c6, 9r6c8
braid[5]: r5n9{c5 c3}- r4c1{n9 n7}- r9c1{n7 n2}- r7c3{n2 n7}- b8n7{r7c4 .} => -9r9c5
braid[3]: r2c6{n2 n9}- r4c4{n2 n9}- c5n9{r5 .} => -2r2c4
braid[5]: r8n2{c7 c6}- b8n9{r8c6 r7c4}- r7c3{n9 n7}- r5c3{n7 n9}- r4n9{c1 .} => -2r7c7
braid[4]: r7c9{n7 n6}- r7c7{n6 n9}- r8c2{n7 n9}- r9n9{c1 .} => -7r8c9
Single(s): 3r8c9, 7r8c2, 9r3c2
braid[2]: r4n9{c4 c1}- c3n9{r5 .} => -9r7c4
Single(s): 9r8c6, 2r2c6, 2r8c7
braid[4]: r9c1{n9 n2}- r7c3{n2 n9}- r5n9{c3 c5}- c5n2{r5 .} => -9r9c7
Single(s): 4r9c7, 7r9c9, 6r7c9, 4r6c9, 5r6c3, 4r4c3, 9r7c7, 2r7c3, 3r1c3, 6r1c5, 1r1c6, 2r1c1, 7r3c3, 1r3c1, 3r3c6, 6r4c6, 3r4c7, 5r4c5, 9r5c3, 7r4c1, 2r4c8
Candidate leading to a T&E contradiction => -2r6c2
braid[3]: r5c5{n9 n2}- r6n2{c5 c8}- b6n9{r6c8 .} => -9r4c4
braid[7]: r5n9{c5 c3}- r6c2{n9 n7}- r4c1{n7 n2}- r9c1{n2 n7}- r7c3{n7 n2}- r7c4{n2 n7}- b5n7{r4c4 .} => -9r9c5
braid[8]: r5c5{n9 n2}- r6c2{n9 n7}- r4c1{n7 n2}- r6c6{n7 n9}- r9c5{n2 n7}- r8c6{n7 n2}- r8c2{n2 n9}- r9c1{n9 .} => -9r5c3
Single(s): 9r5c5
braid[7]: r9c5{n7 n2}- b5n7{r4c4 r6c6}- r6n2{c6 c8}- r5n2{c8 c3}- r7c3{n2 n9}- r9c1{n9 n7}- b4n7{r4c1 .} => -7r7c4
braid[3]: r6c6{n2 n7}- r2n9{c6 c4}- c4n7{r2 .} => -2r2c6
braid[6]: r9c5{n7 n2}- r7c4{n2 n9}- r7c3{n9 n2}- r5c3{n2 n7}- r6c2{n7 n9}- r8c2{n9 .} => -7r9c1
braid[3]: r6c2{n9 n7}- c3n9{r3 r7}- b7n7{r7c3 .} => -9r3c2
braid[7]: r5c3{n7 n2}- r6c2{n7 n9}- b5n7{r4c4 r6c6}- c6n2{r6 r8}- r7c4{n2 n9}- r7c3{n9 n7}- r8c2{n7 .} => -7r4c1
Single(s): 7r3c1, 8r3c2, 2r1c2, 1r1c1, 3r1c3, 6r1c6, 9r3c3, 3r3c5, 1r3c6, 3r4c6
braid[3]: r5c8{n2 n7}- r6c6{n2 n7}- r4n7{c4 .} => -2r6c8
Box/line: 2r6b5 => -2r4c4
braid[3]: r9c1{n2 n9}- r8c2{n9 n7}- b8n7{r8c6 .} => -2r9c5
Single(s): 7r9c5
braid[2]: r2c5{n2 n8}- r2c7{n8 .} => -2r2c4
braid[2]: r3c9{n4 n2}- r9c9{n2 .} => -4r6c9
braid[2]: r2n2{c7 c5}- c4n2{r3 .} => -2r7c7
braid[4]: r8c9{n3 n7}- r8c2{n7 n9}- r9c1{n9 n2}- b9n2{r9c7 .} => -3r8c7
Single(s): 3r8c9, 6r6c9, 7r7c9, 2r7c3, 7r5c3, 2r5c8, 9r6c2, 2r4c1, 9r7c4, 7r2c4, 9r2c6, 5r4c4, 4r1c4, 8r1c8, 5r1c5, 2r2c7, 8r2c5, 2r3c4, 4r3c9, 4r4c3, 6r4c5, 9r4c7, 7r4c8, 5r6c3, 2r6c5, 7r6c6, 4r6c8, 3r6c7, 6r7c7, 7r8c2, 2r8c6, 8r8c7, 9r8c8, 9r9c1, 4r9c7, 2r9c9
|-----------------------|
| 1 2 3 | 4 5 6 | 7 8 9 |
| 4 5 6 | 7 8 9 | 2 3 1 |
| 7 8 9 | 2 3 1 | 5 6 4 |
|-----------------------|
| 2 1 4 | 5 6 3 | 9 7 8 |
| 6 3 7 | 8 9 4 | 1 2 5 |
| 8 9 5 | 1 2 7 | 3 4 6 |
|-----------------------|
| 3 4 2 | 9 1 8 | 6 5 7 |
| 5 7 1 | 6 4 2 | 8 9 3 |
| 9 6 8 | 3 7 5 | 4 1 2 |
|-----------------------|

