The New Sudoku Players' Forum

by **champagne** » Tue Apr 01, 2025 8:20 am

This seems to me closer to what did blue.

If my remark is correct, there must be a morphing process leading from a min lex solution grid to the "magic corner" of the loki family.
This would help to see if a new high belongs to the family, but up to now, I don't have it.

The "vicinity" applied to the new high has good chances to find a bridge to the family if it is one member,
but it also should deliver many new highs

by **champagne** » Tue Apr 01, 2025 1:05 pm

Some doubts going back reading this post of Blue

http://forum.enjoysudoku.com/tridagon-t45572-30.html
"champagne"
Asssuming that a tridagon pattern in the solution is the following

Code: Select all
..x x..
.x. .x.
x.. ..x

x.. x--
.x. -x-
..x --.

where the last digit on the pattern in the last box is anywhere but not in the last cell
"blue"
Nothing to add to this,
this is by far the most common final status in mith's file

I counted these too:

Code: Select all
..x x..
.x. .x.
x.. ..x

x.. x--
.x. -.-
..x --x

mith's list has 2,113,220 puzzles of the first type, over 28026 "starts", and 1,629,623 puzzles of the 2nd type, over 19937 "starts".
FWIW: By big list, has 2,146,660,838 "starts" of the first type (on 1,508,823,488 solution grids), and 821,671,928 of the 2nd type (on 744,278,570 solution grids).
The grid that I listed 24 puzzles/"starts" for, has 17 of first type, and 7 of the 2nd.

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

I have doubts that the "vicinity" search can switch from the first to the second pattern. One possibility is that mith's file is already done of several seeds

by **coloin** » Tue Apr 01, 2025 8:47 pm

Yes those x refer to the diagonal 123 clues ...which are not in the puzzle ...apart from in Box9

champagne wrote:there must be a morphing process leading from a min lex solution grid to the "magic corner" of the loki family.

However the 456789 clues in the "magic corner" [B1B2B4] can be standardised thanks to gsf ....

Code: Select all: +---+---+---+ |49.|.65|7..| |7.5|9.8|...| |.86|74.|5..| +---+---+---+ |.54|..6|...| |8.9|4.7|.6.| |67.|...|...| +---+---+---+ |...|8..|...| |...|..9|.21| |...|...|.5.| +---+---+---+ Morph of Loki expand 49..657..7.59.8....8674.5...54..6...8.94.7.6.67..........8..........9.21.......5. # 49..65...7.59.8....8674.....54......8.9......67.......................xx........x

Maybe this ?
Here are some expands from miths list [all TE3] with same B1B2B4 [456789] clues [ all different solution grids] the 123 clues are in box 9 and are undefined/variable
Could be called family ! The rest of the clues dont seem to be very close it does have to be said, but there is more row swapping that could be done in band3 and stack3..

