The New Sudoku Players' Forum

Website · by **denis_berthier** » Fri Nov 12, 2021 5:56 am

.
It didn't take long to adapt the code for one or3 pattern to a double one in the same row and column. I let the computations run during the night.
The results are quite surprising: there are more such double patterns than I expected.
I used the same convention as before: the detection occurs after all the rules with 5 or less CSP-Variables have been fired (which a priori eliminates all the puzzles in W5 or less).
Among the 21375 puzzles in cbg-000, 147 (0.7%) have this pattern (not necessarily at the start, but it appears during resolution). In many cases, it appears several times.
Here is the full list:

Hidden Text: Show

[Added:]Same remarks as before:
- the presence of the pattern doesn't mean it can be used in any useful way;
- as it currently does nothing, it doesn't change the resolution path one would get without it.
More remarks:
- the percentage is 147/239 = 62% if one considers only the relevant puzzles (those not already solved in W5);
- if the pattern was looked for with higher priority than "just before L6", I think it'd appear in a large proportion of the puzzles;

Website · by **denis_berthier** » Fri Nov 12, 2021 6:05 am

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Out of sheer curiosity, I also tried to see what happened in the case that had the most occurrences of the pattern - the last but one in the list.
(solve "..3.5......71.9.2..8..7..4..7.....9.516.......3...2.57...7....8....9526.....61...")

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 12469 269 3 ! 246 5 468 ! 16789 178 169 ! ! 46 56 7 ! 1 348 9 ! 3568 2 356 ! ! 1269 8 1259 ! 236 7 36 ! 13569 4 13569 ! +-------------------+-------------------+-------------------+ ! 28 7 248 ! 5 1348 3468 ! 13468 9 1346 ! ! 5 1 6 ! 9 348 7 ! 348 38 2 ! ! 89 3 489 ! 46 148 2 ! 1468 5 7 ! +-------------------+-------------------+-------------------+ ! 1369 569 159 ! 7 2 34 ! 13459 13 8 ! ! 7 4 18 ! 38 9 5 ! 2 6 13 ! ! 2389 259 2589 ! 348 6 1 ! 34579 37 3459 ! +-------------------+-------------------+-------------------+ 156 candidates.

There first appears a series of relatively simple rules: only Subsets, bivalue-chains and z-chains (only reversible patterns, no rule with any t-candidate):

Hidden Text: Show

Code: Select all: +-------------------+-------------------+-------------------+ ! 12469 269 3 ! 246 5 68 ! 7 18 169 ! ! 46 56 7 ! 1 348 9 ! 38 2 356 ! ! 169 8 1259 ! 26 7 36 ! 1569 4 13569 ! +-------------------+-------------------+-------------------+ ! 28 7 24 ! 5 138 368 ! 1346 9 146 ! ! 5 1 6 ! 9 34 7 ! 348 38 2 ! ! 89 3 489 ! 46 18 2 ! 146 5 7 ! +-------------------+-------------------+-------------------+ ! 1369 569 159 ! 7 2 4 ! 59 13 8 ! ! 7 4 18 ! 38 9 5 ! 2 6 13 ! ! 389 259 2589 ! 38 6 1 ! 459 7 459 ! +-------------------+-------------------+-------------------+

This is where the pattern appears, all the instances at the same time:
double-or3: n1[r7c8!r7c3!r3c3]+n5[r7c7!r7c3!r3c3] ;
double-or3: n5[r7c7!r7c2!r2c2]+n9[r7c7!r7c2!r1c2] ;
double-or3: n4[r4c3!r4c7!r9c7]+n6[r4c6!r4c7!r3c7] ;
double-or3: n1[r4c5!r4c7!r3c7]+n6[r4c6!r4c7!r3c7] ;
double-or3: n1[r4c5!r4c7!r3c7]+n4[r4c3!r4c7!r9c7] ;
double-or3: n3[r4c7!r4c5!r2c5]+n8[r4c1!r4c5!r2c5] ;

The end in Z6 had nothing noticeable:

Hidden Text: Show

If you're a user of CSP-Rules, I can post the additional code that would allow you to analyse each puzzle as above.

by **shye** » Fri Nov 12, 2021 10:24 am

looking forward to going through these whenever i get the time

moving from bottom to top this time around, just to start with stuff i havent looked at before

the first thing i've noticed isnt exactly a new technique, but something i hadn't fully appreciated yet. in puzzle #20680 there's an interesting sue de coq which has a small-scale firework MSHS as its inverse

