The New Sudoku Players' Forum

[urhegyi]

Or another interesting layout:

Code: Select all

.9.4.8.7...5...1..7...2...84.8...2.9.7..4..3.1.3...8.76...8...3..1...7...2.7.3.1.


Code: Select all

.9.4.8.7.
..5...1..
7...2...8
4.8...2.9
.7..4..3.
1.3...8.7
6...8...3
..1...7..
.2.7.3.1.


[denis_berthier]

(solve ".9.4.8.7.38.....24.1.....9....1.7....72.4.53....5.2....4.....5.53.....82.2.7.3.1.")
singles
biv-chain-rc[3]: r4c9{n8 n9} - r9c9{n9 n6} - r9c1{n6 n8} ==> r4c1 ≠ 8
stte

(solve ".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.")
same solution.


(solve ".9.4.8.7...5...1..7...2...84.8...2.9.7..4..3.1.3...8.76...8...3..1...7...2.7.3.1.")
singles
naked-pairs-in-a-row: r4{c2 c8}{n5 n6} ==> r4c6 ≠ 6, r4c6 ≠ 5, r4c5 ≠ 6, r4c5 ≠ 5, r4c4 ≠ 6, r4c4 ≠ 5
hidden-pairs-in-a-column: c5{n3 n7}{r2 r4} ==> r2c5 ≠ 9, r2c5 ≠ 6
biv-chain[2]: r5n5{c6 c7} - c8n5{r4 r7} ==> r7c6 ≠ 5
finned-swordfish-in-columns: n5{c2 c5 c8}{r4 r6 r9} ==> r9c9 ≠ 5
stte

[denis_berthier]

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

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

I had forgotten to publish my solutions of this interesting example. It's one of the rare* cases where the main ratings differ largely. Here, we have W = 17 but gW = 11.
(In the following resolution paths, I had activated Subsets and Finned Fish, but they play no major role.)

W solution:

Hidden Text: Show

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r779
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************
197 candidates, 1237 csp-links and 1237 links. Density = 6.41%
whip[5]: c5n4{r5 r3} - c3n4{r3 r8} - r9n4{c2 c9} - r9n1{c9 c8} - r3n1{c8 .} ==> r5c6 ≠ 4
whip[8]: b7n3{r8c3 r9c2} - r9n4{c2 c9} - r9n1{c9 c8} - r3n1{c8 c5} - r3n4{c5 c2} - c2n8{r3 r1} - c2n5{r1 r7} - b9n5{r7c7 .} ==> r8c3 ≠ 4
whip[10]: r4c9{n7 n9} - r6c9{n9 n5} - r5c7{n5 n2} - r8c7{n2 n9} - r7n9{c8 c5} - r5c5{n9 n4} - r5c3{n4 n3} - c2n3{r6 r9} - r9c6{n3 n2} - r9c4{n2 .} ==> r9c9 ≠ 7
whip[10]: r4c9{n7 n9} - r6c9{n9 n5} - r5c7{n5 n2} - r8c7{n2 n9} - r7c7{n9 n5} - c8n5{r9 r1} - r7c8{n5 n2} - c3n2{r7 r8} - b7n3{r8c3 r9c2} - c2n5{r9 .} ==> r8c9 ≠ 7
whip[10]: r5n3{c6 c3} - c3n4{r5 r3} - b2n4{r3c5 r1c6} - c6n8{r1 r2} - r4n8{c6 c4} - r1n8{c4 c2} - r3c2{n8 n9} - r6c2{n9 n6} - c4n6{r6 r8} - r8n3{c4 .} ==> r4c6 ≠ 3
whip[11]: c6n4{r1 r4} - r4n8{c6 c4} - r1c4{n8 n7} - r1c8{n7 n5} - r2n5{c9 c1} - b1n9{r2c1 r3c2} - c2n8{r3 r1} - c2n4{r1 r9} - r9n5{c2 c9} - c9n1{r9 r2} - r2c4{n1 .} ==> r1c6 ≠ 9
whip[11]: c6n4{r1 r4} - r4n8{c6 c4} - r1c4{n8 n9} - r1c8{n9 n5} - r2n5{c9 c1} - b1n9{r2c1 r3c2} - c2n8{r3 r1} - c2n4{r1 r9} - r9n5{c2 c9} - c9n1{r9 r2} - r2c4{n1 .} ==> r1c6 ≠ 7
whip[13]: r3c3{n4 n7} - r2c3{n7 n6} - r7c3{n6 n2} - r8c3{n2 n3} - r5c3{n3 n4} - r5c5{n4 n9} - r3c5{n9 n1} - r2n1{c4 c9} - r3c8{n1 n9} - r7n9{c8 c7} - r8c9{n9 n4} - r9c9{n4 n5} - r9c2{n5 .} ==> r3c2 ≠ 4
x-wing-in-rows: n4{r3 r5}{c3 c5} ==> r4c5 ≠ 4
whip[8]: r6n1{c5 c4} - r2n1{c4 c9} - r3n1{c8 c5} - c5n4{r3 r5} - r5n9{c5 c7} - r7n9{c7 c8} - b3n9{r1c8 r1c9} - c9n6{r1 .} ==> r6c5 ≠ 9
whip[14]: r2c3{n6 n7} - r3c3{n7 n4} - r5n4{c3 c5} - b2n4{r3c5 r1c6} - r1n8{c6 c4} - r2c6{n8 n9} - b2n7{r2c6 r3c5} - r2c4{n7 n1} - r2n8{c4 c7} - r3c7{n8 n9} - r5n9{c7 c4} - r8n9{c4 c9} - c9n4{r8 r9} - c9n1{r9 .} ==> r1c2 ≠ 6
whip[14]: b8n6{r8c4 r7c5} - b8n9{r7c5 r8c6} - r8n3{c6 c3} - r8n6{c3 c1} - r8n2{c1 c7} - r7n2{c8 c3} - r5c3{n2 n4} - r3c3{n4 n7} - c1n7{r2 r9} - c1n4{r9 r1} - r1n6{c1 c9} - r1n7{c9 c8} - r1n5{c8 c2} - r7c2{n5 .} ==> r8c4 ≠ 7
whip[15]: r5n9{c6 c7} - r4c9{n9 n7} - r4c5{n7 n6} - b8n6{r7c5 r8c4} - r8n9{c4 c9} - r8n4{c9 c1} - r4c1{n4 n2} - r4c8{n2 n3} - r4c2{n3 n4} - r5c3{n4 n3} - b7n3{r8c3 r9c2} - r9n4{c2 c9} - c9n1{r9 r2} - c4n1{r2 r6} - c4n3{r6 .} ==> r4c6 ≠ 9
whip[15]: c7n8{r2 r3} - r3c2{n8 n9} - r3c8{n9 n1} - b2n1{r3c5 r2c4} - r2n8{c4 c6} - r2n9{c6 c9} - r4c9{n9 n7} - r6c9{n7 n5} - c7n5{r5 r7} - r7c2{n5 n6} - r6c2{n6 n3} - r4c2{n3 n4} - r5c3{n4 n2} - r7n2{c3 c8} - b6n2{r4c8 .} ==> r2c7 ≠ 7