Code: Select all: ....65...7.59.84...8674.9...54.9...88.9......67.58....5............5..21...6795.3 # 492165387715938462386742915254396178839217654671584239543821796967453821128679543 ....65.877.59.8......74..95.54..78..8.9..67..67..8.......85467.5......21......5.8 # 491365287735928416286741395154237869829516734673489152912854673548673921367192548 ....65.877.59.8.6....74.....54.87...8.9...7..67..9.8........5.85......21....5497. # 493265187715938462286741395354687219829413756671592834937126548548379621162854973 .9..65......9.8....8.74.9...54.9..878.94.7.5.67.....49....7459..67...421.4......3 # 493265718715938264286741935154692387839417652672853149328174596567389421941526873 .9..65......9.8....8.74.9...54.97.8.8.94...5767.....49....7459..67...421.4......3 # 493265718715938264286741935154697382839412657672853149328174596567389421941526873 .9..65.....59.86...8674.5...54.79.688.9..6.7567.............75......7.21547...9.6 # 492165387715938642386742519254379168839216475671584293128693754963457821547821936 .9..65.....59.86...8674.9...54..9.8.8.94.....67.....49947...56.....9.42......4.93 # 491365278735928614286741935154639782829417356673852149947283561318596427562174893 .9..65..8..5.......8674..9..54.978..8.96.4...67..8.......4..78.5......21......6.3 # 492365178715928364386741592254197836839654217671283459963412785547836921128579643 .9..658.....9.8....8.74.....54....688.9..6.7467.48..9....6.478.54....621.6......3 # 492365817715928436386741259254197368839256174671483592923614785547839621168572943 .9..658....59.8....8674.5...54.9..868.9.....567.58..........45.....5..21547...9.8 # 493165872715928364286743519354291786829376145671584293162839457938457621547612938 .9..658....59.8....8674.5...54.96.7.8.94.7....7...........7.9....7....21.4....7.3 # 493265817715938246286741539354896172829417365671352498562173984937584621148629753 4...65...7.59.84....674.5...54......8.96.4.5767.5...49......9.4...4...21948...6.5 # 491265378725938416386741592154897263839624157672513849217356984563489721948172635 4...65...7.59.84....674.5...54.79...8.9....7.67.....4.948...6.........21......8.4 # 492365187735918462186742539354679218829451376671283945948127653563894721217536894 4...65...7.59.86....674.....54.9..688.96.4.5.67.......9.8...47......9.26......9.3 # 491265837725938614386741295254193768819674352673852149938526471147389526562417983 4...65.7.7.59.8.64..6.......54..76..8.96.4...67.58.4..968...54....8.6.21......8.6 # 492165378715938264386742915254317689839624157671589432968271543543896721127453896 49..65...7.5...4...8674.9...54.9..8.8.9......67.58..49547...69........21......7.4 # 491365278725918436386742915154296387839174562672583149547821693963457821218639754 49..65...7.59.8....8674.....54.96.788.9..7.6567........48.............21.....9..3 # 493165287725938614186742359254396178839217465671854932348521796967483521512679843 49..65...7.59.8....8674.....54.96.878.9..7..567........47..........7..21.....9..3 # 493165278725938614186742359254396187839217465671854932347521896968473521512689743 49..65...7.59.8....8674.....54.97.688.9..6.7567........48.............21.....9..3 # 493165287725938614186742359254397168839216475671854932348521796967483521512679843 49..65...7.59.86...8674.5...54..7..68.94.6...67.......9...........6.9.21...8..9.3 # 493165287725938614186742539354287196819456372672391845941523768538679421267814953 49..65..87.5.......8674..9..54.9.8..8.94.....67.58.....67...48....6...21......6.3 # 492165738735928164186743592254396817819472356673581249367219485548637921921854673 49..65..87.59.8......74..59.54.9....8.94..5..67..........67.485.......215.....6.3 # 492365718735918246186742359254896137819437562673251894921673485367584921548129673 49..65.7....9.8....8674..59.54.879..8.9..6...67..9.....6..........85.621...67.5.3 # 491365872735928164286741359154287936829536417673194285562413798347859621918672543 49..65.787.5.......8674.....54.8.9..8.9......67.59....56....4.....65..21....7.653 # 492365178735918264186742539354287916829136745671594382563821497947653821218479653 49..65.787.5.......8674..9..54.9.8..8.94.....67.58.....67....8....6..721......6.3 # 493265178725918364186743592254396817839471256671582439367124985548639721912857643 49..65.787.5....46.8674.....54.8.9..8.9......67..9....56....4.....65..21....7...3 # 492365178735918246186742539354187962829536714671294385563821497947653821218479653 49..65.787.59.8......74..59.54.9....8.94..5..67..........67.485..7....215.....7.3 # 491365278735928146286741359154897632829436517673152894912673485367584921548219763 49..65.8.7.5.......8674...9.54.9.8..8.94.....67.58....567...4.8...65..21......6.. # 491265783735918246286743519154396872829471365673582194567129438348657921912834657 49..65.8.7.5.......8674..59.54.879..8.9..6...67..9....54....69.....7.521....5...3 # 491365782735928164286741359154287936829136475673594218542813697368479521917652843 49..65.8.7.5....46.8674.....54.86...8.9..76..67..9....54....96......4.21......4.3 # 491365782735928146286741395354186279819257634672493518543812967967534821128679453 49..65.8.7.5....46.8674.....54.86...8.9..76..67..9....54....96.....7..21........3 # 493165782715928346286743195154386279839257614672491538541832967368579421927614853 49..65.8.7.5....46.8674.....54.876..8.9..6...67..9....54....96......4.21......4.3 # 491365782725918346386742195154287639839156274672493518543821967967534821218679453 49..657..7.59.84...8674.9...54.9.............67.85....567....4....57.6.1....8.573 # 491365782735928416286741935154293867829617354673854129567139248348572691912486573 49..658..7.59.8....8674.....54.8..9......6...67..9...8.67...48....6...21...85.763 # 493165872715928346286743159154382697839576214672491538367219485548637921921854763 49..658..7.59.8....8674.....54.9..8......6...67..8...9.67...4.8...6...21...85.763 # 493165872715928346286743195154392687839576214672481539367219458548637921921854763 49..658..7.59.8....8674.9...54.8...9...4.....67..9..8454....69......4.2.....79..3 # 491365872725918346386742915154286739839457261672193584543821697967534128218679453 49..658..7.59.8....8674.9...54.9..68.....6...67..8..9..67...48........2.....5...3 # 491265837735918246286743951154392768829576314673481592367129485548637129912854673 49..658..7.59.8....8674.9...54.9..8......6...67..8...9.67...4.8....5.72.........3 # 491365872725918364386742915154293687839576241672481539267139458913854726548627193 49..658..7.59.86.....74.9...54....6.8.9......67......9...85.7.65......2..4....5.3 # 492365871715928634386741952154289367829637415673514289931852746567493128248176593

