The New Sudoku Players' Forum

[blue]

Here's something that dobrichev kept around, from the old Programmer's Forum.

Below is a copy-paste with nested quotes as closer as possible to the original thread from the programmers forum. Some links are broken, some point to this forum and work.

Thanks Mladen.
---

This is a follow up to a post in this thread, where I wrote:

There are also 137 grids where all 18 2-row and 2-column UA18 are minimal.
I don't know if that list has been published.

In 2005, Red Ed published the complete list of 127 grids where all 36 2-digit UA18 are minimal.
There are 15 grids that appear in both lists.
This is one of them:

Code: Select all

123456789456789231789123645231564897564897312897231456375618924618942573942375168   


These are the 137 grids where all 2-row and 2-column UAs, are (minimal) UA18s.

Code: Select all

    123456789456789231789123645231564897564897312897231456375618924618942573942375168
    123456789456789231789123645231564897564897312897231456375942168618375924942618573
    123456789456789231789123645231564897564897312978312564395248176617935428842671953
    123456789456789231789123645231564897564897312978312564395671428617248953842935176
    123456789456789231789123645231564978564897123897231564375942816618375492942618357
    123456789456789231789123645231564978564897123897312456348671592672935814915248367
    123456789456789231789123645231564978564897123897312456375941862618275394942638517
    123456789456789231789123645231564978564978312978231456395617824617842593842395167
    123456789456789231789123645231564978564978312978231456395842167617395824842617593
    123456789456789231789123645231564978645897312897312456368275194572941863914638527
    123456789456789231789123645231564978645897312897312456368941527572638194914275863
    123456789456789231789123645231564978645897312978231456367915824592348167814672593
    123456789456789231789123645231564978645897312978231456394618527517942863862375194
    123456789456789231789123645231645897564978312897312456375294168618537924942861573
    123456789456789231789123645231645897564978312897312456375861924618294573942537168
    123456789456789231789123645231645897564978312978231456347592168692814573815367924
    123456789456789231789123645231645897564978312978231456395862174617394528842517963
    123456789456789231789123645231648597564972318897315426375291864618534972942867153
    123456789456789231789123645231678594564912378897345126348567912672891453915234867
    123456789456789231789123645231897456564231897978645123347518962692374518815962374
    123456789456789231789123645231897456564231897978645123347962518692518374815374962
    123456789456789231789123645231897564564231978978564312347915826692348157815672493
    123456789456789231789123645231897564564312897897645312375961428618274953942538176
    123456789456789231789123645231897564645231897897645312374518926518962473962374158
    123456789456789231789123645231978456564312897897645312375294168618537924942861573
    123456789456789231789123645231978456645231897978564312367815924592347168814692573
    123456789456789231789123645231978456645231897978564312394617528517842963862395174
    123456789456789231789123645234561897567894312891237456372945168615378924948612573
    123456789456789231789123645234561978567894123891237564372945816615378492948612357
    123456789456789231789123645234561978568974312971238456392845167615397824847612593
    123456789456789231789123645234567918567891423891234567372615894615948372948372156
    123456789456789231789123645234567918567891423891234567372948156615372894948615372
    123456789456789231789123645234578916568931472971264358345892167697315824812647593
    123456789456789231789123645234578916568931472971264358392817564615342897847695123
    123456789456789231789123645234597168567831924891264573345972816678315492912648357
    123456789456789231789123645234597168567831924891264573372918456615342897948675312
    123456789456789231789123645234597816567831492891264357345972168678315924912648573
    123456789456789231789123645234597816567831492891264357372918564615342978948675123
    123456789456789231789123645234615897567948312891372456345297168678531924912864573
    123456789456789231789123645234675918567918423891342567372561894615894372948237156
    123456789456789231789123645234675918567918423891342567372894156615237894948561372
    123456789456789231789123645234975168567318924891642573345261897678594312912837456
    123456789456789231789123645234975168567318924891642573345297816678531492912864357
    123456789456789231789123645234975168567318924891642573372594816615837492948261357
    123456789456789231789123645235817496817964352964235817392578164578641923641392578
    123456789456789231789123645235817964817964523964235178392578416578641392641392857
    123456789456789231789123645235964178817235964964817523392641857578392416641578392
    123456789456789231789123645235964817817235496964817352392641578578392164641578923
    123456789456789231789123645237561894561894372894237156342675918675918423918342567
    123456789456789231789123645237561894561894372894237156342918567675342918918675423
    123456789456789231789123645237918456561342897894675312342597168675831924918264573
    123456789456789231789123645237918456561342897894675312378561924612894573945237168
    123456789456789231789123645237945168561378924894612573342561897675894312918237456
    123456789456789231789123645237945168561378924894612573378291456612534897945867312
    123456789456789231789123645237945168561378924894612573378561492612894357945237816
    123456789456789231789123645238514976514697823697238514362845197845971362971362458
    123456789456789231789123645238514976514697823697238514362971458845362197971845362
    123456789456789231789123645238514976514697823697238514375861492861942357942375168
    123456789456789231789123645238514976514697823697238514375942168861375492942861357
    123456789456789231789123645238697514514238976697514823375861492861942357942375168
    123456789456789231789132546234567918567891423891324657372615894615948372948273165
    123456789456789231789132546234675918567918423891243657372561894615894372948327165
    123456789456789231789132546237615894561948372894273165342567918675891423918324657