whip[14]: r3n4{c3 c5} - r3n1{c5 c8} - c9n1{r2 r9} - r9n4{c9 c1} - b4n4{r4c1 r5c3} - c3n3{r5 r8} - c3n2{r8 r7} - b7n7{r7c3 r8c1} - r8n6{c1 c4} - c3n6{r8 r2} - c3n7{r2 r3} - c7n7{r3 r7} - r7c5{n7 n9} - r5c5{n9 .} ==> r1c2 ≠ 4
whip[13]: r3c2{n9 n8} - r1c2{n8 n5} - r1c8{n5 n7} - r3c7{n7 n9} - r3c8{n9 n1} - b2n1{r3c5 r2c4} - r2n9{c4 c6} - b2n7{r2c6 r3c5} - c5n4{r3 r5} - r5n9{c5 c4} - r8n9{c4 c9} - c9n4{r8 r9} - r9n1{c9 .} ==> r1c1 ≠ 9
whip[15]: c6n5{r6 r5} - r5n3{c6 c3} - r8n3{c3 c4} - b8n6{r8c4 r7c5} - r7c2{n6 n5} - c7n5{r7 r2} - c7n8{r2 r3} - r3c2{n8 n9} - r6c2{n9 n6} - c4n6{r6 r4} - r4n8{c4 c6} - r2n8{c6 c4} - r2n1{c4 c9} - r2n9{c9 c6} - b8n9{r8c6 .} ==> r6c6 ≠ 3
finned-x-wing-in-columns: n3{c3 c6}{r5 r8} ==> r8c4 ≠ 3
whip[16]: c2n4{r4 r9} - c2n3{r9 r6} - c2n6{r6 r7} - c2n5{r7 r1} - b1n9{r1c2 r2c1} - r3c2{n9 n8} - c7n8{r3 r2} - r2c6{n8 n7} - r2c4{n7 n1} - r6n1{c4 c5} - c5n6{r6 r4} - c5n7{r4 r7} - r7c3{n7 n2} - r8c1{n2 n7} - c3n7{r8 r3} - c7n7{r3 .} ==> r4c2 ≠ 9
whip[16]: b4n9{r6c2 r4c1} - r4c9{n9 n7} - r6c9{n7 n5} - r5c7{n5 n2} - b4n2{r5c3 r6c1} - r6c6{n2 n7} - r4c5{n7 n6} - b4n6{r4c1 r6c2} - r7c2{n6 n5} - c7n5{r7 r2} - r1c8{n5 n7} - r4c8{n7 n3} - b4n3{r4c2 r5c3} - r5c4{n3 n9} - r1c4{n9 n8} - r2n8{c4 .} ==> r6c8 ≠ 9
whip[17]: r3c2{n9 n8} - r3c7{n8 n7} - r3c3{n7 n4} - b2n4{r3c5 r1c6} - r1n8{c6 c4} - r2c6{n8 n7} - b1n7{r2c1 r1c1} - r8n7{c1 c3} - b7n3{r8c3 r9c2} - r9c6{n3 n2} - r9c4{n2 n7} - r7c5{n7 n6} - r7c2{n6 n5} - r1c2{n5 n9} - r1c8{n9 n5} - r9c8{n5 n1} - r3c8{n1 .} ==> r3c5 ≠ 9
whip[4]: c7n7{r8 r3} - r3c3{n7 n4} - r3c5{n4 n1} - c8n1{r3 .} ==> r9c8 ≠ 7
whip[6]: c4n1{r6 r2} - b2n9{r2c4 r2c6} - r5n9{c6 c7} - r8n9{c7 c9} - c9n4{r8 r9} - c9n1{r9 .} ==> r6c4 ≠ 9
whip[6]: r3n9{c8 c2} - c2n8{r3 r1} - r1c4{n8 n7} - r1c8{n7 n5} - r2c7{n5 n8} - b2n8{r2c4 .} ==> r1c9 ≠ 9
whip[10]: c2n5{r9 r1} - c2n8{r1 r3} - b1n9{r3c2 r2c1} - b2n9{r2c6 r1c4} - r1c8{n9 n7} - r3c7{n7 n9} - r3c8{n9 n1} - r9c8{n1 n2} - r8c7{n2 n7} - c1n7{r8 .} ==> r9c1 ≠ 5
whip[1]: b7n5{r9c2 .} ==> r1c2 ≠ 5
naked-pairs-in-a-block: b1{r1c2 r3c2}{n8 n9} ==> r2c1 ≠ 9
whip[1]: c1n9{r6 .} ==> r6c2 ≠ 9
whip[6]: r9n1{c8 c9} - r9n5{c9 c2} - c2n4{r9 r4} - c2n3{r4 r6} - r5c3{n3 n2} - c7n2{r5 .} ==> r9c8 ≠ 2
whip[5]: r3n4{c3 c5} - r3n1{c5 c8} - r9c8{n1 n5} - r1n5{c8 c9} - r1n6{c9 .} ==> r1c1 ≠ 4
singles ==> r3c3 = 4, r1c6 = 4, r5c5 = 4
whip[2]: c5n9{r7 r4} - r5n9{c4 .} ==> r7c7 ≠ 9
whip[3]: b2n9{r2c4 r2c6} - r5n9{c6 c7} - c9n9{r4 .} ==> r8c4 ≠ 9
biv-chain[3]: b8n6{r8c4 r7c5} - b8n9{r7c5 r8c6} - r8n3{c6 c3} ==> r8c3 ≠ 6
whip[5]: r7c2{n5 n6} - r6c2{n6 n3} - r5c3{n3 n2} - c7n2{r5 r8} - r7n2{c7 .} ==> r7c7 ≠ 5
