Sudokus with a nice form

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Sudokus with a nice form

Postby urhegyi » Thu Dec 10, 2020 10:28 pm

Often one encounters sudokus with a nice pattern. But mostly they have all very easy solutions. Is it because of the large number of clues?
Example I saw yesterday on a forum:
Code: Select all
...3.9.....5.2.8...63...14..5614839...........8425371..18...95...9.7.2.....8.6...

pattern.png
pattern.png (15.4 KiB) Viewed 258 times

So I removed four clues from the center. It gives a nice puzzle with 28 clues which is relatively hard to solve.
Code: Select all
...3.9.....5.2.8...63...14..56...39...........84.5371..18...95...9.7.2.....8.6...

10-12-28clue.png
10-12-28clue.png (15.53 KiB) Viewed 255 times
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Re: Sudokus with a nice form

Postby denis_berthier » Fri Dec 11, 2020 3:54 am

urhegyi wrote:Often one encounters sudokus with a nice pattern. But mostly they have all very easy solutions. Is it because of the large number of clues?

Yes. The more clues you will remove from the original puzzle, the harder it will become (unless the clues you remove are redundant).
The only purpose of proposing a "nice pattern" is all in the name. In a Sudoku puzzles book, they make it look better. Unfortunately, it generally implies that they are not very interesting for the manual solver.

"Nice patterns" generally require many clues to make the pattern visible. But, It's harder to find hard puzzles with many clues.
I've recently proposed a few puzzles with perfect symmetries or nice patterns; it often took me hours of processor time to find a few puzzles hard enough to be interesting. Even so, they may not be interesting in the sense manual solvers consider it, i.e. they may not display many special patterns such as Fish....
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Re: Sudokus with a nice form

Postby m_b_metcalf » Fri Dec 11, 2020 8:40 am

denis_berthier wrote:"Nice patterns" generally require many clues to make the pattern visible. But, It's harder to find hard puzzles with many clues.

I disagree with the first statement. The Patterns Game has many nice patterns with a clue count in the low 20s:
Code: Select all
 7 . . . . . . . 3
 . 2 . 4 . . . 8 .
 . . 1 . . . 5 . .
 . 8 . 9 . 5 . . .
 . . . . 3 . . . .
 . . . 2 . 8 . 6 .
 . . 5 . . . 1 . .
 . 4 . . . 9 . 2 .      21 clues
 3 . . . . . . . 7      SE=10.7, jpf

The second statement is true (especially for minimal puzzles), but there are examples such as this one from Game 54:
Code: Select all
 . . 1 . 2 . 3 . .
 . 2 . . 3 . . 4 .
 3 . . 5 . 6 . . 2
 . . 5 . . . 1 . .
 1 7 . . . . . 6 8
 . . 8 . . . 4 . .
 8 . . 4 . 1 . . 3
 . 1 . . 5 . . 8 .  28 clues
 . . 9 . 8 . 6 . .  ED=9.3/9.3/8.8 - Mauricio


Regards,

Mike
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Re: Sudokus with a nice form

Postby 1to9only » Fri Dec 11, 2020 9:00 am

You can put the sudoku line in a pattern.txt file, and use gsf.exe to generate puzzles with same pattern and with unique solutions.
Generate thousands of them, and a number of high ratings will normally show up.
Code: Select all
gsf.exe -n10000 -gto{-3+3}p -euniq() -f%v -opuzzles.txt < pattern.txt

Code: Select all
...9.3.....5.8.1...68...47..8915634...........5134798..12...53...7.3.2.....5.9... ED=6.6/1.2/1.2
...9.2.....7.1.3...36...24..6317582...........9182367..15...96...8.9.4.....5.7... ED=6.7/1.2/1.2
...6.2.....3.8.9...14...28..3517964...........4652379..27...85...8.9.3.....7.8... ED=6.8/1.2/1.2
...1.7.....5.6.4...87...96..3462179...........7259814..59...38...3.1.2.....4.3... ED=6.9/1.5/1.5
...6.3.....5.1.3...14...67..6259184...........9832751..46...98...7.8.4.....2.4... ED=7.0/1.2/1.2
...9.3.....9.4.2...31...97..9418672...........7632914..85...41...7.3.8.....8.5... ED=7.1/2.6/2.6
...3.1.....5.2.1...13...47..4175926...........9283451..76...95...4.7.8.....1.5... ED=7.2/1.2/1.2
...3.9.....7.1.6...29...85..5674138...........1386279..68...57...4.2.9.....6.7... ED=7.3/1.2/1.2
...8.9.....6.5.9...97...85..8547621...........6913257..24...79...8.4.3.....9.5... ED=7.7/1.2/1.2
...2.9.....8.5.7...25...63..9654821...........5719236..19...47...4.6.8.....7.4... ED=8.3/1.2/1.2
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Re: Sudokus with a nice form