by **champagne** » Wed Apr 02, 2025 7:24 am

In line with your post, but using my boxes 5689 magic square, we must end in one of these 2 patterns.

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 type 1 type 2

Only one of the valid six permutations in the four boxes can give the “type 1 pattern”
But the “type 2” can come from 2 permutations, another criteria must select the canonical one.

Relabelling can be applied to the solution grid to reach

Code: Select all: 451 267 .x. .x. x.. ..x

can be followed by

Code: Select all: 451 267 .2. .3. 3.. ..1

or

Code: Select all: 451 267 .3. .1. 2.. ..3

This does not lead to a huge number of magic squares. I think that “blue” did the enumeration in a similar way.

I am not clear on what gives the “vicinity” applied to build mith’s file, but I am now convinced that I was heavily wrong thinking that all was derived from the “loki” seed.

I’ll try to see with “mith” what he did

by **blue** » Wed Apr 02, 2025 8:23 am

champagne wrote:Some doubts going back reading this post of Blue

http://forum.enjoysudoku.com/tridagon-t45572-30.html

(...)

I have doubts that the "vicinity" search can switch from the first to the second pattern. One possibility is that mith's file is already done of several seeds

It doesn't happen very often with {-1,+1}, even given that the solution grid is changing ... but it does happen:

Code: Select all: tridagon digits: 1,2,3 magic square: B1245 type 1 +-------+-------+-------+ +-------+-------+-------+ | . . . | . 4 5 | . 6 . | | 8 7 1 | 3 4 5 | 9 6 2 | | 5 . 9 | 6 . 7 | . 8 . | | 5 2 9 | 6 1 7 | 3 8 4 | | . . . | 8 9 . | . . . | | 3 6 4 | 8 9 2 | 7 1 5 | +-------+-------+-------+ +-------+-------+-------+ | . . 7 | . . . | . . . | | 2 5 7 | 1 6 3 | 4 9 8 | | 4 . 8 | 5 . 9 | . . . | | 4 1 8 | 5 2 9 | 6 3 7 | | 6 . . | 4 7 . | . . . | | 6 9 3 | 4 7 8 | 5 2 1 | +-------+-------+-------+ +-------+-------+-------+ | 9 8 5 | . . . | 2 4 . | | 9 8 5 | 7 3 1 | 2 4 6 | | . . . | . . . | . . . | | 1 3 6 | 2 5 4 | 8 7 9 | | 7 4 . | . . . | 1 . 3 | | 7 4 2 | 9 8 6 | 1 5 3 | +-------+-------+-------+ +-------+-------+-------+ {-2r7c7,+8r6c7} --> type 2 +-------+-------+-------+ +-------+-------+-------+ | . . . | . 4 5 | . 6 . | | 8 7 1 | 2 4 5 | 3 6 9 | | 5 . 9 | 6 . 7 | . 8 . | | 5 2 9 | 6 3 7 | 4 8 1 | | . . . | 8 9 . | . . . | | 3 6 4 | 8 9 1 | 5 7 2 | +-------+-------+-------+ +-------+-------+-------+ | . . 7 | . . . | . . . | | 2 5 7 | 3 1 8 | 6 9 4 | | 4 . 8 | 5 . 9 | . . . | | 4 1 8 | 5 6 9 | 2 3 7 | | 6 . . | 4 7 . | 8 . . | | 6 9 3 | 4 7 2 | 8 1 5 | +-------+-------+-------+ +-------+-------+-------+ | 9 8 5 | . . . | . 4 . | | 9 8 5 | 1 2 3 | 7 4 6 | | . . . | . . . | . . . | | 1 3 6 | 7 5 4 | 9 2 8 | | 7 4 . | . . . | 1 . 3 | | 7 4 2 | 9 8 6 | 1 5 3 | +-------+-------+-------+ +-------+-------+-------+ ....45.6.5.96.7.8....89......7......4.85.9...6..47....985...24..........74....1.3 871345962529617384364892715257163498418529637693478521985731246136254879742986153 ....45.6.5.96.7.8....89......7......4.85.9...6..47.8..985....4..........74....1.3 871245369529637481364891572257318694418569237693472815985123746136754928742986153