whip[5]: b1n7{r2c3 r1c1} - c1n5{r1 r2} - c7n5{r2 r5} - r6c9{n5 n9} - r4c9{n9 .} ==> r2c9 ≠ 7
whip[5]: r1n6{c9 c1} - b1n5{r1c1 r2c1} - c7n5{r2 r5} - r6c9{n5 n9} - r4c9{n9 .} ==> r1c9 ≠ 7
whip[1]: c9n7{r6 .} ==> r4c8 ≠ 7, r6c8 ≠ 7
whip[5]: r5c3{n2 n3} - r6c2{n3 n6} - r7n6{c2 c5} - b8n9{r7c5 r8c6} - r8n3{c6 .} ==> r7c3 ≠ 2
whip[1]: r7n2{c8 .} ==> r8c7 ≠ 2
naked-pairs-in-a-column: c3{r2 r7}{n6 n7} ==> r8c3 ≠ 7
whip[5]: c7n7{r8 r3} - r3n8{c7 c2} - r1n8{c2 c4} - r1n7{c4 c1} - b7n7{r9c1 .} ==> r7c8 ≠ 7
whip[1]: b9n7{r8c7 .} ==> r3c7 ≠ 7
naked-pairs-in-a-row: r3{c2 c7}{n8 n9} ==> r3c8 ≠ 9
biv-chain[4]: b9n7{r8c7 r7c7} - c7n2{r7 r5} - r5c3{n2 n3} - r8n3{c3 c6} ==> r8c6 ≠ 7
whip[5]: r4c9{n7 n9} - c5n9{r4 r7} - c5n7{r7 r3} - b3n7{r3c8 r1c8} - c8n9{r1 .} ==> r4c6 ≠ 7
whip[5]: r4c9{n7 n9} - c5n9{r4 r7} - c5n7{r7 r3} - b3n7{r3c8 r1c8} - c8n9{r1 .} ==> r4c4 ≠ 7
whip[5]: c7n5{r2 r5} - c7n2{r5 r7} - r7c8{n2 n9} - c5n9{r7 r4} - r5n9{c4 .} ==> r1c8 ≠ 5
hidden-pairs-in-a-row: r1{n5 n6}{c1 c9} ==> r1c1 ≠ 7
whip[1]: b1n7{r2c3 .} ==> r2c4 ≠ 7, r2c6 ≠ 7
biv-chain[3]: r3n7{c5 c8} - r1c8{n7 n9} - r7n9{c8 c5} ==> r7c5 ≠ 7
whip[1]: b8n7{r9c6 .} ==> r9c1 ≠ 7
biv-chain[4]: b8n6{r8c4 r7c5} - b8n9{r7c5 r8c6} - r2c6{n9 n8} - b5n8{r4c6 r4c4} ==> r4c4 ≠ 6
biv-chain[4]: c7n5{r2 r5} - c7n2{r5 r7} - r7n7{c7 c3} - b1n7{r2c3 r2c1} ==> r2c1 ≠ 5
singles ==> r1c1 = 5, r1c9 = 6
whip[4]: r8c4{n2 n6} - r7c5{n6 n9} - r8c6{n9 n3} - r8c3{n3 .} ==> r8c1 ≠ 2
whip[5]: r2c6{n9 n8} - r4c6{n8 n2} - r5c4{n2 n3} - c3n3{r5 r8} - r8c6{n3 .} ==> r6c6 ≠ 9
whip[4]: r2c1{n6 n7} - r8c1{n7 n4} - r8c9{n4 n9} - r6n9{c9 .} ==> r6c1 ≠ 6
whip[5]: r2c6{n9 n8} - r4c6{n8 n2} - r5c4{n2 n3} - c3n3{r5 r8} - r8c6{n3 .} ==> r5c6 ≠ 9
whip[2]: r5n9{c7 c4} - b2n9{r1c4 .} ==> r2c7 ≠ 9
whip[3]: r5n9{c4 c7} - c9n9{r4 r8} - c6n9{r8 .} ==> r2c4 ≠ 9
whip[6]: c8n3{r4 r6} - r6c2{n3 n6} - r7c2{n6 n5} - r7c8{n5 n9} - r7c5{n9 n6} - r4n6{c5 .} ==> r4c8 ≠ 2
biv-chain[3]: r5c3{n3 n2} - b6n2{r5c7 r6c8} - b6n3{r6c8 r4c8} ==> r4c2 ≠ 3
whip[6]: r9c8{n5 n1} - b3n1{r3c8 r2c9} - c4n1{r2 r6} - r6n3{c4 c2} - r5c3{n3 n2} - b6n2{r5c7 .} ==> r6c8 ≠ 5
whip[1]: c8n5{r9 .} ==> r9c9 ≠ 5
biv-chain[3]: r6c1{n9 n2} - r6c8{n2 n3} - r4c8{n3 n9} ==> r4c1 ≠ 9, r6c9 ≠ 9
hidden-single-in-a-row ==> r6c1 = 9
biv-chain[4]: r3n7{c5 c8} - b3n1{r3c8 r2c9} - c9n5{r2 r6} - c9n7{r6 r4} ==> r4c5 ≠ 7
singles ==> r4c9 = 7, r6c9 = 5, r2c7 = 5, r3c7 = 8, r3c2 = 9, r1c2 = 8, r5c6 = 5
whip[1]: c6n3{r9 .} ==> r9c4 ≠ 3
naked-pairs-in-a-column: c5{r4 r7}{n6 n9} ==> r6c5 ≠ 6
x-wing-in-columns: n9{c6 c9}{r2 r8} ==> r8c7 ≠ 9
stte