Code: Select all: Sue de Coq approach: Firework MSHS approach: .--------------------.-------------------.-----------------. .--------------------.-------------------.-----------------. | 123-5 12567 1357 | 4 3567 356 | 67 8 9 | |x123-5 12567 1357 | 4 3567 356 | 67 8 9 | |#459 45679 579 | 1 8 569 | 2 67 3 | | 459 45679 579 | 1 8 569 | 2 67 3 | | 8 679 379 | 367 3679 2 | 1 5 4 | | 8 679 379 | 367 3679 2 | 1 5 4 | :--------------------+-------------------+-----------------: :--------------------+-------------------+-----------------: |#24-5 47-25 6 | 9 1 8 | 3 27 257 | | 245 457-2 6 | 9 1 8 | 3 27 257 | |#123-5#125 #135 | 236-5 236-5 7 | 9 4 8 | |x123-5 125 135 |x236-5x236-5 7 | 9 4 8 | |#239-5 789-25 789-35| 235 235 4 | 567 1267 1257 | | 2359 5789-2 5789-3| 235 235 4 | 567 1267 1257 | :--------------------+-------------------+-----------------: :--------------------+-------------------+-----------------: |#59 3 4 | 257 2579 1 | 8 279 6 | | 59 3 4 | 257 2579 1 | 8 279 6 | | 6 1589 1589 | 2578 24579 59 | 457 3 1257 | | 6 1589 1589 | 2578 24579 59 | 457 3 1257 | | 7 1589 2 | 3568 34569 3569 | 45 19 15 | | 7 1589 2 | 3568 34569 3569 | 45 19 15 | '--------------------'-------------------'-----------------' '--------------------'-------------------'-----------------' skfr 8.9 ...4....9....8.2..8....2154..69183.......7948.....4....34..18.66......3.7.2......

fireworks on 2 and 3 in r5c1b4 along with 1c1 & 6r5 make four placements to go in four cells, all other candidates removed
additional positions for 2&3 in b4 also eliminated (pattern is rank0)

the SDC picks up some cannibalised elims on 5s in b4 which the alternative doesnt immediately get, but the basics that follow from the firework (locked 5s in r5) handle it
looking at this with T&L, the SDC is 7 cell truths, whereas the firework MSHS is 6 line truths (a firework always accounts for two line truths, one per row and column), but if we insist on accounting for the 5s eliminations in b4, we have to add 5r5 as a truth and then they become equivalent, 7 truths each for either perspective

so naturally i went to look for another generated puzzle where the inverse is less truths than the SDC (with the additional restraint that each technique must get the same eliminations), and it wasnt too hard to find (っ◔◡◔)っ

Code: Select all: Sue de Coq: Firework MSHS: .---------------.---------------.----------------. .---------------.---------------.----------------. | 128 279 3 | 479 5 1479 | 6 149 289 | | 128 279 3 | 479 5 1479 | 6 149 289 | | 4 67 19 | 8 2 67 | 3 19 5 | | 4 67 19 | 8 2 67 | 3 19 5 | | 268 5 189 | 469 16 3 | 48-2 7 289 | | 268 5 189 | 469 16 3 |*48-2 7 289 | :---------------+---------------+----------------: :---------------+---------------+----------------: | 7 8 2 | 69 3 69 | 1 5 4 | | 7 8 2 | 69 3 69 | 1 5 4 | | 9 4 5 | 1 78 2 | 78 36 36 | | 9 4 5 | 1 78 2 |x78 36 36 | | 3 1 6 | 45 78 45 | 9 2 78 | | 3 1 6 | 45 78 45 | 9 2 78 | :---------------+---------------+----------------: :---------------+---------------+----------------: |#168 3 #189 | 2 #16 57-16|#457 #49 #679 | | 168 3 189 | 2 16 x57-16|x457 49 679 | | 5 26 4 | 367 9 8 |#27 36 1 | | 5 26 4 | 367 9 8 | 27 36 1 | | 126 269 7 | 356 4 156 |#25 8 369-2| | 126 269 7 | 356 4 156 | 25 8 2369 | '---------------'---------------'----------------' '---------------'---------------'----------------' skfr 7.1 ..3.5.6..4..82.3.5.5...3.7.782.3.1549451.2...316...92..3.2.....5.4.98..1..7.4..8.