Postby denis_berthier » Fri Dec 11, 2020 9:38 am

1to9only wrote:You can put the sudoku line in a pattern.txt file, and use gsf.exe to generate puzzles with same pattern and with unique solutions.
Generate thousands of them, and a number of high ratings will normally show up.
Code: Select all
gsf.exe -n10000 -gto{-3+3}p -euniq() -f%v -opuzzles.txt < pattern.txt

What does the -gto{-3+3}p mean?
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Re: Sudokus with a nice form

Postby JPF » Fri Dec 11, 2020 11:23 am

a bit of work and you can get what you want!

Code: Select all
 . . . | 1 . 2 | . . .
 . . 3 | . 4 . | 2 . .
 . 2 5 | . . . | 6 1 .
-------+-------+-------
 . 7 1 | 5 2 4 | 3 6 .
 . . . | . . . | . . .
 . 5 4 | 6 3 8 | 1 7 .
-------+-------+-------
 . 6 9 | . . . | 7 4 .
 . . 7 | . 9 . | 5 . .
 . . . | 4 . 7 | . . .    ED=9.0/9.0/2.6

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Re: Sudokus with a nice form

Postby denis_berthier » Fri Dec 11, 2020 11:57 am

JPF wrote:a bit of work and you can get what you want!

Code: Select all
 . . . | 1 . 2 | . . .
 . . 3 | . 4 . | 2 . .
 . 2 5 | . . . | 6 1 .
-------+-------+-------
 . 7 1 | 5 2 4 | 3 6 .
 . . . | . . . | . . .
 . 5 4 | 6 3 8 | 1 7 .
-------+-------+-------
 . 6 9 | . . . | 7 4 .
 . . 7 | . 9 . | 5 . .
 . . . | 4 . 7 | . . .    ED=9.0/9.0/2.6

