The New Sudoku Players' Forum

[m_b_metcalf]

A dearth of new postings, so try this one, posted by joel64 in a Patterns Game. It's very hard, but has a dirty secret (in fact, two).

Mike

Code: Select all

 1 . . 2 . . . . 3
 . 4 . . 5 . . . .
 . . 2 . . 6 7 . .
 8 . . 3 . . 1 . .
 . 5 . . . . . 9 .
 . . 6 . . 2 . . 4
 . . 8 7 . . 6 . .
 . . . . 8 . . 2 .
 9 . . . . 4 . . 7

1..2....3.4..5......2..67..8..3..1...5.....9...6..2..4..87..6......8..2.9....4..7

[denis_berthier]

.
I haven't found the dirty secret (my mum is watching), but let me give it a go.

SER = 8.6

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 1     6789  579   ! 2     479   789   ! 4589  4568  3     !
   ! 367   4     379   ! 189   5     13789 ! 289   168   12689 !
   ! 35    389   2     ! 1489  1349  6     ! 7     1458  1589  !
   +-------------------+-------------------+-------------------+
   ! 8     279   479   ! 3     4679  579   ! 1     567   256   !
   ! 2347  5     1347  ! 1468  1467  178   ! 238   9     268   !
   ! 37    1379  6     ! 1589  179   2     ! 358   3578  4     !
   +-------------------+-------------------+-------------------+
   ! 2345  123   8     ! 7     1239  1359  ! 6     1345  159   !
   ! 34567 1367  13457 ! 1569  8     1359  ! 3459  2     159   !
   ! 9     1236  135   ! 156   1236  4     ! 358   1358  7     !
   +-------------------+-------------------+-------------------+
203 candidates