(note:both techniques dont appear until after locked 78 pair in b5)

firework on 7s in r7c7b9, along with 5r7, 4c7 & 8c7 make four placements to go in four cells, all other candidates removed
in T&L this is 5 line truths but accounting for the r9c9 elimination the SDC gets it becomes 6 truths (adding in 2c7)
the SDC in comparison is 8 cell truths

so for some cases it seems, you could use this pattern to more easily get eliminations than the equivalent SDC

furthermore, this i think extends beyond just sue de coq. any ALS rule/MSLS made of cells in a row and column and of which the intersection cell is also used, will have a firework tuple/MSHS inverse. to refer back to one of the initial example puzzles, Triple Laser by Qinlux:

Code: Select all: .---------------------.-------------------.--------------------. | 123-679 4 5 |#67 #6789 #89 |#268 #189 #123-89| | 2369 2369 269 | 1 45689 4589 | 568-2 7 #2389 | | 8 169 1679 | 56-7 2 3 | 456 459-1 #149 | :---------------------+-------------------+--------------------: | 23456 2356 246 | 9 358 7 | 1 4568 #48 | | 145679 1569 14679 | 25 158 1258 | 3 45689 #4789 | | 13579 8 179 | 4 135 6 | 5-7 2 #79 | :---------------------+-------------------+--------------------: | 12469 1269 3 | 267 14679 1249 | 2478 148 5 | | 12459 7 1249 | 8 1459 12459 | 24 3 6 | | 12456 1256 8 | 3 14567 1245 | 9 14 12-47 | '---------------------'-------------------'--------------------' skfr 8.3 .45.........1...7.8...23......9.71........3...8.4.6.2...3.....5.7.8....6......9..

the MSLS is made up of 11 cell truths
the firework MSHS instead made of 5 line truths (after basics removes 3 from r9c9 then we can use 3r1 rather than a firework on 3s)
accounting for elims the MSLS gets on 7s in b2&6, we bump up to 7 line truths, still well under the MSLS's 11

this might be worthwhile for the manual solver, as large-scale SDC's and related ALS/MSLS techniques can be difficult, and cannibal eliminations are tricky also

Website · by **denis_berthier** » Sat Nov 13, 2021 4:53 am

Hi shye
None of these 3 examples is very convincing:

Code: Select all: skfr 8.9 ...4....9....8.2..8....2154..69183.......7948.....4....34..18.66......3.7.2......

Can be solved in W6

Code: Select all: skfr 7.1 ..3.5.6..4..82.3.5.5...3.7.782.3.1549451.2...316...92..3.2.....5.4.98..1..7.4..8.

Can be solved in BC3

Code: Select all: skfr 8.3 .45.........1...7.8...23......9.71........3...8.4.6.2...3.....5.7.8....6......9..

Can be solved in Z4

shye wrote:a firework always accounts for two line truths, one per row and column

It's always 3. Unless you change the definition you have given in a previous post, you must always add the block.
There's no way of proving the or3 relation without the hypothesis that there's no candidate outside the block (except in one place), i.e. that all the candidates for CSP-Variable rn (except one) are also candidates for CSP-Variable bn and same for column c.

by **shye** » Sat Nov 13, 2021 8:17 am

denis_berthier wrote:
shye wrote:a firework always accounts for two line truths, one per row and column

It's always 3. Unless you change the definition you have given in a previous post, you must always add the block.
There's no way of proving the or3 relation without the hypothesis that there's no candidate outside the block (except in one place), i.e. that all the candidates for CSP-Variable rn (except one) are also candidates for CSP-Variable bn and same for column c.

so the method i was using to make that count was T&L, and i think truths must not be inherently the same as CSP-variables. i would like to know a brief definition of what a CSP-variable is

truths and links can be defined briefly:
a truth is a selection of candidates of which at least one must be true (ie: all the positions for x in a house, or all the candidates within a cell)
a link says that at most one of a selection of candidates can be true (ie: at most one of x can be in a house, at most one candidate can be in a cell)

with this definition a firework is made up of two truths (one per line) and one link (the box) all on a single digit
since the candidate is counted twice within the intersecting cell, one from each the row and column, the box link only removes one of those two from that cell
and so the remaining positions, the intersecting cell and the positions outside the intersecting box, form a new truth because there is one more total truths than links. much like forming a strong link at the two ends of a reversible chain

hopefully that makes sense. i can assure you that my counting is correct with this method

if it matters, here is the count of total truths and links in each of the SDC vs FMSHS examples i posted above (counting locked candidates and cannibal elims for both, to be fair and account for every elimination):