Here's one where the "odd box" in the magic square changes from box 5 to box 2:

Code: Select all: tridagon digits: 1,2,3 magic square: B1245 type 2 +-------+-------+-------+ +-------+-------+-------+ | 4 5 . | . . . | . . . | | 4 5 1 | 3 7 8 | 2 6 9 | | 6 . 7 | 9 . 5 | . . . | | 6 2 7 | 9 1 5 | 8 4 3 | | . 8 9 | . . . | . . . | | 3 8 9 | 4 6 2 | 7 5 1 | +-------+-------+-------+ +-------+-------+-------+ | . 6 4 | . 8 7 | . . 5 | | 1 6 4 | 2 8 7 | 9 3 5 | | . . . | 6 . . | 4 . . | | 5 3 8 | 6 9 1 | 4 2 7 | | 9 7 . | 5 . . | . . . | | 9 7 2 | 5 4 3 | 6 1 8 | +-------+-------+-------+ +-------+-------+-------+ | . . . | 8 . 6 | 1 7 4 | | 2 9 5 | 8 3 6 | 1 7 4 | | . . . | . . 4 | 3 . 2 | | 8 1 6 | 7 5 4 | 3 9 2 | | 7 . . | . . . | . 8 . | | 7 4 3 | 1 2 9 | 5 8 6 | +-------+-------+-------+ +-------+-------+-------+ {-7r7c8,+9r5c6} --> type 1 +-------+-------+-------+ +-------+-------+-------+ | 4 5 . | . . . | . . . | | 4 5 3 | 7 2 8 | 6 1 9 | | 6 . 7 | 9 . 5 | . . . | | 6 1 7 | 9 3 5 | 2 4 8 | | . 8 9 | . . . | . . . | | 2 8 9 | 4 6 1 | 7 5 3 | +-------+-------+-------+ +-------+-------+-------+ | . 6 4 | . 8 7 | . . 5 | | 1 6 4 | 2 8 7 | 9 3 5 | | . . . | 6 . 9 | 4 . . | | 5 3 8 | 6 1 9 | 4 2 7 | | 9 7 . | 5 . . | . . . | | 9 7 2 | 5 4 3 | 8 6 1 | +-------+-------+-------+ +-------+-------+-------+ | . . . | 8 . 6 | 1 . 4 | | 3 2 5 | 8 7 6 | 1 9 4 | | . . . | . . 4 | 3 . 2 | | 8 9 6 | 1 5 4 | 3 7 2 | | 7 . . | . . . | . 8 . | | 7 4 1 | 3 9 2 | 5 8 6 | +-------+-------+-------+ +-------+-------+-------+ 45.......6.79.5....89.......64.87..5...6..4..97.5........8.6174.....43.27......8. 451378269627915843389462751164287935538691427972543618295836174816754392743129586 45.......6.79.5....89.......64.87..5...6.94..97.5........8.61.4.....43.27......8. 453728619617935248289461753164287935538619427972543861325876194896154372741392586