Simlpest-first solution in W7: Show

t-whip[5]: c7n4{r1 r8} - r7n4{c8 c1} - c1n2{r7 r5} - c7n2{r5 r2} - c7n9{r2 .} ==> r1c7≠5, r1c7≠8
biv-chain[4]: c2n8{r3 r1} - r1n6{c2 c8} - r1n5{c8 c3} - r3c1{n5 n3} ==> r3c2≠3
biv-chain[4]: c1n6{r8 r2} - r1n6{c2 c8} - r1n5{c8 c3} - r3c1{n5 n3} ==> r8c1≠3
biv-chain[4]: r1n5{c8 c3} - r3c1{n5 n3} - r6c1{n3 n7} - b6n7{r6c8 r4c8} ==> r4c8≠5
t-whip[4]: r3c2{n8 n9} - c3n9{r2 r4} - r4n4{c3 c5} - c4n4{r5 .} ==> r3c4≠8
biv-chain[5]: c1n6{r8 r2} - r1n6{c2 c8} - r1n5{c8 c3} - r3c1{n5 n3} - r6c1{n3 n7} ==> r8c1≠7
z-chain[5]: r2n7{c3 c6} - b2n3{r2c6 r3c5} - r3c1{n3 n5} - r1n5{c3 c8} - r1n6{c8 .} ==> r1c2≠7
t-whip[3]: r8n7{c2 c3} - b1n7{r2c3 r2c1} - c1n6{r2 .} ==> r8c2≠6
z-chain[5]: r6c1{n3 n7} - r2c1{n7 n6} - r1n6{c2 c8} - r1n5{c8 c3} - r3c1{n5 .} ==> r5c1≠3, r7c1≠3
z-chain[5]: r1n5{c8 c3} - r3c1{n5 n3} - b2n3{r3c5 r2c6} - c6n8{r2 r5} - c9n8{r5 .} ==> r1c8≠8
whip[4]: r1n8{c6 c2} - b1n6{r1c2 r2c1} - r2n7{c1 c3} - r2n3{c3 .} ==> r2c6≠8
finned-swordfish-in-columns: n8{c6 c2 c9}{r5 r1 r3} ==> r3c8≠8
t-whip[5]: r3n3{c5 c1} - r6c1{n3 n7} - r2c1{n7 n6} - c2n6{r1 r9} - r9n2{c2 .} ==> r9c5≠3
t-whip[5]: r6c1{n7 n3} - r3c1{n3 n5} - b3n5{r3c9 r1c8} - r1n6{c8 c2} - r2c1{n6 .} ==> r5c1≠7
t-whip[4]: c1n7{r6 r2} - b1n6{r2c1 r1c2} - r1n8{c2 c6} - r1n7{c6 .} ==> r6c5≠7
z-chain[5]: r5n7{c6 c3} - r1n7{c3 c6} - r1n8{c6 c2} - r1n6{c2 c8} - r4c8{n6 .} ==> r4c5≠7
t-whip[5]: r1n5{c8 c3} - r3c1{n5 n3} - r6c1{n3 n7} - r2c1{n7 n6} - r1n6{c2 .} ==> r1c8≠4
z-chain[5]: r1c8{n5 n6} - b1n6{r1c2 r2c1} - r8n6{c1 c4} - c4n5{r8 r6} - c7n5{r6 .} ==> r9c8≠5
t-whip[5]: r4n5{c6 c9} - r4n2{c9 c2} - c1n2{r5 r7} - r7n4{c1 c8} - r7n5{c8 .} ==> r8c6≠5
z-chain[7]: r4n4{c3 c5} - r1n4{c5 c7} - r8n4{c7 c1} - c1n6{r8 r2} - c1n7{r2 r6} - b4n3{r6c1 r6c2} - b4n1{r6c2 .} ==> r5c3≠4
t-whip[6]: c1n6{r8 r2} - r1n6{c2 c8} - r1n5{c8 c3} - b1n7{r1c3 r2c3} - c3n9{r2 r4} - c3n4{r4 .} ==> r8c1≠4
hidden-pairs-in-a-column: c1{n2 n4}{r5 r7} ==> r7c1≠5
finned-x-wing-in-rows: n5{r4 r7}{c6 c9} ==> r8c9≠5
swordfish-in-columns: n4{c1 c4 c8}{r7 r5 r3} ==> r5c5≠4, r3c5≠4
z-chain[3]: r4n5{c9 c6} - r7n5{c6 c9} - b3n5{r3c9 .} ==> r6c8≠5
z-chain[4]: c5n6{r5 r9} - r9n2{c5 c2} - r7c1{n2 n4} - r5n4{c1 .} ==> r5c4≠6
whip[1]: c4n6{r9 .} ==> r9c5≠6
hidden-triplets-in-a-column: c5{n4 n6 n7}{r1 r4 r5} ==> r5c5≠1, r4c5≠9, r1c5≠9
biv-chain[4]: b4n2{r4c2 r5c1} - r5n4{c1 c4} - r4c5{n4 n6} - r4c8{n6 n7} ==> r4c2≠7
t-whip[5]: r1n8{c6 c2} - r3c2{n8 n9} - b4n9{r4c2 r4c3} - r4n4{c3 c5} - r1c5{n4 .} ==> r1c6≠7
biv-chain[3]: r1n7{c3 c5} - r1n4{c5 c7} - r8n4{c7 c3} ==> r8c3≠7
hidden-single-in-a-block ==> r8c2=7
biv-chain[4]: c8n4{r7 r3} - b2n4{r3c4 r1c5} - r1n7{c5 c3} - r1n5{c3 c8} ==> r7c8≠5
whip[1]: c8n5{r3 .} ==> r3c9≠5
t-whip[5]: b2n4{r3c4 r1c5} - r1c7{n4 n9} - r1c6{n9 n8} - c2n8{r1 r3} - r3c9{n8 .} ==> r3c4≠1
t-whip[5]: r7n9{c6 c9} - r8c9{n9 n1} - r3c9{n1 n8} - r2n8{c7 c4} - r1c6{n8 .} ==> r8c6≠9
biv-chain[5]: r8c6{n1 n3} - c5n3{r7 r3} - r3c1{n3 n5} - r8c1{n5 n6} - c4n6{r8 r9} ==> r9c4≠1
whip[5]: r8c9{n1 n9} - r3c9{n9 n8} - c2n8{r3 r1} - b1n6{r1c2 r2c1} - r2c8{n6 .} ==> r2c9≠1
whip[5]: c5n3{r3 r7} - r8c6{n3 n1} - c9n1{r8 r7} - r7n9{c9 c6} - r7n5{c6 .} ==> r3c5≠1
whip[1]: r3n1{c9 .} ==> r2c8≠1
biv-chain[3]: r1n6{c2 c8} - r2c8{n6 n8} - b2n8{r2c4 r1c6} ==> r1c2≠8
singles ==> r3c2=8, r1c6=8
naked-pairs-in-a-column: c9{r3 r8}{n1 n9} ==> r7c9≠9, r7c9≠1, r2c9≠9
singles ==> r7c9=5, r6c7=5, r4c6=5
whip[1]: b5n7{r5c6 .} ==> r5c3≠7
whip[1]: b5n9{r6c5 .} ==> r6c2≠9
whip[1]: b9n9{r8c9 .} ==> r8c4≠9
naked-pairs-in-a-block: b4{r5c3 r6c2}{n1 n3} ==> r6c1≠3
singles ==> r6c1=7, r4c8=7
whip[1]: b6n6{r5c9 .} ==> r2c9≠6
whip[1]: c1n3{r3 .} ==> r2c3≠3
hidden-pairs-in-a-column: c4{n5 n6}{r8 r9} ==> r8c4≠1
naked-pairs-in-a-row: r8{c1 c4}{n5 n6} ==> r8c3≠5
biv-chain[3]: r4c3{n9 n4} - r8n4{c3 c7} - r1c7{n4 n9} ==> r1c3≠9
biv-chain[3]: b1n9{r2c3 r1c2} - b1n6{r1c2 r2c1} - r2n3{c1 c6} ==> r2c6≠9
hidden-single-in-a-column ==> r7c6=9
biv-chain[4]: r3n1{c9 c8} - c8n5{r3 r1} - r1n6{c8 c2} - r1n9{c2 c7} ==> r3c9≠9
singles ==> r3c9=1, r8c9=9
whip[1]: r3n9{c5 .} ==> r2c4≠9
naked-single ==> r2c4=1
x-wing-in-rows: n1{r5 r8}{c3 c6} ==> r9c3≠1
biv-chain[3]: r5c4{n8 n4} - r4c5{n4 n6} - b6n6{r4c9 r5c9} ==> r5c9≠8
stte