...4....9....8.2..8....2154..69183.......7948.....4....34..18.66......3.7.2......
SDC = 15 (7 truths ; 8 links)
FMSHS = 14 (7 truths ; 7 links)

..3.5.6..4..82.3.5.5...3.7.782.3.1549451.2...316...92..3.2.....5.4.98..1..7.4..8.
SDC = 17 (8 truths ; 9 links)
FMSHS = 12 (6 truths ; 6 links)

denis_berthier wrote:None of these 3 examples is very convincing

the point was to show how it is more efficient to use this inverse than the equivalent SDC/ALS technique

Website · by **denis_berthier** » Sat Nov 13, 2021 9:25 am

shye wrote:i would like to know a brief definition of what a CSP-variable is

An informal one would be: any of the 324 2D-cells introduced in my extended Sudoku board (published in May 2007).

shye wrote:truths and links can be defined briefly:
a truth is a selection of candidates of which at least one must be true (ie: all the positions for x in a house, or all the candidates within a cell)
a link says that at most one of a selection of candidates can be true (ie: at most one of x can be in a house, at most one candidate can be in a cell)

"Truth" is Allan Barker's renaming of my CSP-Variables (without ever referring to them). It is a ridiculous name. In his approach (exact covers), there's no reason not to call them "Base Set".
"Link" with this definition is also a ridiculous name. In his approach, it should remain "Cover Set".
At least, he explictly writes what the standard names are: "General logic starts with the basic idea of base sets that are truths, and cover sets that are links."

shye wrote:with this definition a firework is made up of two truths (one per line) and one link (the box) all on a single digit
since the candidate is counted twice within the intersecting cell, one from each the row and column, the box link only removes one of those two from that cell
and so the remaining positions, the intersecting cell and the positions outside the intersecting box, form a new truth because there is one more total truths than links. much like forming a strong link at the two ends of a reversible chain
hopefully that makes sense. i can assure you that my counting is correct with this method

No, it doesn't make sense to add "Truths" to a pattern while trying to prove it. (And, in the present case, I can see no proof at all.)
Instead of trying to prove the or3 conclusion, try to define the pattern without mentioning the block (which is equivalent to not using CSP-Variable bn, as n is fixed).

Allan has never defined any concept of complexity for his patterns. As a result, Xsudo provides no guarantee that patterns with fewer "Truths" are found before some with more "Truths". Indeed, several counter-examples were provided at that time.
Worse, Xsudo doesn't find all the patterns with n "Truths". Said otherwise, Xsudo is not complete (and Allan unambiguously admitted this).

by **shye** » Sat Nov 13, 2021 10:56 am

ok, well naming schemes aside can we agree that for the examples i presented, the firework approach proves more efficient than its inverse (SDC/ALS)? i fear youre veering the conversation further away from the actual point with every remark

at least i think i have an idea of what a CSP-variable is now. might i ask a question then, how much CSP-variables make up a two-string kite? example below
because if it is 2, which i would expect, then i do not see why a firework must be 3. im not that bothered if you use it being 3 for your complexity scaling, but i do not understand the reasoning for it

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

9r1c9 = 9r1c23 - 9r23c1 = 9r9c1

Website · by **denis_berthier** » Sat Nov 13, 2021 12:22 pm

shye wrote:ok, well naming schemes aside can we agree that for the examples i presented, the firework approach proves more efficient than its inverse (SDC/ALS)? i fear youre veering the conversation further away from the actual point with every remark

There's nothing to agree or disagree upon as long as you haven't defined a measure of complexity. As I said, and this is right on the point, Xsudo doesn't propose one. What's yours? Are you adopting mine (nb of CSP-Variables)?

shye wrote:at least i think i have an idea of what a CSP-variable is now. might i ask a question then, how much CSP-variables make up a two-string kite? example below
because if it is 2, which i would expect, then i do not see why a firework must be 3. im not that bothered if you use it being 3 for your complexity scaling, but i do not understand the reasoning for it
Code: Select all
+-------+-------+-------+ | 8 . . | 1 2 3 | 4 5 x | | . . . | . . . | . . . | | . . . | . . . | . . . | +-------+-------+-------+ | 6 . . | . . . | . . . | | 7 . . | . . . | . . . | | 1 . . | . . . | . . . | +-------+-------+-------+ | 2 . . | . . . | . . . | | 3 . . | . . . | . . . | | x . . | . . . | . . -9| +-------+-------+-------+