JPF


A difficult puzzle, solvable in W9

Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r779
***********************************************************************************************
169 candidates, 1008 csp-links and 1008 links. Density = 7.1%
whip[1]: r1n3{c9 .} ==> r3c9 ≠ 3
whip[1]: b5n9{r5c6 .} ==> r5c9 ≠ 9, r5c1 ≠ 9, r5c2 ≠ 9, r5c7 ≠ 9, r5c8 ≠ 9
whip[1]: b6n9{r6c9 .} ==> r1c9 ≠ 9, r2c9 ≠ 9, r3c9 ≠ 9, r9c9 ≠ 9
whip[1]: b4n9{r6c1 .} ==> r1c1 ≠ 9, r2c1 ≠ 9, r3c1 ≠ 9
whip[1]: r3n9{c6 .} ==> r2c4 ≠ 9, r2c6 ≠ 9
naked-pairs-in-a-block: b2{r2c4 r3c5}{n7 n8} ==> r3c4 ≠ 8, r3c4 ≠ 7, r1c5 ≠ 8, r1c5 ≠ 7
finned-x-wing-in-columns: n2{c3 c8}{r5 r9} ==> r9c9 ≠ 2
biv-chain[4]: r9c3{n2 n8} - r1c3{n8 n6} - r1c5{n6 n5} - r9n5{c5 c1} ==> r9c1 ≠ 2
z-chain[5]: r9n5{c1 c5} - r1c5{n5 n6} - r1c3{n6 n8} - c7n8{r1 r5} - r4n8{c9 .} ==> r9c1 ≠ 8
whip[5]: c5n6{r9 r1} - r1c3{n6 n8} - r3n8{c1 c9} - r4n8{c9 c1} - r7n8{c1 .} ==> r9c5 ≠ 8
z-chain[6]: r8n6{c9 c6} - r2c6{n6 n5} - r2c9{n5 n7} - b2n7{r2c4 r3c5} - r3n8{c5 c1} - r4n8{c1 .} ==> r8c9 ≠ 8
t-whip-rn[6]: r9n5{c1 c5} - r9n6{c5 c9} - r8n6{c9 c6} - r2n6{c6 c1} - r2n1{c1 c2} - r9n1{c2 .} ==> r9c1 ≠ 3
whip[6]: r4n8{c9 c1} - b7n8{r8c1 r8c2} - b1n8{r1c2 r1c3} - c7n8{r1 r5} - c7n4{r5 r1} - c2n4{r1 .} ==> r9c9 ≠ 8
whip[8]: r1n3{c8 c9} - c9n5{r1 r5} - c9n4{r5 r3} - c9n7{r3 r2} - b2n7{r2c4 r3c5} - r3c1{n7 n8} - r1c3{n8 n6} - r1c5{n6 .} ==> r1c8 ≠ 5
z-chain[4]: r8n6{c9 c6} - r2c6{n6 n5} - c8n5{r2 r5} - c8n2{r5 .} ==> r8c9 ≠ 2
whip[7]: r9n3{c9 c2} - r5n3{c2 c1} - r5n6{c1 c3} - r1c3{n6 n8} - r1c8{n8 n9} - r1c7{n9 n4} - r1c2{n4 .} ==> r8c8 ≠ 3
z-chain[5]: r8c8{n8 n2} - c4n2{r8 r7} - c4n8{r7 r2} - r3n8{c5 c9} - r4n8{c9 .} ==> r8c1 ≠ 8
whip[5]: c8n3{r1 r9} - r9n9{c8 c7} - c7n8{r9 r5} - c3n8{r5 r9} - r9n2{c3 .} ==> r1c8 ≠ 8
whip[6]: r4n8{c1 c9} - r3n8{c9 c5} - r7n8{c5 c4} - c4n2{r7 r8} - r8c8{n2 n8} - r2n8{c8 .} ==> r1c1 ≠ 8
whip[8]: r4n8{c1 c9} - r3n8{c9 c5} - r7n8{c5 c4} - c4n2{r7 r8} - r8c8{n2 n8} - r2n8{c8 c2} - r1c3{n8 n6} - r5n6{c3 .} ==> r5c1 ≠ 8