Unique solution found.
BxB rating = 14
Max buffer filling: 53346 - 53346 /1000000
Run time = 3m51s

Execution finished.

It shows that there is a Braid[14] that comes up in *** Test in T&E(B14,1)
Generally the braids are y<= the T&E(Bx,1)
it shows that the solving was stagnated and waiting for that braid[14] to get another elimination.
This braid was not in the original puzzle output, I modified the source a bit to show more.
Now I don't know if every B14B puzzle has a braid[14] and so on for every BxB. It would mean that there is just one Braid, needed for solving, that dictates the BxB level
I will try more with other puzzles.

[denis_berthier]

I got a more detailed process for that B14B
it shows that the solving was stagnated and waiting for that braid[14] to get another elimination.
This braid was not in the original puzzle output, I modified the source a bit to show more.

Which source ?

Now I don't know if every B14B puzzle has a braid[14] and so on for every BxB. It would mean that there is just one Braid, needed for solving, that dictates the BxB level
I will try more with other puzzles.

It isn't a braid[14] in the resolution path. Its is a braid[14] in some T&E(cand) to eliminate cand.
Every B14B puzzle has at least one such elimination. But it may also have one or more eliminations like that, each using one or more braid[14].
What's true is, for large values of B, it happens that the hardest step is reached only once.
You may have a hard time proving that this is always true; it is not.
.

[Paquita]

i used AI to get the Java source in C++ and compiled that. The Java source I got from the SHC jar, I used a site that reads the jar as several Java Class files. I do not intend to spread that source, I understand it is copyrighted by the author. I am just trying to understand the BxB rating.

I was wondering about the fact that nothing happens for quite some levels, what was the change that got the elimination process going again, and that was the braid[14]. It was at level 14 because it takes 14 steps. It is indeed a T&E elimination and as such was not in the original output.

[Paquita]

Another thing that I do not fully understand yet is the mix of braids and T&E elimination. In the PBC, the braids are one way to solve and the T&E another and are proven to be equally potent.

[denis_berthier]

i used AI to get the Java source in C++ and compiled that. The Java source I got from the SHC jar, I used a site that reads the jar as several Java Class files. I do not intend to spread that source, I understand it is copyrighted by the author. I am just trying to understand the BxB rating.
I was wondering about the fact that nothing happens for quite some levels, what was the change that got the elimination process going again, and that was the braid[14]. It was at level 14 because it takes 14 steps. It is indeed a T&E elimination and as such was not in the original output.

Can you send me the change you made? (I already have the source.)

I hadn't noticed that a braid[14] was missing in the SHC output.I've tested the SHC on thousands of cases with SudoRules and I found no difference in ratings but I didn't check individual resolution paths. My question is, as the final BxB found by the SHC is correct, is it only a matter of some braids not being printed out?
[Edit]: I think François uses an output buffer within the T&E(Bp) procedure, in order not to output T&E steps that don't allow to conclude anything. This is probably where the bug is.


