The New Sudoku Players' Forum

[urhegyi]

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 (15.4 KiB) Viewed 1034 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 (15.53 KiB) Viewed 1031 times

[denis_berthier]

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....

[m_b_metcalf]

"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

[1to9only]

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


[denis_berthier]

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?

[JPF]

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

[denis_berthier]

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

.

[1to9only]

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

[denis_berthier]

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.

[coloin]

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

gridchecker v1.23

gridchecker --similar --relabel 3 < puzzle.txt>moreminimalpuzzlesofthesamepattern.txt

[denis_berthier]

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.

[coloin]

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

[JPF]

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

[denis_berthier]

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

[urhegyi]

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.