    123456789456789231789132546241568973675391824938247165317924658562813497894675312
    123456789456789231789231564231897456564312897978645312347168925692573148815924673
    123456789456789231789231564231897456645123978978645312367914825592368147814572693
    123456789456789231789231564231897645645312978897645312368924157572168493914573826
    123456789456789231789231564234867195518943627697512843372695418861374952945128376
    123456789456789231789231564234895617518627943697143852375918426862374195941562378
    123456789456789231789231564267394815348517926591628347672943158834175692915862473
    123456789456789231789312456231564897564897312978231645347925168692148573815673924
    123456789456789231789312456231564897564897312978231645395628174617943528842175963
    123456789456789231789312456231564978564978312978123564347691825692835147815247693
    123456789456789231789312456231564978564978312978123564395841627617295843842637195
    123456789456789231789312456231564978645897312897231564368925147572148693914673825
    123456789456789231789312456231564978645897312897231564374628195518943627962175843
    123456789456789231789312456231567948567948312948123567374891625615274893892635174
    123456789456789231789312456231567948567948312948123567395671824672834195814295673
    123456789456789231789312456231568974568974312974123568345691827692837145817245693
    123456789456789231789312456231568974568974312974123568397841625615297843842635197
    123456789456789231789312456231578964578964312964123578347891625615247893892635147
    123456789456789231789312456231578964578964312964123578395641827642837195817295643
    123456789456789231789312456231597648597648312648123597364971825815264973972835164
    123456789456789231789312456231597648597648312648123597375861924862934175914275863
    123456789456789231789312456231645978645978312978123645367591824592834167814267593
    123456789456789231789312456231645978645978312978123645394861527517294863862537194
    123456789456789231789312456231648975648975312975123648364591827592837164817264593
    123456789456789231789312456231678945678945312945123678367891524514267893892534167
    123456789456789231789312456231678945678945312945123678394561827562837194817294563
    123456789456789231789312456231897564564123897978645123347268915692571348815934672
    123456789456789231789312456231897564564123897978645123395274618617538942842961375
    123456789456789231789312456231897645645123897897645312368571924572934168914268573
    123456789456789231789312456231978564564123978978564312347691825692835147815247693
    123456789456789231789312456231978645645123978978645312367591824592834167814267593
    123456789456789231789312456247168593691573824835924167368247915572691348914835672
    123456789456789231789312456247591368691834572835267914368925147572148693914673825
    123456789456789231789312456247693518538147692691528347375861924862934175914275863
    123456789456789231789312456247693815691825347835147692368571924572934168914268573
    123456789456789231789312456247963518538147962961528347395671824672834195814295673
    123456789456789231789312456248673915671925348935148672367591824592834167814267593
    123456789456789231789312456267593148348671592591824673672935814834167925915248367
    123456789456789231789312456274195863538627194961843527395274618617538942842961375
    123456789456789231789312456274861395538294617961537842395628174617943528842175963
    123456789456789231789312456274963518538174962961528374395841627617295843842637195
    123456789456789231789312456275943618638175942941628375394861527517294863862537194
    123456789456789231789312456294638175375194862618527394537941628861275943942863517
    123456789456789231798213645235894176841627953967135428384962517579341862612578394
    123456789456789231798213645249671853675938412831524976362845197587192364914367528
    123456789456789231798213645271364958364895127985172364512647893647938512839521476
    123456789457289163689173452231597846765834291894621537378915624516342978942768315
    123456789457289163689173452234968517516734928978512634365897241741325896892641375
    123456789457289163689173452235741896816392574974568231392817645568924317741635928
    123456789457289163689173452235964817816735924974812635392641578568397241741528396
    123456789457289163689173452238514697564397821791628345376945218815762934942831576
    123456789457289163689173452241968537365724918978315246534897621716532894892641375
    123456789457289163689173452245968317316745928978312645564897231731524896892631574
    123456789457289163689173452294618375365794821718532694536947218871325946942861537
    123456789457289163689713254235967841716348925894521376362895417578134692941672538
    123456789457289163689713254261374895395861427874592631538127946746938512912645378
    123456789457289163689713254278341695316925478945867312564192837792638541831574926
    123456789457289163698137524249875631536921478871364952364592817712648395985713246
    123456789457289163698317254235891476741632895986574312379145628564728931812963547
    123456789457289163698317254239168547765924318841735692374691825512843976986572431
    123456789457289163698317254245891376781632495936574812379145628564728931812963547
    123456789457289163698317254281574396735692418946831572369725841512948637874163925
    123456789457289163698317254284563971539174628716928435365791842841632597972845316
    123456789457289163698317254284691375539872416716534892365748921841925637972163548
    123456789457289163869713245231875496648392517795164328386521974572948631914637852
    123456789457289163869713245231964578594837621786521394378142956642395817915678432
    123456789457289163869713245298361574315874692674592831536927418742138956981645327
    123456789457289163896317245231645978745892631968731524379124856582963417614578392
    123456789457289163896317245285693471641875932739142658312564897574928316968731524
    123456789457289631869713245236594817578162394914378526345927168691835472782641953
    123456789457289631896317245249635817368172594715948326531864972682791453974523168
    123456789457289631896317245249731568635892174781645392312974856574168923968523417
    123456789457289631896317245285731964641892573739645812312578496574963128968124357
    123456789457289631968731245241573896639812457785964123374625918596148372812397564