gW solution:

Hidden Text: Show

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = gW+SFin
*** Using CLIPS 6.32-r779
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************
197 candidates, 1237 csp-links and 1237 links. Density = 6.41%
166 g-candidates, 1156 csp-glinks and 676 non-csp glinks
whip[5]: c5n4{r5 r3} - c3n4{r3 r8} - r9n4{c2 c9} - r9n1{c9 c8} - r3n1{c8 .} ==> r5c6 ≠ 4
whip[8]: b7n3{r8c3 r9c2} - r9n4{c2 c9} - r9n1{c9 c8} - r3n1{c8 c5} - r3n4{c5 c2} - c2n8{r3 r1} - c2n5{r1 r7} - b9n5{r7c7 .} ==> r8c3 ≠ 4
g-whip[9]: b4n9{r6c2 r4c123} - r4c9{n9 n7} - r6c9{n7 n5} - b6n9{r6c9 r5c7} - r7n9{c7 c8} - r8c9{n9 n4} - r9c9{n4 n1} - c8n1{r9 r3} - c5n1{r3 .} ==> r6c5 ≠ 9
whip[10]: r4c9{n7 n9} - r6c9{n9 n5} - r5c7{n5 n2} - r8c7{n2 n9} - r7n9{c8 c5} - r5c5{n9 n4} - r5c3{n4 n3} - c2n3{r6 r9} - r9c6{n3 n2} - r9c4{n2 .} ==> r9c9 ≠ 7
whip[10]: r4c9{n7 n9} - r6c9{n9 n5} - r5c7{n5 n2} - r8c7{n2 n9} - r7c7{n9 n5} - c8n5{r9 r1} - r7c8{n5 n2} - c3n2{r7 r8} - b7n3{r8c3 r9c2} - c2n5{r9 .} ==> r8c9 ≠ 7
whip[10]: r5n3{c6 c3} - c3n4{r5 r3} - b2n4{r3c5 r1c6} - c6n8{r1 r2} - r4n8{c6 c4} - r1n8{c4 c2} - r3c2{n8 n9} - r6c2{n9 n6} - c4n6{r6 r8} - r8n3{c4 .} ==> r4c6 ≠ 3
g-whip[10]: r9n1{c8 c9} - b9n5{r9c9 r7c789} - r7c2{n5 n6} - r8n6{c3 c4} - b8n2{r8c4 r8c6} - r8n3{c6 c3} - b7n2{r8c3 r7c3} - r5c3{n2 n4} - r5c5{n4 n9} - b8n9{r7c5 .} ==> r9c8 ≠ 2
g-whip[9]: c9n6{r1 r2} - c9n1{r2 r9} - c9n5{r9 r6} - b6n7{r6c9 r456c8} - r9c8{n7 n5} - b3n5{r1c8 r2c7} - r2n8{c7 c456} - r1c4{n8 n9} - r1c8{n9 .} ==> r1c9 ≠ 7
g-whip[10]: c2n8{r1 r3} - r3n4{c2 c5} - r3n1{c5 c8} - r3n9{c8 c7} - c7n8{r3 r2} - c7n7{r2 r789} - r9c8{n7 n5} - r9c2{n5 n3} - b4n3{r4c2 r5c3} - r5n4{c3 .} ==> r1c2 ≠ 4
whip[10]: c6n4{r1 r4} - c6n8{r4 r2} - r1c4{n8 n9} - r1c8{n9 n5} - r2n5{c9 c1} - b1n9{r2c1 r3c2} - c2n4{r3 r9} - r9n5{c2 c9} - c9n1{r9 r2} - r2c4{n1 .} ==> r1c6 ≠ 7
whip[10]: c6n4{r1 r4} - c6n8{r4 r2} - r1c4{n8 n7} - r1c8{n7 n5} - r2n5{c9 c1} - b1n9{r2c1 r3c2} - c2n4{r3 r9} - r9n5{c2 c9} - c9n1{r9 r2} - r2c4{n1 .} ==> r1c6 ≠ 9
whip[11]: c9n7{r6 r2} - b3n1{r2c9 r3c8} - r9c8{n1 n5} - r1c8{n5 n9} - r7c8{n9 n2} - b6n2{r4c8 r5c7} - c7n5{r5 r2} - c1n5{r2 r1} - b1n7{r1c1 r3c3} - r2c3{n7 n6} - r7c3{n6 .} ==> r4c8 ≠ 7
whip[11]: c9n7{r6 r2} - b3n1{r2c9 r3c8} - r9c8{n1 n5} - r1c8{n5 n9} - r7c8{n9 n2} - b6n2{r4c8 r5c7} - c7n5{r5 r2} - c1n5{r2 r1} - b1n7{r1c1 r3c3} - r2c3{n7 n6} - r7c3{n6 .} ==> r6c8 ≠ 7
whip[1]: b6n7{r6c9 .} ==> r2c9 ≠ 7