9r1c9 = 9r1c23 - 9r23c1 = 9r9c1

I need no kite; the elimination is done by a generic g-whip[2] (using the same cells as the kite):
g-whip[2]: r1n9{c9 c123} - c1n9{r2 .} ==> r9c9≠9

As for your pattern, my complexity scale was not designed to measure patterns that don't produce any elimination. But your kite example has convinced me that this can be defined as 2; the block is used only for providing contradiction links.

by **shye** » Sat Nov 13, 2021 1:47 pm

denis_berthier wrote:
shye wrote:ok, well naming schemes aside can we agree that for the examples i presented, the firework approach proves more efficient than its inverse (SDC/ALS)? i fear youre veering the conversation further away from the actual point with every remark

There's nothing to agree or disagree upon as long as you haven't defined a measure of complexity. As I said, and this is right on the point, Xsudo doesn't propose one. What's yours? Are you adopting mine (nb of CSP-Variables)?

i may have mentioned it earlier in the thread, but i do not have a rigorous system for measuring the complexity of a pattern, it isnt something i really concern myself with. but for the purposes of comparing two techniques as i did above, i had to use some metric; T&L is what i know well enough, and counting the truths in each approach seemed (at least for this case) a nice way to draw that comparison. but i can tell you have your reservations towards Xsudo and its approach, so i wont continue that discussion

I need no kite; the elimination is done by a generic g-whip[2] (using the same cells as the kite):
g-whip[2]: r1n9{c9 c123} - c1n9{r2 .} ==> r9c9≠9

As for your pattern, my complexity scale was not designed to measure patterns that don't produce any elimination. But your kite example has convinced me that this can be defined as 2; the block is used only for providing contradiction links.

ok, so as far as im concerned these are equivalent (and do correct me if this is wrong, ive avoided using your terminology prior only because of lack of understanding)

a g-whip[2]/two-string kite consists of two CSP-variables/truths and one contradiction link/link
as a result of each technique, r1c9 & r9c1 contain at least one 9

if we can agree on that full statement, and that it has two CSP-variables, then i would expect the same to be valid in a firework

ill try a slight rewording. i can run the same logic on both of these example grids and get the same result:

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

in each grid, we are considering positions for 9 in row 1 and 9 in column 1, making a total of two 9s to consider
at most one 9 can be placed within b1p2347 (one of the two 9s)
so at least one of the remaining positions, marked with x's, must hold that second 9 (or potentially both of them, this is not important here)

i didnt use a third CSP-variable that i was aware of in that definition, so im unsure why it must be 3 like you say it should

im getting very tired now, ill respond to anything newly posted much later. hopefully this is clear or helpful

by **yzfwsf** » Sat Nov 13, 2021 3:28 pm

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

From a fish’s point of view, the PM grid on the left is different from the PM grid on the right. In the PM grid on the right, xr1c1 is an endo fin.

Website · by **denis_berthier** » Sat Nov 13, 2021 3:53 pm

shye wrote:
I need no kite; the elimination is done by a generic g-whip[2] (using the same cells as the kite):
g-whip[2]: r1n9{c9 c123} - c1n9{r2 .} ==> r9c9≠9
As for your pattern, my complexity scale was not designed to measure patterns that don't produce any elimination. But your kite example has convinced me that this can be defined as 2; the block is used only for providing contradiction links.

ok, so as far as im concerned these are equivalent (and do correct me if this is wrong, ive avoided using your terminology prior only because of lack of understanding)

We had this discussion already. They allow the same elimination. That doesn't mean they are the same thing. In particular, the elimination is not proven the same way.

shye wrote:a g-whip[2]/two-string kite consists of two CSP-variables/truths and one contradiction link/link
as a result of each technique, r1c9 & r9c1 contain at least one 9

I don't (want to) know how many contradiction links there are in my g-whip[2]. This is totally irrelevant to define its size (2).

shye wrote:if we can agree on that full statement, and that it has two CSP-variables, then i would expect the same to be valid in a firework

I can't see your point here. I already said I finally agreed on size 2 for your pattern.
In my quick dirty coding, I've used rows, columns, blocks, numbers - not the generic concepts. It made it look like having a bn CSP-Variable was necessary. But, after looking at it more carefully, it isn't.