whip[9]: r5c2{n8 n3} - r9c2{n3 n1} - r9c1{n1 n5} - r9c5{n5 n6} - r8n6{c6 c9} - c9n1{r8 r7} - c5n1{r7 r5} - c5n7{r5 r3} - b2n8{r3c5 .} ==> r2c2 ≠ 8
whip[2]: r4n8{c9 c1} - b1n8{r3c1 .} ==> r1c9 ≠ 8
whip[6]: r4n8{c9 c1} - r3n8{c1 c5} - r2n8{c4 c8} - r8c8{n8 n2} - c4n2{r8 r7} - r7n8{c4 .} ==> r5c9 ≠ 8
whip-cn[7]: c8n3{r9 r1} - c8n9{r1 r2} - c2n9{r2 r1} - c2n4{r1 r8} - c2n8{r8 r5} - c3n8{r5 r1} - c7n8{r1 .} ==> r9c8 ≠ 8
t-whip[6]: r2n1{c1 c2} - r2n9{c2 c8} - r1c8{n9 n3} - r9c8{n3 n2} - c3n2{r9 r5} - r5n6{c3 .} ==> r2c1 ≠ 6
singles ==> r2c6 = 6, r1c5 = 5, r7c6 = 5, r9c1 = 5, r9c5 = 6, r8c9 = 6
t-whip[7]: r2n1{c1 c2} - r2n9{c2 c8} - r1c8{n9 n3} - r9c8{n3 n2} - c3n2{r9 r5} - r6c1{n2 n9} - r4c1{n9 .} ==> r2c1 ≠ 8
biv-chain[4]: r2c1{n1 n7} - c4n7{r2 r5} - r5c5{n7 n1} - b8n1{r7c5 r8c6} ==> r8c1 ≠ 1
biv-chain[5]: c5n7{r3 r5} - r5n1{c5 c6} - r8n1{c6 c2} - r8n4{c2 c1} - r3n4{c1 c9} ==> r3c9 ≠ 7
z-chain[5]: c9n1{r7 r9} - c9n3{r9 r1} - r1n7{c9 c1} - r3n7{c1 c5} - c5n8{r3 .} ==> r7c9 ≠ 8
t-whip[5]: r9n2{c3 c8} - c8n3{r9 r1} - c8n9{r1 r2} - r2c2{n9 n1} - b7n1{r9c2 .} ==> r7c1 ≠ 2
z-chain-rc[5]: r8c6{n3 n1} - r7c5{n1 n8} - r7c1{n8 n1} - r9c2{n1 n8} - r5c2{n8 .} ==> r8c2 ≠ 3
z-chain[5]: r7n2{c4 c9} - r6n2{c9 c1} - c1n9{r6 r4} - c1n8{r4 r3} - c5n8{r3 .} ==> r7c4 ≠ 8
swordfish-in-rows: n8{r3 r4 r7}{c5 c9 c1} ==> r2c9 ≠ 8
z-chain[5]: c9n8{r4 r3} - r3n4{c9 c1} - r8n4{c1 c2} - r8n8{c2 c4} - r2n8{c4 .} ==> r5c8 ≠ 8
x-wing-in-columns: n8{c4 c8}{r2 r8} ==> r8c2 ≠ 8
biv-chain[3]: r3c9{n4 n8} - b6n8{r4c9 r5c7} - b6n4{r5c7 r5c9} ==> r1c9 ≠ 4
z-chain[6]: r6n2{c1 c9} - c9n9{r6 r4} - b6n8{r4c9 r5c7} - b9n8{r9c7 r8c8} - c8n2{r8 r9} - c3n2{r9 .} ==> r5c1 ≠ 2
z-chain[7]: c9n1{r7 r9} - c9n3{r9 r1} - c9n7{r1 r2} - r2c1{n7 n1} - r7n1{c1 c5} - r8c6{n1 n3} - r7c4{n3 .} ==> r7c9 ≠ 2
hidden-single-in-a-row ==> r7c4 = 2
whip[1]: b8n3{r8c6 .} ==> r8c1 ≠ 3
whip[1]: b9n2{r9c8 .} ==> r5c8 ≠ 2
singles ==> r5c8 = 5, r2c9 = 5, r1c9 = 7, r1c8 = 3
hidden-pairs-in-a-row: r9{n1 n3}{c2 c9} ==> r9c2 ≠ 8
biv-chain[3]: r9c7{n8 n9} - r1n9{c7 c2} - c2n8{r1 r5} ==> r5c7 ≠ 8
stte