whip[11]: r1c6{n4 n8} - c2n8{r1 r3} - r3n4{c2 c5} - r3n1{c5 c8} - r3n9{c8 c7} - c7n8{r3 r2} - b3n7{r2c7 r1c8} - r1c4{n7 n9} - b1n9{r1c1 r2c1} - c1n5{r2 r9} - r9c8{n5 .} ==> r1c1 ≠ 4
hidden-single-in-a-row ==> r1c6 = 4
whip[9]: b8n6{r8c4 r7c5} - b8n9{r7c5 r8c6} - r8n3{c6 c3} - r8n6{c3 c1} - r8n2{c1 c7} - r7n2{c8 c3} - b7n7{r7c3 r9c1} - c1n4{r9 r4} - r5c3{n4 .} ==> r8c4 ≠ 7
g-whip[11]: r5c5{n4 n9} - b8n9{r7c5 r8c456} - r8c9{n9 n4} - c1n4{r8 r9} - b4n4{r4c1 r5c3} - b4n3{r5c3 r456c2} - r9c2{n3 n5} - r9c9{n5 n1} - r2n1{c9 c4} - r3c5{n1 n7} - r3c3{n7 .} ==> r4c5 ≠ 4
singles ==> r5c5 = 4, r3c3 = 4
whip[8]: c7n8{r2 r3} - r3c2{n8 n9} - b2n9{r3c5 r1c4} - r5n9{c4 c6} - r8n9{c6 c9} - r4c9{n9 n7} - r6c9{n7 n5} - c6n5{r6 .} ==> r2c7 ≠ 9
whip[10]: r3c2{n9 n8} - r1n8{c2 c4} - r1n7{c4 c8} - r3c7{n7 n9} - r3c8{n9 n1} - r9n1{c8 c9} - c9n4{r9 r8} - b9n9{r8c9 r7c8} - c5n9{r7 r4} - r5n9{c4 .} ==> r1c1 ≠ 9
whip[5]: c2n8{r1 r3} - b1n9{r3c2 r2c1} - r2n6{c1 c9} - r2n5{c9 c7} - c7n8{r2 .} ==> r1c2 ≠ 6
g-whip[7]: r1n6{c9 c1} - r2n6{c1 c9} - c3n6{r2 r789} - r7c2{n6 n5} - r1n5{c2 c8} - b9n5{r7c8 r9c9} - c9n1{r9 .} ==> r1c9 ≠ 9
whip[10]: b8n6{r7c5 r8c4} - b8n9{r8c4 r8c6} - r8n3{c6 c3} - c3n7{r8 r2} - b2n7{r2c4 r1c4} - r1n8{c4 c2} - r3c2{n8 n9} - b2n9{r3c5 r2c4} - r5n9{c4 c7} - c9n9{r6 .} ==> r7c5 ≠ 7
whip[6]: r3c2{n9 n8} - r1c2{n8 n5} - r7c2{n5 n6} - r7c5{n6 n9} - b2n9{r3c5 r1c4} - r1n8{c4 .} ==> r2c1 ≠ 9
whip[1]: c1n9{r6 .} ==> r4c2 ≠ 9, r6c2 ≠ 9
hidden-pairs-in-a-column: c2{n8 n9}{r1 r3} ==> r1c2 ≠ 5
whip[1]: c2n5{r9 .} ==> r9c1 ≠ 5
whip[4]: c5n1{r3 r6} - c5n7{r6 r4} - r4c9{n7 n9} - r2n9{c9 .} ==> r3c5 ≠ 9
whip[2]: c5n9{r7 r4} - r5n9{c4 .} ==> r7c7 ≠ 9
whip[3]: b2n9{r2c4 r2c6} - r5n9{c6 c7} - c9n9{r4 .} ==> r8c4 ≠ 9
whip[5]: r9n5{c9 c2} - b7n3{r9c2 r8c3} - r5c3{n3 n2} - c7n2{r5 r8} - r7n2{c7 .} ==> r7c7 ≠ 5
whip[5]: b2n9{r2c4 r2c6} - r5n9{c6 c7} - c7n5{r5 r2} - r2n8{c7 c4} - c4n1{r2 .} ==> r6c4 ≠ 9
whip[6]: r4c9{n7 n9} - r4c5{n9 n6} - r6c5{n6 n1} - b2n1{r3c5 r2c4} - r2n9{c4 c6} - c6n8{r2 .} ==> r4c6 ≠ 7
whip[7]: c8n1{r9 r3} - c9n1{r2 r9} - b9n5{r9c9 r7c8} - r1c8{n5 n9} - r1c2{n9 n8} - r1c4{n8 n7} - r3c5{n7 .} ==> r9c8 ≠ 7
whip[4]: c8n7{r3 r7} - r7c7{n7 n2} - r7c3{n2 n6} - r2c3{n6 .} ==> r2c7 ≠ 7
whip[7]: r4c9{n7 n9} - r4c5{n9 n6} - c5n7{r4 r3} - r3n1{c5 c8} - b3n7{r3c8 r1c8} - c8n9{r1 r7} - r7c5{n9 .} ==> r4c4 ≠ 7
whip[7]: c8n7{r3 r7} - r7c7{n7 n2} - r7c3{n2 n6} - r2c3{n6 n7} - b2n7{r2c4 r1c4} - r1n8{c4 c2} - r3n8{c2 .} ==> r3c7 ≠ 7
