.
Thanks for your solutions.
Here is my simplest-first solution, using only two of the 5 most frequent impossible patterns (besides Tridagon) and with all the chains restricted to length 6.
There are more impossible patterns that lead to eliminations, but none that allows to have shorter chains.
- Code: Select all
hidden-pairs-in-a-column: c6{n2 n6}{r1 r3} ==> r3c6≠9, r3c6≠7, r3c6≠4, r3c6≠3, r1c6≠9, r1c6≠4, r1c6≠3
hidden-single-in-a-block ==> r3c4=7
The impossible patterns that will be used:
- Code: Select all
Trid-OR3-relation for digits 3, 9 and 4 in blocks:
b2, with cells (marked #): r1c4, r2c6, r3c5
b3, with cells (marked #): r1c9, r2c8, r3c7
b5, with cells (marked #): r5c4, r6c6, r4c5
b6, with cells (marked #): r5c9, r6c7, r4c8
with 3 guardians (in cells marked @): n5r5c4 n8r5c4 n2r5c9
+-------------------------+-------------------------+-------------------------+
! 1246 23469 13469 ! 349# 5 26 ! 7 8 349# !
! 45 3459 7 ! 1 8 349# ! 2 349# 6 !
! 246 23469 8 ! 7 349# 26 ! 349# 1 5 !
+-------------------------+-------------------------+-------------------------+
! 24567 2345679 3469 ! 34589 349# 34589 ! 13489 349# 12349 !
! 245 23459 349 ! 34589#@ 7 1 ! 3489 6 2349#@ !
! 8 1 349 ! 6 2 349# ! 349# 5 7 !
+-------------------------+-------------------------+-------------------------+
! 3 467 146 ! 489 149 4789 ! 5 2 1489 !
! 147 8 5 ! 2 6 3479 ! 1349 3479 1349 !
! 9 47 2 ! 3458 134 34578 ! 6 347 1348 !
+-------------------------+-------------------------+-------------------------+
EL14c30-OR5-relation for digits: 3, 4 and 9
in cells (marked #): (r5c9 r4c4 r4c5 r4c8 r6c3 r6c6 r6c7 r3c5 r3c7 r2c6 r2c8 r1c3 r1c4 r1c9)
with 5 guardians (in cells marked @) : n2r5c9 n5r4c4 n8r4c4 n1r1c3 n6r1c3
+-------------------------+-------------------------+-------------------------+
! 1246 23469 13469#@ ! 349# 5 26 ! 7 8 349# !
! 45 3459 7 ! 1 8 349# ! 2 349# 6 !
! 246 23469 8 ! 7 349# 26 ! 349# 1 5 !
+-------------------------+-------------------------+-------------------------+
! 24567 2345679 3469 ! 34589#@ 349# 34589 ! 13489 349# 12349 !
! 245 23459 349 ! 34589 7 1 ! 3489 6 2349#@ !
! 8 1 349# ! 6 2 349# ! 349# 5 7 !
+-------------------------+-------------------------+-------------------------+
! 3 467 146 ! 489 149 4789 ! 5 2 1489 !
! 147 8 5 ! 2 6 3479 ! 1349 3479 1349 !
! 9 47 2 ! 3458 134 34578 ! 6 347 1348 !
+-------------------------+-------------------------+-------------------------+
EL14c1s-OR4-relation for digits: 3, 4 and 9
in cells (marked #): (r8c6 r8c7 r8c9 r5c9 r6c6 r6c7 r4c5 r4c8 r2c6 r2c8 r3c5 r3c7 r1c4 r1c9)
with 4 guardians (in cells marked @) : n7r8c6 n1r8c7 n1r8c9 n2r5c9
+-------------------------+-------------------------+-------------------------+
! 1246 23469 13469 ! 349# 5 26 ! 7 8 349# !
! 45 3459 7 ! 1 8 349# ! 2 349# 6 !
! 246 23469 8 ! 7 349# 26 ! 349# 1 5 !
+-------------------------+-------------------------+-------------------------+
! 24567 2345679 3469 ! 34589 349# 34589 ! 13489 349# 12349 !
! 245 23459 349 ! 34589 7 1 ! 3489 6 2349#@ !
! 8 1 349 ! 6 2 349# ! 349# 5 7 !
+-------------------------+-------------------------+-------------------------+
! 3 467 146 ! 489 149 4789 ! 5 2 1489 !
! 147 8 5 ! 2 6 3479#@ ! 1349#@ 3479 1349#@ !
! 9 47 2 ! 3458 134 34578 ! 6 347 1348 !
+-------------------------+-------------------------+-------------------------+
z-chain[4]: c6n5{r9 r4} - c6n8{r4 r7} - r7n7{c6 c2} - r9c2{n7 .} ==> r9c6≠4
z-chain[4]: r7n6{c2 c3} - b7n1{r7c3 r8c1} - c1n7{r8 r4} - c1n6{r4 .} ==> r1c2≠6, r3c2≠6
Notice that the forthcoming Trid-OR3-whips are related. They appear in several parts because there's no "blocked" version of ORk-chains (and therefore simpler rules are allowed to interrupt them before they can do more eliminations).