These are the 15 grids appear in both lists.

Code: Select all

   123456789456789231789123645231564897564897312897231456375618924618942573942375168
    123456789456789231789123645231564897564897312897231456375942168618375924942618573
    123456789456789231789123645231564897564897312978312564395248176617935428842671953
    123456789456789231789123645231564897564897312978312564395671428617248953842935176
    123456789456789231789123645231564978564897123897231564375942816618375492942618357
    123456789456789231789123645231564978645897312897312456368275194572941863914638527
    123456789456789231789123645231564978645897312897312456368941527572638194914275863
    123456789456789231789123645231645897564978312897312456375294168618537924942861573
    123456789456789231789123645231645897564978312897312456375861924618294573942537168
    123456789456789231789123645231897456564231897978645123347518962692374518815962374
    123456789456789231789123645231897456564231897978645123347962518692518374815374962
    123456789456789231789123645231978456564312897897645312375294168618537924942861573
    123456789456789231789123645234615897567948312891372456345297168678531924912864573
    123456789456789231789123645234975168567318924891642573345261897678594312912837456
    123456789456789231789123645237945168561378924894612573378561492612894357945237816

The grids are in minlex form.

In the two big lists, most of the grids have (non-trivial) automorphisms.
[ 78 from the list of 127, and 123 from the list of 137 ]
In the intersection, every grid has automorphisms.

Good job, blue.

It would be interesting to compare the estimated number of puzzles in these 15 monster grids to the average number of puzzles in a random grid.
On the one hand, intuitively the automorphism trends to lower puzzle count. On other hand, the low number of short-sized UA trends to higher puzzle count.

It would be interesting to compare the estimated number of puzzles in these 15 monster grids to the average number of puzzles in a random grid.
On the one hand, intuitively the automorphism trends to lower puzzle count. On other hand, the low number of short-sized UA trends to higher puzzle count.