With this made clear, what I'd like is examples of use that really reduce the rating of an elimination (in terms of CSP-Variables).

by **ghfick** » Sun Nov 14, 2021 12:10 am

totuan wrote:Hi shye,
Very nice find!
Someone can find many way to present the same deductions, but based on your pattern I can find deductions quite easier and faster. Your examples are very nice and I’m especially like Cobra Roll, Roman Candle V2, Pear and Rocket.
I’ll study more and thank you for your sharing!

totuan

Like totuan said, this is a very nice new technique ! I am just starting out. The very first 'Firework Triple' is available to human solvers. To get those exclusions, YZF_Sudoku offers a rather elaborate MSLS :

MSLS : 29 Cells r23456c1239+r5c456,r79c12,r46c5,r8c13,29 Links 23r2,1r3,23r4,3r6,479c1,9c2,479c3,4789c9,6b1,156b4,1258b5,1256b7
12 Eliminations:r3c8<>1,r2c7<>2,r9c9<>4,r1c1<>6,r6c37,r1c1,r5c3,r9c9<>7,r1c9<>8,r1c19<>9

The Firework Triple is far easier to spot than the MSLS or any of the ALS moves.

Bravo !

by **yzfwsf** » Sun Nov 14, 2021 1:53 am

ghfick wrote: To get those exclusions, YZF_Sudoku offers a rather elaborate MSLS :
MSLS : 29 Cells r23456c1239+r5c456,r79c12,r46c5,r8c13,29 Links 23r2,1r3,23r4,3r6,479c1,9c2,479c3,4789c9,6b1,156b4,1258b5,1256b7
12 Eliminations:r3c8<>1,r2c7<>2,r9c9<>4,r1c1<>6,r6c37,r1c1,r5c3,r9c9<>7,r1c9<>8,r1c19<>9
The Firework Triple is far easier to spot than the MSLS or any of the ALS moves.

In fact, for the same deletion, my solver also gave an ALS-XZ, which should be the complement of shye's Fire Triple. There is a technique called TSDC( Triple segments SDC) can also find this structure.

Code: Select all: Almost Locked Set XZ-Rule: A=r1c45678 {126789},B=r123456c9 {1234789}, X=12, Z=/ => r3c8<>1 r2c7<>2 r9c9<>4 r1c1<>6 r1c1<>7 r3c4<>7 r6c7<>7 r9c9<>7 r1c9<>8 r1c9<>9 r1c1<>9

I agree that this is a good discovery. I am hesitant to include it in the solver.

by **shye** » Mon Nov 15, 2021 6:36 am

denis_berthier wrote:They allow the same elimination. That doesn't mean they are the same thing. In particular, the elimination is not proven the same way.

ok, then i do not understand your notation & reasoning like i thought i did. ill probably stop trying lol

denis_berthier wrote:I can't see your point here. I already said I finally agreed on size 2 for your pattern.
In my quick dirty coding, I've used rows, columns, blocks, numbers - not the generic concepts. It made it look like having a bn CSP-Variable was necessary. But, after looking at it more carefully, it isn't.

With this made clear, what I'd like is examples of use that really reduce the rating of an elimination (in terms of CSP-Variables).

ah, my bad, i misread your initial post (thought you meant the kite pattern was size 2). sorry about that

for examples, some of my first few i posted are very difficult without the fireworks (at least with what yzf_sudoku offers)
in particular this puzzle:

Code: Select all: Roman Candle V2 (minimal) skfr: 9.2 ..98..7......6.5..4...5...37.........35...28.........68...2...4.2..7....1.6..39..

(after whips[1]) firework MSHS of size 8, one step solution

CSP-variables & eliminations: Show

yzfwsf wrote:In fact, for the same deletion, my solver also gave an ALS-XZ, which should be the complement of shye's Fire Triple. There is a technique called TSDC( Triple segments SDC) can also find this structure.

i didnt know of triple segment SDC, that sounds exactly like the complement to these small hidden sets! i didnt realise until afterwards that some SDC's didnt have an exact hidden counterpart, only when the box ALS aligned in a miniline

ghfick wrote:The Firework Triple is far easier to spot than the MSLS or any of the ALS moves.