François told me a few weeks ago he can't work now on a screen due to eye problems. So, if any bug is found, we must manage by ourselves.
[Edit]: I've sent him an email too ask what he thinks of it. Even if he can"'t work on it, he may have some idea of what's happening.
.

[denis_berthier]

Another thing that I do not fully understand yet is the mix of braids and T&E elimination. In the PBC, the braids are one way to solve and the T&E another and are proven to be equally potent.

yes: solvable by T&E(1) = solvable by ordinary braids of any length = in B.
and as a result: solvable by T&E(Bp, 1) = solvable by Bp-braids of any total length = in BpB.
.

[Paquita]

This is the change

Hidden Text: Show

char TE::TE1(Jeu& jeu, std::vector<int>& nArray, int n, int n2, int n3, int n4) {
int n5 = 0, n6 = 0;
bool bl;
do {
char c = appliquer_regles_resolution(jeu, nArray, n, n2, n3, n4, (profmax == 1 ? afficher : false));
if (c == 'S' || c == 'F') return c;

bl = false;
std::vector<int> candidates = jeu.candid_apres(n5, n6);
for (int val : candidates) {
n5 = val / 10;
n6 = val % 10;
if (profmax == 1 && jeu.cell[n5].candidat[n6].sol) continue;

if (n >= 7) {
Jeu::copier(jeu, J1);
if (TE0(J1, n5, n6) != 'F') continue;
}

Jeu::copier(jeu, J1);
//**// c = appliquer_regles_resolution(J1, nArray, n, n2, n5, n6, false);
c = appliquer_regles_resolution(J1, nArray, n, n2, n5, n6, true);
if (c != 'F') continue;

if (afficher && profmax == 1) {
X::print("\n Candidate leading to a T&E contradiction => -" +
TB::conv(std::to_string(n6) + jeu.cell[n5].nom()));
}
jeu.supprimern(n5, n6);
bl = true;
break;
}
} while (bl);
return 'I';
}

and this bool bl becomes true as well

Hidden Text: Show

char TB::appliquer(Jeu& jeu, const std::vector<int>& nArray, int n, int n2, bool bl) {
int n3 = 73;
stop_inco.clear();
nombre = 0;
if (n != 0 && jeu.cell[n].candidat[n2].existe) {
jeu.valider(n, n2);
if (bl) {
std::cout << "\nAssume " << conv(std::to_string(n2) + Cellule::nom(n)) << " => ";
}
if (!stop_inco.empty()) {
n3 = 70;
}
else if (jeu.est_solution()) {
n3 = 83;
}
}
int n4 = -1;
while (n3 == 73) {
int n5 = -1;
for (size_t i = 0; i < nArray.size(); ++i) {
if (!chercher(jeu, nArray[i], bl, n4)) continue;
n5 = static_cast<int>(i);
n4 = n5;
break;
}
if (n5 == -1) break;
++nombre;
if (!stop_inco.empty()) {
n3 = 70;
break;
}
if (jeu.est_solution()) {
n3 = 83;
break;
}
}
return static_cast<char>(n3);
}

//**// c = appliquer_regles_resolution(J1, nArray, n, n2, n5, n6, false); I changed false to true, the boolean display option
c = appliquer_regles_resolution(J1, nArray, n, n2, n5, n6, true);

The braid[14] that leads to a contraduction was not printed originally, just the remark : Candidate leading to a T&E contradiction =>

I used the same puzzle in the two previous output examples, one with this new change. It is indeed just a difference of not printing all the elimination steps. No change in the calculation

[denis_berthier]

.
Just received an answer from François. In essence, he says there's no bug. The braid[14] doesn't appear explicitly in the output; it is implicit in the first line after *** Test in T&E(B14,1)

Code: Select all

Candidate leading to a T&E contradiction => -7r5c5

He also says this can be changed by a Boolean §(as you did).

Another way to get the details is to add n7r5c5 to the original puzzle and to try to solve it with braids. You'll get the desired contradiction.

My position is, there's no reason to change anything in the SHC - the purpose of which is to classify puzzles, not to printout detailed resolution paths.
(Changing the Boolean would lead to very long outputs, including all the useless tries involved in T&E - not shown in Paquita's output.)
.