In this posting, Red Ed proposed a way to estimate the number N of valid puzzles in a solution grid.
This number N is such that : N = P * 2^81
P is estimated by simulation.
For all the 6.67*10^21 grids, the average value of P is 0.36

Here are the estimated value of P for the 15 "monster grids" :

Code: Select all

123456789456789231789123645231564897564897312897231456375618924618942573942375168   0.684
123456789456789231789123645231564897564897312897231456375942168618375924942618573   0.686
123456789456789231789123645231564897564897312978312564395248176617935428842671953   0.664
123456789456789231789123645231564897564897312978312564395671428617248953842935176   0.666
123456789456789231789123645231564978564897123897231564375942816618375492942618357   0.686
123456789456789231789123645231564978645897312897312456368275194572941863914638527   0.668
123456789456789231789123645231564978645897312897312456368941527572638194914275863   0.667
123456789456789231789123645231645897564978312897312456375294168618537924942861573   0.685
123456789456789231789123645231645897564978312897312456375861924618294573942537168   0.685
123456789456789231789123645231897456564231897978645123347518962692374518815962374   0.667
123456789456789231789123645231897456564231897978645123347962518692518374815374962   0.666
123456789456789231789123645231978456564312897897645312375294168618537924942861573   0.686
123456789456789231789123645234615897567948312891372456345297168678531924912864573   0.704
123456789456789231789123645234975168567318924891642573345261897678594312912837456   0.704
123456789456789231789123645237945168561378924894612573378561492612894357945237816   0.694

JPF

Average of 0.36 means 36% of all possible combinations of givens/non-givens result in a single-solution, not necessarily minimal puzzle, OK?

Definitely the leak of short-sized UA dominates.

Grids with more valid (non-minimal) puzzles must have slightly smaller average number of clues in their minimal puzzles. Are there some estimations?

What about these 4 grids having only 3 U4 + U6?

Code: Select all

123456789456789132789213645275941368638527914941638257394175826517862493862394571
123456789456789231789231564234968175867125493915374826348617952592843617671592348
123456789456789231789231564218593647347628195695174823531962478864317952972845316
123456789456789231798213645239174856574628913681395427367841592815962374942537168   


MD

Definitely the leak of short-sized UA dominates.

This is the probability that an unavoidable set is unhit - the mcn will be relevant...... and most of the puzzles will be non-minimal - as you state.

i think there are better ways to estimate the number of minimal puzzles [eleven estimated that there were x10 more minimal puzzles in the SFB grid than the MC grid ] [SFB grid is the only one of Red Ed's 127 "Vipers" which has a 17-puzzle]

C

Average of 0.36 means 36% of all possible combinations of givens/non-givens result in a single-solution, not necessarily minimal puzzle, OK?

Yes.

What about these 4 grids having only 3 U4 + U6?

Code: Select all

123456789456789132789213645275941368638527914941638257394175826517862493862394571   0.719
123456789456789231789231564234968175867125493915374826348617952592843617671592348   0.721
123456789456789231789231564218593647347628195695174823531962478864317952972845316   0.690
123456789456789231798213645239174856574628913681395427367841592815962374942537168   0.658

JPF

Thank you.

The second one has none U4 and the following U6

Code: Select all

{31,32,51,52,91,92}
{34,36,54,56,94,96}
{52,54,59,62,64,69}   

Note that only the first 2 are disjoint, the third intersects first two at r5c2 and r5c4.

[champagne]

I was thinking of searching all 18 with 2 clues in a band.

In fact, I wanted to have a direct proof that no 17 exists with 2 clues in a band, something implicitly accepted by blue based on the results of other investigations.
Is it something already done??? (not as an indirect effect of all the invalid crossing patterns)

As the start can only be one of the 416 band patterns, this is an interesting case to study. The best code in this case could be significantly different from the 17 search " as of blue "

[blue]

I was thinking of searching all 18 with 2 clues in a band.

In fact, I wanted to have a direct proof that no 17 exists with 2 clues in a band, something implicitly accepted by blue based on the results of other investigations.
Is it something already done??? (not as an indirect effect of all the invalid crossing patterns)

I did check for 17's with 2 clues in a band, in the confirmation that I reported here.