I think mith did "twins" transformations too, for puzzles that have unavoidable sets in the clues -- not exacly a "vicintity" operation.

by **coloin** » Wed Apr 02, 2025 1:58 pm

blue wrote:I think mith did "twins" transformations too, for puzzles that have unavoidable sets in the clues -- not exacly a "vicintity" operation.

he certainly did a complete twin process... and yes I tended to use the new twin puzzles as new seeds.
Im just waiting to see how many of the 67K grids in miths file have the loki 3-corner pattern. [ 1032 known patterns]
My list was from ~ 10K grids .. so expecting 250 of them when its finished ...
but the puzzles dont seem to be too connected... so probably just an exercise...

by **champagne** » Wed Apr 02, 2025 2:27 pm

Hi blue,

good examples giving more credibility to the possibility to have mith's file derived from a unique seed.
All your solution grids are in mith's file and seen the skfr rating, likely all of them in the file.

So far, with a new solution grid, I see no easy way to tell if a bridge to mith' file exists.

by **coloin** » Wed Apr 02, 2025 5:23 pm

348 of the 67K solution grids in miths file had the loki 3-corner pattern, which is more x 5 more than random expectation.
Maybe they are connected somewhat - and we surmize that mith predominantly did a {-1+1} , expanding and minimizing .....