.
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Re: Sudokus with a nice form

Postby 1to9only » Fri Dec 11, 2020 12:26 pm

denis_berthier wrote:What does the -gto{-3+3}p mean?

From the gsf help, which as a recent user I've found rather obscure/frustrating to decipher:

-gTNA Generate puzzles of type T with optional parameters N and A

t Treat each input file as a template and generate -nN puzzles per template, filling only the template clues.

o +/-NX...: a sequence of -N and/or +N operands with option suffixes.
  • -N: delete all combinations of N clues;
  • +N: add all combinations of N clues.
p the input puzzle is a pattern -- only change original clues
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Re: Sudokus with a nice form

Postby denis_berthier » Fri Dec 11, 2020 2:08 pm

1to9only wrote:
denis_berthier wrote:What does the -gto{-3+3}p mean?

From the gsf help, which as a recent user I've found rather obscure/frustrating to decipher:

-gTNA Generate puzzles of type T with optional parameters N and A

t Treat each input file as a template and generate -nN puzzles per template, filling only the template clues.

o +/-NX...: a sequence of -N and/or +N operands with option suffixes.
  • -N: delete all combinations of N clues;
  • +N: add all combinations of N clues.
p the input puzzle is a pattern -- only change original clues


Thanks; I'll try this.
I'm a recent user of gsf's program. I knew only the option whith an input pattern, not with a puzzle, but I understand it makes sense to look for close-by puzzles.
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Re: Sudokus with a nice form

Postby coloin » Fri Dec 11, 2020 4:37 pm

dobrichev's "gridchecker" program does the same without the verbose

gridchecker v1.23

gridchecker --similar --relabel 3 < puzzle.txt>moreminimalpuzzlesofthesamepattern.txt
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Re: Sudokus with a nice form

Postby denis_berthier » Fri Dec 11, 2020 5:05 pm

coloin wrote:dobrichev's "gridchecker" program does the same without the verbose
gridchecker v1.23
gridchecker --similar --relabel 3 < puzzle.txt>moreminimalpuzzlesofthesamepattern.txt

but, as far as I can see, it works only on Windows.
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Re: Sudokus with a nice form

Postby coloin » Fri Dec 11, 2020 5:16 pm

denis_berthier wrote:but, as far as I can see, it works only on Windows.

Possibly and also I am using an older version - for which that input works ....

this works on the new version..
gridcheckernew --similar --relabel 3 --minimals --unique < puzzle.txt > morepuzzles.txt
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Re: Sudokus with a nice form

Postby JPF » Fri Dec 11, 2020 11:49 pm

as the initial pattern probably doesn't have any minimal puzzles, here is a minimal puzzle with symmetry included in that pattern:

Code: Select all
 . . . | 1 . 2 | . . .
 . . 3 | . 4 . | 5 . .
 . 1 6 | . . . | 2 7 .
-------+-------+-------
 . 5 8 | . . . | 1 4 .
 . . . | . . . | . . .
 . 7 2 | . . . | 3 6 .
-------+-------+-------
 . 3 7 | . . . | 6 5 .
 . . 1 | . 9 . | 7 . .
 . . . | 8 . 7 | . . .    ED=9.0/9.0/3.4

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Re: Sudokus with a nice form

Postby denis_berthier » Sat Dec 12, 2020 6:28 am

JPF wrote:as the initial pattern probably doesn't have any minimal puzzles, here is a minimal puzzle with symmetry included in that pattern:
Code: Select all
 . . . | 1 . 2 | . . .
 . . 3 | . 4 . | 5 . .
 . 1 6 | . . . | 2 7 .
-------+-------+-------
 . 5 8 | . . . | 1 4 .
 . . . | . . . | . . .
 . 7 2 | . . . | 3 6 .
-------+-------+-------
 . 3 7 | . . . | 6 5 .
 . . 1 | . 9 . | 7 . .
 . . . | 8 . 7 | . . .    ED=9.0/9.0/3.4

JPF


I don't see how to use symmetry here.
Otherwise, it has a Jellyfish near the start and then it's solved in W7:

Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r779
***********************************************************************************************
209 candidates, 1351 csp-links and 1351 links. Density = 6.22%
hidden-pairs-in-a-row: r7{n8 n9}{c1 c9} ==> r7c9 ≠ 4, r7c9 ≠ 2, r7c9 ≠ 1, r7c1 ≠ 4, r7c1 ≠ 2
whip[1]: r7n2{c5 .} ==> r8c4 ≠ 2, r9c5 ≠ 2
whip[1]: r7n4{c6 .} ==> r8c4 ≠ 4, r8c6 ≠ 4
whip[1]: b9n1{r9c9 .} ==> r9c5 ≠ 1
finned-x-wing-in-rows: n4{r3 r8}{c9 c1} ==> r9c1 ≠ 4
whip[2]: r7n9{c1 c9} - b6n9{r4c9 .} ==> r5c1 ≠ 9
whip[2]: r7n9{c9 c1} - b4n9{r4c1 .} ==> r5c9 ≠ 9
whip[3]: r7n9{c1 c9} - c7n9{r9 r5} - b4n9{r5c2 .} ==> r1c1 ≠ 9
whip[3]: r7n9{c9 c1} - c3n9{r9 r5} - b6n9{r5c7 .} ==> r1c9 ≠ 9
jellyfish-in-columns: n9{c2 c8 c3 c7}{r9 r2 r5 r1} ==> r9c9 ≠ 9, r9c1 ≠ 9, r5c6 ≠ 9, r5c4 ≠ 9, r2c9 ≠ 9, r2c6 ≠ 9, r2c4 ≠ 9, r2c1 ≠ 9
whip[1]: b2n9{r3c6 .} ==> r3c1 ≠ 9, r3c9 ≠ 9
z-chain[4]: r1n6{c9 c5} - r2c6{n6 n8} - c2n8{r2 r8} - b9n8{r8c8 .} ==> r1c9 ≠ 8
whip[5]: r1n7{c1 c5} - r2c4{n7 n6} - r2c6{n6 n8} - r3n8{c6 c9} - r7n8{c9 .} ==> r1c1 ≠ 8
whip[6]: r1n7{c1 c5} - r1n5{c5 c3} - r3c1{n5 n8} - r3n4{c1 c9} - r8n4{c9 c2} - c2n8{r8 .} ==> r1c1 ≠ 4
whip[6]: r9c7{n4 n9} - r7c9{n9 n8} - r3c9{n8 n3} - r1n3{c9 c5} - r9n3{c5 c8} - r9n1{c8 .} ==> r9c9 ≠ 4
whip[7]: b1n9{r2c2 r1c3} - c7n9{r1 r9} - c7n4{r9 r1} - r1c2{n4 n8} - r1c8{n8 n3} - r3c9{n3 n8} - r7c9{n8 .} ==> r5c2 ≠ 9
whip[5]: r9c7{n4 n9} - r7n9{c9 c1} - b4n9{r6c1 r5c3} - c3n4{r5 r1} - c7n4{r1 .} ==> r9c2 ≠ 4
whip[7]: c8n1{r9 r2} - r2n9{c8 c2} - r9c2{n9 n6} - r5c2{n6 n4} - r5c3{n4 n9} - r5c8{n9 n8} - r5c7{n8 .} ==> r9c8 ≠ 2
whip[5]: c7n8{r1 r5} - c8n8{r5 r8} - r7c9{n8 n9} - b6n9{r6c9 r5c8} - c8n2{r5 .} ==> r3c9 ≠ 8
z-chain[3]: r3c9{n4 n3} - r1n3{c8 c5} - r1n6{c5 .} ==> r1c9 ≠ 4
whip[5]: c7n8{r1 r5} - c8n8{r5 r8} - r7c9{n8 n9} - b6n9{r6c9 r5c8} - c8n2{r5 .} ==> r2c9 ≠ 8
z-chain[5]: r1n3{c9 c5} - r9n3{c5 c8} - r9n1{c8 c9} - r2c9{n1 n6} - r1c9{n6 .} ==> r3c9 ≠ 3
singles ==> r3c9 = 4, r9c7 = 4
whip[1]: r3n3{c6 .} ==> r1c5 ≠ 3
biv-chain-rc[3]: r9c3{n5 n9} - r7c1{n9 n8} - r3c1{n8 n5} ==> r8c1 ≠ 5, r9c1 ≠ 5, r1c3 ≠ 5
hidden-single-in-a-column ==> r9c3 = 5
hidden-pairs-in-a-row: r1{n5 n7}{c1 c5} ==> r1c5 ≠ 8, r1c5 ≠ 6
stte
denis_berthier
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Location: Paris

Re: Sudokus with a nice form

Postby urhegyi » Sat Jan 30, 2021 5:36 pm

Another layout in the form of an eight:
Code: Select all
.9.4.8.7.38.....24.1.....9....1.7....72.4.53....5.2....4.....5.53.....82.2.7.3.1.

Code: Select all
.9.4.8.7.
38.....24
.1.....9.
...1.7...
.72.4.53.
...5.2...
.4.....5.
53.....82
.2.7.3.1.

Code: Select all
.9.4.8.7.3.5...1.4.1..2..9....1.7...9...4...1...5.2....4..8..5.5.1...7.2.2.7.3.1.

Code: Select all
.9.4.8.7.
3.5...1.4
.1..2..9.
...1.7...
9...4...1
...5.2...
.4..8..5.
5.1...7.2
.2.7.3.1.
Last edited by urhegyi on Sat Jan 30, 2021 6:24 pm, edited 2 times in total.
urhegyi
 
Posts: 343
Joined: 13 April 2020

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