[coloin]

I was thinking of searching all 18 with 2 clues in a band.

In fact, I wanted to have a direct proof that no 17 exists with 2 clues in a band, something implicitly accepted by blue based on the results of other investigations.
Is it something already done??? (not as an indirect effect of all the invalid crossing patterns)

As the start can only be one of the 416 band patterns, this is an interesting case to study. The best code in this case could be significantly different from the 17 search " as of blue "

and also it was shown that there were 18-puzzles which had 2 clues in a band
here
using serg's patterns it proved there could not be a 17 with 2 clues in a band

[champagne]

Hi Coloin,
your link is what I had in mind.
You show 2 examples of 18 clues with 2 bands, I drafted some code as a variant of the 17 clues search, it seems feasible to code a full scan knowing that only one of the 416 bands can produce a band with 2 clues.
As this band has isomorphisms, the collection of bands 2 is relatively small.

[champagne]

and also it was shown that there were 18-puzzles which had 2 clues in a band
here

from preliminary investigations, it seems that a 18 clues with 2 clues in a band must have a distribution 279 or 288. Your link shows both cases

[coloin]

Yes its not that clear !
Sergs invalid patterns showed

Code: Select all

+-----+-----+-----+
|. . .|. x x|x x x|
|. . .|. x x|x x x|
|. . .|. x x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+
and also
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|. . .|x x x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+
|. . .|. x x|. x x|
|. . .|. x x|. x x|
|x x x|. x x|. x x|
+-----+-----+-----+
and also
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|. . .|x x x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+
|. . .|. , x|x x x|
|. . .| . .x|x x x|
|x x x| . .x|x x x|
+-----+-----+-----+  are invalid

Code: Select all

029   099  099
199   199  199
199   122  119  are invalid

therefore
033
199
199 is needed

these distributions with 18 clues have valid puzzles

033 033
123 132
132 132

these cannot bed rerduced to 17 clues because

Code: Select all

099   029   099   099
099   199   199   199
199   199   122   119  are invalid

[champagne]

Yes its not that clear !
......
these distributions with 18 clues have valid puzzles

033 033
123 132
132 132

My first draft of code just showed that with a first band having 2 clues, the second band could not produce a "valid bands 1+2" with less than 7 clues. Knowing that we had no 17 clues having a band with 2 clues, it could only be 279 or 288.

But this was some fresh code, so it's good to have another view.
I am now drafting the band 3 process (derived from the ongoing 17 search 665 code).

EDIT: The 9 ED valid bands with 2 clues have the 2 clues in different boxes. This fits with your table.
EDIT2: in your table, the "stacks" (stack if the 2 clues are in band 1) have all 6 clues, but this is not established on my side, I can not use this property.

[champagne]

Hi coloin,
you wrote

and here is one example of a puzzle of the first pattern

Code: Select all

+---+---+---+
|...|...|2..|
|...|498|...|
|...|...|.15|
+---+---+---+
|...|9..|...|
|...|.52|...|
|.8.|...|.36|
+---+---+---+
|...|.8.|59.|
|...|...|...|
|2..|..6|..7|
+---+---+---+  18 clues

and here is one example of a puzzle of the second pattern

Code: Select all

+---+---+---+
|...|...|...|
|...|345|...|
|...|...|671|
+---+---+---+
|...|9..|...|
|...|.16|...|
|.2.|...|.84|
+---+---+---+
|...|4..|.9.|
|...|.27|...|
|1..|...|..5|
+---+---+---+  18 clues

I have now more than 50 18-puzzles with these 2 patterns .....

====================

The draft to search the 18 with a band having 2 clues is now ready to be tested.
I would be glad to get your file to check the code

BTW this task reactivated an old dream which was to have an alternative process to search the 17 clues using mainly minimal solutions for a band/2bands instead of the full expansion done in blue's design.

Things seen preparing this draft could produce a very efficient process.

[coloin]

Glad to help ..... spurred me to find them in my files... and make a few more ..... hope 20 is enough [ out of 103 made]

EDIT - here is the 103 for the record as it was never posted !