whip[1]: c7n7{r8 .} ==> r7c8 ≠ 7
naked-pairs-in-a-row: r3{c2 c7}{n8 n9} ==> r3c8 ≠ 9
g-whip[5]: c7n5{r2 r5} - b6n2{r5c7 r456c8} - r7c8{n2 n9} - c5n9{r7 r4} - r5n9{c4 .} ==> r1c8 ≠ 5
hidden-pairs-in-a-row: r1{n5 n6}{c1 c9} ==> r1c1 ≠ 7
whip[1]: b1n7{r2c3 .} ==> r2c4 ≠ 7, r2c6 ≠ 7
biv-chain[3]: r2c6{n9 n8} - r2c7{n8 n5} - r5n5{c7 c6} ==> r5c6 ≠ 9
biv-chain[4]: b8n6{r8c4 r7c5} - b8n9{r7c5 r8c6} - r2c6{n9 n8} - b5n8{r4c6 r4c4} ==> r4c4 ≠ 6
biv-chain[3]: c4n6{r8 r6} - r6c2{n6 n3} - b7n3{r9c2 r8c3} ==> r8c3 ≠ 6, r8c4 ≠ 3
finned-x-wing-in-rows: n3{r8 r5}{c3 c6} ==> r6c6 ≠ 3
whip[4]: r5c3{n2 n3} - r6c2{n3 n6} - r7n6{c2 c5} - r4n6{c5 .} ==> r7c3 ≠ 2
whip[1]: r7n2{c8 .} ==> r8c7 ≠ 2
naked-pairs-in-a-column: c3{r2 r7}{n6 n7} ==> r8c3 ≠ 7
biv-chain[4]: r8n3{c6 c3} - r5c3{n3 n2} - c7n2{r5 r7} - c7n7{r7 r8} ==> r8c6 ≠ 7
whip[1]: b8n7{r9c6 .} ==> r9c1 ≠ 7
biv-chain[4]: c1n7{r2 r8} - r8c7{n7 n9} - r3c7{n9 n8} - r2c7{n8 n5} ==> r2c1 ≠ 5
singles ==> r1c1 = 5, r1c9 = 6
whip[4]: r8c3{n2 n3} - r8c6{n3 n9} - r7c5{n9 n6} - b7n6{r7c2 .} ==> r8c1 ≠ 2
whip[5]: r2c6{n9 n8} - r4c6{n8 n2} - r5c4{n2 n3} - c3n3{r5 r8} - r8c6{n3 .} ==> r6c6 ≠ 9
whip[6]: c8n3{r4 r6} - b6n2{r6c8 r5c7} - r7c7{n2 n7} - r8c7{n7 n9} - b3n9{r3c7 r2c9} - c6n9{r2 .} ==> r4c8 ≠ 9
whip[6]: c7n8{r3 r2} - b3n5{r2c7 r2c9} - c9n1{r2 r9} - c9n4{r9 r8} - r8n9{c9 c6} - r2c6{n9 .} ==> r3c7 ≠ 9
singles ==> r3c7 = 8, r2c7 = 5, r3c2 = 9, r1c2 = 8, r5c6 = 5
whip[1]: c6n3{r9 .} ==> r9c4 ≠ 3
finned-x-wing-in-rows: n9{r1 r5}{c4 c8} ==> r6c8 ≠ 9
biv-chain[4]: r4n8{c4 c6} - r2c6{n8 n9} - r1c4{n9 n7} - r9c4{n7 n2} ==> r4c4 ≠ 2
biv-chain[4]: r6c2{n6 n3} - r5c3{n3 n2} - r5c7{n2 n9} - r6n9{c9 c1} ==> r6c1 ≠ 6
biv-chain[4]: c4n6{r6 r8} - r7c5{n6 n9} - c8n9{r7 r1} - r1n7{c8 c4} ==> r6c4 ≠ 7
biv-chain[4]: b8n9{r8c6 r7c5} - c8n9{r7 r1} - r1c4{n9 n7} - r9c4{n7 n2} ==> r8c6 ≠ 2
biv-chain[3]: r9c1{n4 n2} - r8n2{c3 c4} - r8n6{c4 c1} ==> r8c1 ≠ 4
hidden-single-in-a-row ==> r8c9 = 4
naked-pairs-in-a-block: b9{r9c8 r9c9}{n1 n5} ==> r7c8 ≠ 5
hidden-single-in-a-row ==> r7c2 = 5
whip[1]: c2n6{r6 .} ==> r4c1 ≠ 6
finned-x-wing-in-rows: n9{r8 r5}{c7 c6} ==> r4c6 ≠ 9
whip[2]: r5n9{c4 c7} - c9n9{r6 .} ==> r2c4 ≠ 9
biv-chain[3]: b2n9{r1c4 r2c6} - r8n9{c6 c7} - r5n9{c7 c4} ==> r4c4 ≠ 9
naked-triplets-in-a-row: r4{c4 c6 c8}{n3 n8 n2} ==> r4c2 ≠ 3, r4c1 ≠ 2
finned-x-wing-in-columns: n2{c1 c6}{r9 r6} ==> r6c4 ≠ 2
biv-chain[3]: r6c6{n7 n2} - c1n2{r6 r9} - r9c4{n2 n7} ==> r9c6 ≠ 7
stte