[m_b_metcalf]

I was testing my code for (close your eyes) double backdoors, and that was almost the lowest rating I found. The highest was:

Code: Select all

 1 2 . 3 . . . . .
 4 . . . . . 3 . .
 . . 3 . 5 . . 2 .
 6 . . . 7 . . 8 .
 . . 2 1 . . 4 . .
 . . . . . 2 . . 6
 . 7 . . 8 . . 9 .
 . . 4 7 . . 5 . .
 . . . . . 9 . . 7   ED=11.2/11.2/10.6

12.3.....4.....3....3.5..2.6...7..8...21..4.......2..6.7..8..9...47..5.......9..7

from champagne in Game 195.

Mike

[denis_berthier]

I was testing my code for (close your eyes) double backdoors, and that was almost the lowest rating I found.

Do you mean that, for SER < 8.6:
1) you've found no puzzle with double backdoors (but possibly with single ones)
or
2) all the puzzles you've tested have single backdoors

In case 2, could you check with the controlled-bias collection?

[RSW]

I was testing my code for (close your eyes) double backdoors

My solver finds double, triple, quad etc., anti-backdoors, and came up with these:

Hidden Text: Show

Anti-backdoors
(Candidate eliminations that yield stte solution)
-4r1c7 & -5r1c3
-4r7c8 & -5r1c3
-6r1c8 & -4r1c7
-6r2c1 & -4r1c7
-3r2c6 & -4r1c7
-3r3c1 & -4r1c7
-3r5c7 & -4r1c7
-3r6c1 & -4r1c7
-5r8c1 & -4r1c7
-4r3c4 & -6r1c8
-2r4c2 & -6r1c8
-4r4c5 & -6r1c8
-4r5c1 & -6r1c8
-1r5c3 & -6r1c8
-9r6c2 & -6r1c8
-2r7c1 & -6r1c8
-4r7c8 & -6r1c8
-4r8c3 & -6r1c8
-2r9c5 & -6r1c8
-4r3c4 & -6r2c1
-2r4c2 & -6r2c1
-4r4c5 & -6r2c1
-4r5c1 & -6r2c1
-1r5c3 & -6r2c1
-9r6c2 & -6r2c1
-2r7c1 & -6r2c1
-4r7c8 & -6r2c1
-4r8c3 & -6r2c1
-2r9c5 & -6r2c1
-4r3c4 & -3r2c6
-4r7c8 & -3r2c6
-4r7c8 & -3r3c1
-4r7c8 & -3r5c7
-2r9c5 & -3r5c7
-4r7c8 & -3r6c1
-5r8c1 & -4r7c8
-2r9c5 & -6r8c2

But I'm too lazy (and not smart enough) to try to find a solution that exploits them.

[m_b_metcalf]

I was testing my code for (close your eyes) double backdoors, and that was almost the lowest rating I found.

Do you mean that, for SER < 8.6:
1) you've found no puzzle with double backdoors

Subsequently I found puzzles with lower SERs (the first one is a rarity):

Code: Select all

...........36.97...294.735..62...94...........57...23..957.341...15.26...........   ED=8.2/8.2/5.4   
1.2..3....4.5.....3....64...7.....8.........59.8...3....9..12.....8....4....5..78   ED=8.3/8.3/8.3   
1......2..3..2.........14.3....5..67.2.4..1....8..3.4...7.6.9..9..7.5.....49.....   ED=8.4/8.4/8.4   
..87......3...92..6......5.5..8...7...........1...3..4.2......9..76...8......43..   ED=8.5/8.5/3.8   
1.2..3....4.5.....5....63...7.....5.........78.9...6....1..92.....7....4....5..68   ED=8.5/8.5/8.4   

Mike