EDIT More - added the 8 found by champagne

TOTAL 111 puzzles

Code: Select all

1...........2......................7..38....46...5...9.8..9.1..7...1.6...2.3..5..
1...........2......................7.3.8....46...5...9.8..9.1..7...1.6...2.3..5..
1...........2......................7.4.5....86...1...2.8..9.4...7.8..3....9..65..
1...........2......................73....4..96..8....2..4..18...7..3.6...2..9.5..
1...........2......................73...1...46...5...2.8..9.1...7.4..3...2.8..5..
1...........2......................73...1...9..28....6..4.9.3..7...3.1....84..5..
1...........2......................73...1..8.6..8....2..4.9.3...7..3.1...2.7..5..
1...........2......................73...4...66..8....2..4.9..8..7...1.9..2...7.1.
1...........2......................73...4...96..8....2..4.6.8...7...16...2...95..
1...........2......................75...1...46...3...2.8..9.1...7.8..3...2.4..5..
1...........2......................75...1...46...5...2..74..1....28..3....8.9.5..
1...........2......................75...1...46...5...2.8..9.1...7.8..3...2.7..5..
1...........2......................75...1...46...5...2.8..9.5...7.8..3...2.4..1..
1...........2......................75...1...46...5...2.8..9.5...7.8..3...2.7..1..
1...........2......................75...1...46..3....2.8..9.5....28..6....7.5.1..
1...........2......................75...3...4..69....8.2..4.1...8.6..3..7...1.5..
1...........2......................75...3...4..69....8.2..4.1...9.6..3..7...1.5..
1...........2......................75...3...46...1...2.8..9.1...2.8..3...7.4..5..
1...........2......................85...1...46...3...2.8.6..1...7..4.3...2.9..5..
1...........2......................93...1...6..28....4..4.9.3...2..3.1....87..5..
1...........2......................93...1...6.7.8....4.4..9.3....8.3.1...2.7..5..
1...........2......................95...1...76...5...2..8.4.1....98..3....27..5..
1...........2......................95...1...76...5...2.8..4.1...2.8..3...9.7..5..
1...........2......................99...1...4..3.5...6.4..9.1...7.8..3...2.6..5..
1...........2.....................8.5..9...2.3...1..4..8..3.1....9.6.3...2.7..5..
1...........2.....................9.3...1..8...65...4...4.9.3...7...31....27..5..
1...........2.....................9.3...1..8...75...4...4.9.3..7....31....27..5..
1...........2....................9..5...1.8..6...5...3..3.6...5..98...2...27....4
1...........2...................82..5...1.8..6...4.9...8.....1...7.6...4.2.7....3
1...........2..................3...78...1...2.9...8..6..3...1....74..3...2.7..5..
1...........2..................4...27...1...46...5...9.5....1...4.8..3...2.7..5..
1...........2..................7.3....49..8...2.4..9..3...1..5.7...6..2...5....4.
1...........2..................7.3....49..8...2.4..9..3...1..5.7...6..2...9....4.
1...........2..................7.3....49..8...2.5..9..3...1..4.7...6..2...9....5.
1...........2..................8..2.7..3..8..6...5.9....8.1...5.5......4..27....1
1...........2................2.3...9..3.1...4.9...8..64..9..1........3...8.7..5..
1...........2................26....1..4.1...3.6..5...73...7..9.7..8...2........4.
1...........2................26....1..4.1...3.8..5...73...7..9.7..8...2........4.
1...........2................3.6.2..4...1.8..6...5.9..........5..98....4..27....1
1...........2................3.6.2..5...1.8..6...5.9..........5..98....4..27....1
1...........2................3.7.2..4...1.8..6...5.9...8.3....1..28....4........7
1...........2................4....8.5...1..6.6...5..7...24..1....98..3......3.5..
1...........2................4.6.2....25..8..6...3.9..........5..98....43....1..7
1...........2................4.6.2....25..8..6...3.9..........5..98....43...1...7
1...........2................6.1...2..5.3...4.4...9..8.7.5..1........3...8.6..5..
1...........2................67....2..5..4..64....9..8......7..9...1.3....26..5..
1...........2................7....8.5...1..6.6...5..4...27..1....98..3......4.5..
1...........2................7....8.5...1..6.6...5..4...27..1....98..3......6.5..
1...........2................8.....95...1...36...5...2..29..1....98..4......7.5..
1...........2................8.....95...1...46...5...2..29..1....98..3.......45..
1...........2................87..2....4.1.8..6...5.9..3....6..5..28....4........7