BTW, noticing this puzzle is from Mauricio, it seems he hasn't been here for a long time. Does anyone have news of him?

(*) Considering that there are about 2.5477e+25 non-isomorphic Sudoku puzzles** (with 0.065% relative error), 1,000,000,000 puzzles with some particular property would still be statistically extremely rare. One should always keep in mind this basic observation when meeting the word "rare" in the Sudoku context. Indeed, 99.9% of the minimal puzzles have W ≤ 7 and 99.99% have W ≤ 9.
(**) References:
<> "Unbiased Statistics of a CSP - A Controlled-Bias Generator", International Joint Conferences on Computer, Information, Systems Sciences and Engineering (CISSE 09), December 4-12, 2009, Springer. Published as a chapter of the book Innovations in Computing Sciences and Software Engineering, Khaled Elleithy Editor, pp. 11-17, Springer, 2010, ISBN 97890481911133.
<> Pattern-Based Constraint Satisfaction and Logic Puzzles (first or second edition), Lulu.com Publishers

[JPF]

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

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

I agree with you Mike!
Here is an other example with the same pattern:

Code: Select all

 . . 1 | . 2 . | 3 . .
 . 4 . | . 1 . | . 5 .
 6 . . | 3 . 5 | . . 1
-------+-------+-------
 . . 6 | . . . | 7 . .
 2 1 . | . . . | . 6 3
 . . 5 | . . . | 1 . .
-------+-------+-------
 5 . . | 1 . 8 | . . 9
 . 9 . | . 6 . | . 3 .
 . . 8 | . 9 . | 5 . .    ED=9.8/1.2/1.2


and more:

Code: Select all

..1.2.3...2..4..5.5..1.3..2..6...7..17.....68..4...5..7..8.9..6.1..7..3...9.1.8..   ED = 9.4/9.4/9.1
..1.2.3...2..1..4.5..6.7..1..3...6..85.....34..9...8..1..9.3..8.8..7..9...5.8.4..   ED = 9.3/9.3/9.2


JPF

[denis_berthier]

Here is an other example with the same pattern:

Code: Select all

 . . 1 | . 2 . | 3 . .
 . 4 . | . 1 . | . 5 .
 6 . . | 3 . 5 | . . 1
-------+-------+-------
 . . 6 | . . . | 7 . .
 2 1 . | . . . | . 6 3
 . . 5 | . . . | 1 . .
-------+-------+-------
 5 . . | 1 . 8 | . . 9
 . 9 . | . 6 . | . 3 .
 . . 8 | . 9 . | 5 . .    ED=9.8/1.2/1.2


and more:

Code: Select all

..1.2.3...2..4..5.5..1.3..2..6...7..17.....68..4...5..7..8.9..6.1..7..3...9.1.8..   ED = 9.4/9.4/9.1
..1.2.3...2..1..4.5..6.7..1..3...6..85.....34..9...8..1..9.3..8.8..7..9...5.8.4..   ED = 9.3/9.3/9.2


JPF

Great examples. I thought the 9.4 and the 9.8 would be very hard for SudoRules, but they are not.
The 9.4 is in W13, the 9.3 in W14 and the 9.8 is not in any Wk but it is in gW13 - and each of them is in the easy part of its rating (I mean they take fewer steps, less time and less memory than most puzzles with the same rating).