Bravo !

happy to hear this, thank you!

by **shye** » Fri Nov 26, 2021 1:14 pm

.
some new stuff to report!
firstly, i made another puzzle:

Code: Select all: +-------+-------+-------+ | . . 5 | . . 2 | 3 7 . | | 1 . . | . 5 . | . . 4 | | 2 . . | 3 . . | . . 1 | +-------+-------+-------+ | 3 . . | 9 . . | . . 6 | | 4 . . | . . . | . 5 . | | . 1 . | . . 8 | 9 . . | +-------+-------+-------+ | . . . | . . . | . . 5 | | . . . | 8 . . | . . . | | . . . | . 4 6 | 2 1 . | +-------+-------+-------+ Kimono - shye skfr 7.7 ..5..237.1...5...42..3....13..9....64......5..1...89..........5...8.........4621. .-------------------------.--------------------.-------------------. |x689 4689 5 | 146 1689 2 | 3 7 #89 | | 1 36789 36789 | 67 5 79 | 68 2 4 | | 2 46789 46789 | 3 6789 479 | 5 689 1 | :-------------------------+--------------------+-------------------: | 3 2578 278 | 9 127 45 | 1478 48 6 | | 4 26789 26789 | 1267 12367 137 | 178 5 2378 | | 567 1 267 | 45 2367 8 | 9 34 237 | :-------------------------+--------------------+-------------------: | 6789 2346789 12346789 | 127 12379 1379 | 4678 34689 5 | | 5679 2345679 1234679 | 8 12379 13579 | 467 3469 379 | |x89-57 35789 3789 | 57 4 6 | 2 1 x3789 | '-------------------------'--------------------'-------------------'

original post

this was made to be a simpler version of Hanabi. it can be thought of with the same "firework exocet" type viewing, but is probably easier in this s-wing-like form:
8r9c1 = 8r1c1&8r9c9 - (8=9)r1c9 - 9r1c1&9r9c9 = 9r9c9
=> -57r9c1
solves with a turbot fish

i thought since exocet is rather complicated/has a lot of situational eliminations, i would try to give a less jargon-filled explanation of both of these puzzles. starting with Kimono
the main idea is that whatever is placed in r1c9 (our base cell) that digit will be placed in r9c1 (the target) because each candidate in the base has a weak link to all but one of the firework candidates
so if its an 8, say, then 8 in column 1 and row 9 become limited to the intersecting box, and therefore takes the intersecting cell (and same with 9)

for Hanabi its the same idea just with more moving parts

Code: Select all: .---------------------.-----------------.----------------. | x689 1 2 | 46-9 7 4689 | 3 5 B89 | | 3 589 569 | 2 69 1 | 4 89 7 | | 4 789 79 | 5 3 89 | 2 1 6 | :---------------------+-----------------+----------------: | 2 59 359 | 3469 169 4569 | 589 7 1589 | | 1 6 3579 | 379 8 579 | 59 4 2 | | x579 4 8 |B79 129 2579 | 6 3 15-9 | :---------------------+-----------------+----------------: | 5679 3 1 | 8 269 2679 | 579 69 4 | | 6789 2 4 | 1 5 679 | 789 689 3 | |xT789-56 5789 5679 |x679 4 3 | 1 2 x589 | '---------------------'-----------------'----------------'

there are two base cells now, r1c9 and r6c4
the candidates of which align with the fireworks 789r9c1b7 suspiciously

lets graph out the combinations of these cells to get a better picture of how they work

Code: Select all: 8r1c9 ------ 9r1c9 -> 8r9c1 | | | | 7r6c4 ------ 9r6c4 -> 7r9c1 | | v v 7r9c1 & 9r9c1 8r9c1 contradiction

in each combination, a value of [789] is placed in r9c1, because the appropriate firework is reduced to one position left
=> -56r9c1
for one of those combinations, 8r1c9 & 7r6c4, it suggests that r9c1 has to hold two candidates which is a contradiction
so there are only 3 working combos, and all of them require either 9r9c1 or 9r6c4, which is a strong link between those candidates
=> -9r1c4, -9r6c9

the remaining eliminations in these puzzles can then be done with 2-string kites (turbot fish)
for neatly tying these pieces together you can consider all possible fireworks in the lines of the f-exocet and then anything incompatible with the bases will lead to kites

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