1...........2................87..2....4.1.8..6...5.9..3...6...5..28....4........7
1...........2................89....75...1...4........6.8..5.1....28..3....7.6.5..
1...........2................89....75...1...4........66...5.1...2.8..3...9..4.5..
1...........2................89....75...1...4........66...5.1...9.8..3...2..4.5..
1...........2...............3......75...1...49...6...2....9.5....78..3...2.7..8..
1...........2...............3..6...79...1...4..7..9..24...9.6........3...2.7..5..
1...........2...............3..6.2..5...1.8..6...5.9..........5.2.8....4.9.7....1
1...........2...............3..8...79...1...4.7.5....28...9.6........3...2.7..5..
1...........2...............4....9..5...1.8..6...5.2......6...5..98....4..27....1
1...........2...............4...9..8..5.1...46...5...2.8.3..1...7.6..3........5..
1...........2...............4..7.2..5...1.8..6...3.9...8.4....7........4.2...8..5
1...........2...............4..7.2..5...1.8..6...3.9...8.4....7........4.2...9..5
1...........2...............5..8...79...1...4.7.3....28...9.6........3...2.7..5..
1...........2...............8...3..6..2.1...7....5...43.....1....98..3..4..7..5..
1...........2...............8..7.2..5...1.8........9..3..6....1..98....4.4..5...7
1...........2...............8.9....75...1...4........64...5.1...9.8..3...2..6.5..
1...........2...............9.3....7........46...1...58....61...2.8..3...7..4.6..
1...........2..............3...7.2..5...1.8....4...9......5...3..98....4..29....6
1...........2..............3...7.2..5...1.8....6...9......5...3..98....4..29....6
1...........2..............3..9....75...1...4.9...8..6.8..5.1........3...2.7..5..
1...........2..............8...1.2..4....53....7..39..........5..98....4..27....1
1...........2..............9...6...7.2.3....4.5..1...28...9.6........3...7.4..5..
1...........2..............9...8...7.2.3....4.5..1...28...9.6........3...7.4..5..
1...........4......................73...1...9..68....2..4.9.3..7...3.1....86..5..
1...........4......................79...1...46...5...2.8..9.6...7.6..3....47..8..
1...........4......................97...1...49...5...2.8..9.7....48..3...2.7..6..
1...........4................8.....75...1...46...5...2....9.6....28..3...4.7..8..
1...........4...............2......75...1...46...5...2....9.6...7.8..3....47..8..
1...........4...............2......79...1...46...5...2....9.6...7.8..3....47..8..
1...........4...............4.2...6.3...1..8........9..7..9.3..8...3.1...2.7..5..
1...........4...............8......75...1...46...5...2....9.6...7.8..3....47..8..
1...........4...............8......79...1...46...5...2....9.6...4.8..3...2.7..8..
1...........4...............8......79...1...46...5...2....9.6...7.8..3....47..8..
1...........4..............3...6...95...1...4........2.8..9.7....48..3...2.7..5..
1...........8...............4...9..7..3.1...4..6.5...8.2.3..1...7.6..3........5..
1...........8...............9...4..75...1...47....3..2.8.9..1........3...6.7..5..
3...........2......................75...1...96...3...2.8..9.1...7.6..3...2.4..5..
3...........2...............2.9....75...1...4.....5..6.8.7..1....9...3..6...3.5..
3...........2...............8......75...1...46...3...2....9.1...7.8..3...2.7..5..
3...........2..............4...3...75...1...4.9......6....5.1...8.6..3...2.9..5..
4...........2......................73..1....4..69....8.2..4.1...8..7.3....1..65..
4...........2.................8....75...3...4..69....1.2..4.3...8....9...7..1.5..
5...........2......................73...1...46..8....2..4..73...7..9.1...2...56..
5...........2................1.....73...1...96...5...8..46..3.......91...2.7..5..
5...........2...............9......73...1...86...5...2....9.1...7.8..3...2.4..5..
5...........2..............3....5..77...1...4.9......6.8.6..1......7.3...2.9..5..
5...........2..............3...5...77...1...4.9......6.8.6..1......7.3...2.9..5..
6...........2..............3..9....25...1...4........8.8..7.1....4..83...2...65..
7...........2..............8.......75..1....4.6.9....8.2..4.1....1.7.3.......85..
9...........2......................75...1...46..3....2..1.9.8...7...43...2...56..
9...........2................28....75...1...4........6.8..9.1....6.4.3...2.7..9..
9...........2................31....7........46....8..2.8..9.1....7..63....47..5..[