Hidden Text: Show

Code: Select all: 49..657..7.59.8....8674.5...54..6...8.94.7.6.67..........8..........9.21.......5. loki 49..65...7.59.8....8674.....54......8.9......67.......................21........3 ...........59.8..6..674..5..54..76..8.96.4...67.59.8......7946.9.8...721..7.....3 492365187715928346386741952254837619839614275671592834523179468968453721147286593 ....65.....59.8.....674...5.54.798..8.94..5..67...........9475.96....4.154.....93 491265378725938614386741925154679832839412567672853149218394756963527481547186293 ....65...7.59.8.64.86.4..95.548.6.....947.....7...94..5.8...74.....8..21...6....3 491265837725938164386741295254816379819473652673529418538192746967384521142657983 ....65...7.59.8.64.8674..95.54..76..8.94.6...67..........8.97.........2........53 492365871735918264186742395354197682829456137671283549543829716967531428218674953 ....65...7.59.84...8674.9...54.....88.94.....67.85...45.......9...5.4.21...67.5.3 492365187735918462186742935254136798819427356673859214541283679367594821928671543 ....65...7.59.84...8674.9...54.9...88.9......67.58....5............5..21...6795.3 492165387715938462386742915254396178839217654671584239543821796967453821128679543 ....65.787..9.8..4.8.74.....54.978..8.96..7..67.58.........69.7.6.....215.....6.3 493165278725938164186742539254397816839621745671584392348216957967853421512479683 ....65.787.59.8....8674..59.54...8..8.9..67..67..8.......8546.7..8...52.5.7....83 491265378725938461386741259254173896819426735673589142932854617168397524547612983 ....65.787.59.8....8674..59.54..9...8.9..6...67........68...4.....85.62....6...83 493165278725938146186742359354289761819476532672513894268397415931854627547621983 ....65.787.59.8....8674..59.54.9.8..8.94..5..67...........794.5..7....21.6....7.3 492365178735918642186742359254693817819427536673581294328179465547836921961254783 ....65.787.59.8..4.8674.....54......8.9..6...67.5.......8...9.7......821...8.95.6 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49..658..7..9.84...8.74.....54......8.94.....67.85..9456....74....58.621...6....3 493165872725938416186742539354296187819473265672851394561329748937584621248617953 49..658..7..9.84...8.74.....54.....88.94.6...67.58..4956....7.4....5..21......58. 493265817725918463186743295254139678839476152671582349562891734348657921917324586 49..658..7..9.84...8.74.....54....688.96.....67.58..9......678.5......219......43 493265817725918436186743259254379168839621574671584392342196785568437921917852643 49..658..7..9.84...8.74.....54..9.688.9......67.58..94...85..4..68....21.47....83 491365872735928416286741359354219768819674235672583194123856947968437521547192683 49..658..7..9.84...8.74.....54..9.688.9......67.85..94...58..4..68....21.47....83 491365872735928416286741359354219768819674235672853194123586947968437521547192683 49..658..7..9.84...8.74.....54.8...9...4...5.67.59..84...6....8..7...62..6....743 491265837735918462286743591154386279829471356673592184342657918917834625568129743 49..658..7..9.84...8.74.....54.8..9....4....567.59..48.6....7.4..7...621...6...8. 493165872725938416186742539354286197819473265672591348268319754937854621541627983 49..658..7..9.84...8.74.....54.97.68...6.....67.58..9....4.678.54....621.6.....43 491265837725938416386741259254197368819623574673584192932416785548379621167852943 49..658..7.5.......8674.9...54.8...98.94.....67.59..8.547...6.8....5.72.....7.5.3 491265837725938146386741952154682379839417265672593481547329618913856724268174593 49..658..7.5.......8674.9...54.8...98.94.....67.59..8.547...6.8....7.52.....5.7.3 491265837725938146386741952154682379839417265672593481547329618913876524268154793 49..658..7.5.......8674.9...54.8...98.94.....67.59..8454....6.8....74521....5...3 492165837735928146186743952354687219829431765671592384543219678968374521217856493 49..658..7.5.......8674.9...54.87.968.9..6...67..9...8567...4.9...6..72.....7...3 493165872715928364286743951154387296839256147672491538567832419348619725921574683 49..658..7.5.......8674.9...54.9....8.95....467.48.....4....6.........21....7.5.3 491365872725918346386742915254697138819523764673481259542139687937856421168274593 49..658..7.5.......8674.9...54.97...8.9..6...67..8...9.67...4......7..21....5.7.3 493265817725918346186743952354197268819326574672584139267831495538479621941652783 49..658..7.59.8....8674.....54......8.9..6...67..8...9....547..56....421.4......3 491265837725938164386741295254319678819576342673482519932154786567893421148627953 49..658..7.59.8....8674.....54....8.8.9..6...67..8...9....547.85......21......5.3 491365872735928416286741395354219687819576234672483159923154768548637921167892543 49..658..7.59.8....8674.....54.8..9......6...67..9...8.67...48....6...21...85.763 493165872715928346286743159154382697839576214672491538367219485548637921921854763 49..658..7.59.8....8674.....54.9..8......6...67..8...9.67...4.8...6...21...85.763 493165872715928346286743195154392687839576214672481539367219458548637921921854763 49..658..7.59.8....8674.5.......7.2.8.9...45.....5..819.75.4.68..........48..6..5 491365872735928614286741539154897326829613457673452981917534268562189743348276195 49..658..7.59.8....8674.5...54.79.8......6...67..8....54....9.8....5.421....9.75. 492165873715938264386742519154379682829516347673284195541627938967853421238491756 49..658..7.59.8....8674.9...54....868.9..6...67..8...9...6.47.856....421.4......3 491365872735928164286741935354197286819256347672483519923614758567839421148572693 49..658..7.59.8....8674.9...54..9.68.....6...67..8..9....654.8..4.....2..6....4.3 493265871715938246286741935354129768829576314671483592932654187548317629167892453 49..658..7.59.8....8674.9...54.8...9...4.....67..9..8454....69......4.2.....79..3 491365872725918346386742915154286739839457261672193584543821697967534128218679453 49..658..7.59.8....8674.9...54.8...9...4.....67.59..8454....6.8....5..21....7.5.3 492365817715928346386741952154687239829413765673592184541239678937856421268174593 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49..658..7.59.86...8674.9...54.79...8.9..6...67......9....547.......7.21..7.....8 491265837725938614386741952154879263839426175672513489218354796943687521567192348 49..658..7.59.86...8674.9...54.97..8.........67..8..9...7....8.....79.21...8547.. 493265817715938642286741953154697238839412576672583194947126385568379421321854769 49..658.77.........8.74...9.54.9..8.8.95.6...67.48..9.567....48...6....1....5..63 493165827725938614186742359354291786819576432672483195567319248938624571241857963

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