.....6..............9........7..8.5..6...3.4.......1..3...1.6....5.9...8.4.5....7
........9..............1....1...4...3....2..8.9......65..6..3....29...1...8.7..4.
........9..............1....1...4...3....7..89.......6..29...1...7.2..4.8..6..3..
.....6..............9.......3...7.5........1...8..2.9...41....8.1.9..6...7..4...3
.....6..............9.......3...7.5........1...8..2.9...21....8.1.9..6...7..4...3
......7..............2.....2...4...55....3.....8.7.1...1.8..9...6.5....2.7.....4.
..3......................6.2....5.9......8..2..73...4.5...2......4.9...39...6...8
....5..............8........3......8.6..1...3..7.6...2...9..4....2..8.9...5..3.1.

[champagne]

thanks a lot coloin, this is ok to start tests.
The entire file later would be a bonus to have a better chance to cover more cases in the process.
The band 3 process, as in the 17 clues search, has many branches depending on the count of clues forced by GUAs 2 and GUAs 3

[coloin]

Of course this 2 clues in a band is on topic ( I thought it was off-topic)
The 2 clues are needed to simultaneously solve the 3 x 18 clue 2-clue UAs ... and only 9 combinations of 2 clues do this.

Maybe your program will find all the 2plus18 puzzles ....they are remote puzzles .... one I saw had no other puzzle within (-2+2) !
I will try to find more meanwhile....

And yes .... there isn’t a valid 17-puzzle with 2/6/9 in the bands .... as I’m sure 2/6/27 is easy to prove invalid - as it is also proved with serg’s Patterns .... With 2 clues in the first band ... the 2nd and 3rd bands have to have 2 clues in every box in the band plus a 3 ( ie 7 or more )

My understanding of the 17 clue search still to do is that the puzzle has to have (566/566) in the bands .... hope we get the answer soon !

[champagne]

And yes .... there isn’t a valid 17-puzzle with 2/6/9 in the bands .... as I’m sure 2/6/27 is easy to prove invalid - as it is also proved with serg’s Patterns .... With 2 clues in the first band ... the 2nd and 3rd bands have to have 2 clues in every box in the band plus a 3 ( ie 7 or more )

In fact, and this is part of the fresh ideas brought in this draft, locking band 1 with 2 clues, if you consider UAs for bands 1+2 with only one mini row left in band 2, any possible band 2 shows a minimum of 7 clues required (with my collection of UAs bands 1+2 " as in the 17 clues search)

My understanding of the 17 clue search still to do is that the puzzle has to have (566/566) in the bands .... hope we get the answer soon !

depends what is soon... Next milestone should come in some days, with around 6% of the solution grids covered. With available power on my side, this would still be 2/3 years of work.

What I wrote above will bring hope for a significant improvement with low clues count (more blue's part 1). I don't know what is the potential for improvement in the 665 distribution. If the results are promising, a new version could come end of this year.

[champagne]

Hi coloin,
The first lot (20 solution grids) had been searched successfully in 1.3 seconds with eight cores working in parallel.
This is in line with my estimate of 6 bands 1+2 per second in the same conditions for the entire search.
Having around 300 000 bands 1+2 to search, this means that the full scan should be solved in one( core x day).
But I have still tests to do before the start.
Could you send the other known 18 in your files

[champagne]

Hi coloin,
I run your 103 and could reproduce them (plus 6 morphs).
I started a generation test and I'll see to-day what branches have been used.
many thanks

EDIT from the first slices processed, I am not expecting many more such 18. the answer for the current code should come within one day