Trid-OR3-whip[6]: r4n7{c2 c1} - r4n2{c1 c9} - r4n1{c9 c7} - c7n8{r4 r5} - OR3{{n8r5c4 n2r5c9 | n5r5c4}} - b4n5{r5c1 .} ==> r4c2≠9, r4c2≠6singles ==> r7c2=6, r7c6=7
- Code: Select all
+-------------------+-------------------+-------------------+
! 1246 2349 13469 ! 349 5 26 ! 7 8 349 !
! 45 3459 7 ! 1 8 349 ! 2 349 6 !
! 246 2349 8 ! 7 349 26 ! 349 1 5 !
+-------------------+-------------------+-------------------+
! 24567 23457 3469 ! 34589 349 34589 ! 13489 349 12349 !
! 245 23459 349 ! 34589 7 1 ! 3489 6 2349 !
! 8 1 349 ! 6 2 349 ! 349 5 7 !
+-------------------+-------------------+-------------------+
! 3 6 14 ! 489 149 7 ! 5 2 1489 !
! 147 8 5 ! 2 6 349 ! 1349 3479 1349 !
! 9 47 2 ! 3458 134 358 ! 6 347 1348 !
+-------------------+-------------------+-------------------+
At least one candidate of a previous EL14c1s-OR4-relation between candidates n7r8c6 n1r8c7 n1r8c9 n2r5c9 has just been eliminated.
There remains an EL14c1s-OR3-relation between candidates: n1r8c7 n1r8c9 n2r5c9
hidden-pairs-in-a-column: c6{n5 n8}{r4 r9} ==> r9c6≠3, r4c6≠9, r4c6≠4, r4c6≠3
EL14c1s-OR3-whip[4]: c1n1{r1 r8} - OR3{{n1r8c9 n1r8c7 | n2r5c9}} - r5c1{n2 n5} - r2c1{n5 .} ==> r1c1≠4
Trid-OR3-whip[6]: r4n7{c2 c1} - r4n2{c1 c9} - r4n1{c9 c7} - c7n8{r4 r5} - OR3{{n8r5c4 n2r5c9 | n5r5c4}} - b4n5{r5c1 .} ==> r4c2≠4, r4c2≠3
Trid-OR3-whip[6]: r4n7{c1 c2} - r4n2{c2 c9} - r4n1{c9 c7} - c7n8{r4 r5} - OR3{{n8r5c4 n2r5c9 | n5r5c4}} - b4n5{r5c1 .} ==> r4c1≠6hidden-single-in-a-block ==> r4c3=6
- Code: Select all
+-------------------+-------------------+-------------------+
! 126 2349 1349 ! 349 5 26 ! 7 8 349 !
! 45 3459 7 ! 1 8 349 ! 2 349 6 !
! 246 2349 8 ! 7 349 26 ! 349 1 5 !
+-------------------+-------------------+-------------------+
! 2457 257 6 ! 34589 349 58 ! 13489 349 12349 !
! 245 23459 349 ! 34589 7 1 ! 3489 6 2349 !
! 8 1 349 ! 6 2 349 ! 349 5 7 !
+-------------------+-------------------+-------------------+
! 3 6 14 ! 489 149 7 ! 5 2 1489 !
! 147 8 5 ! 2 6 349 ! 1349 3479 1349 !
! 9 47 2 ! 3458 134 58 ! 6 347 1348 !
+-------------------+-------------------+-------------------+
At least one candidate of a previous EL14c30-OR5-relation between candidates n2r5c9 n5r4c4 n8r4c4 n1r1c3 n6r1c3 has just been eliminated.
There remains an EL14c30-OR4-relation between candidates: n2r5c9 n5r4c4 n8r4c4 n1r1c3
EL14c1s-OR3-ctr-whip[5]: b1n6{r3c1 r1c1} - c1n1{r1 r8} - c1n7{r8 r4} - c1n2{r4 r5} - OR3{{n1r8c7 n1r8c9 n2r5c9 | .}} ==> r3c1≠4naked-pairs-in-a-row: r3{c1 c6}{n2 n6} ==> r3c2≠2
EL14c1s-OR3-whip[6]: r4n2{c2 c9} - r4n1{c9 c7} - OR3{{n1r8c7 n2r5c9 | n1r8c9}} - c1n1{r8 r1} - r1n2{c1 c6} - r1n6{c6 .} ==> r5c2≠2
Trid-OR3-whip[6]: r4n7{c1 c2} - r4n2{c2 c9} - r4n1{c9 c7} - c7n8{r4 r5} - OR3{{n8r5c4 n2r5c9 | n5r5c4}} - b4n5{r5c1 .} ==> r4c1≠4
EL14c30-OR4-whip[6]: r4n7{c2 c1} - b4n2{r4c1 r5c1} - r3c1{n2 n6} - r1c1{n6 n1} - OR4{{n1r1c3 n2r5c9 n5r4c4 | n8r4c4}} - r4c6{n8 .} ==> r4c2≠5z-chain[4]: r2c1{n4 n5} - r5c1{n5 n2} - r4c2{n2 n7} - r9c2{n7 .} ==> r8c1≠4
t-whip[4]: b4n4{r5c3 r6c3} - c1n4{r5 r2} - c6n4{r2 r8} - r7n4{c4 .} ==> r5c9≠4
whip[4]: b7n4{r9c2 r7c3} - b7n1{r7c3 r8c1} - b9n1{r8c7 r7c9} - c9n8{r7 .} ==> r9c9≠4
t-whip[5]: b4n4{r5c3 r6c3} - b7n4{r7c3 r9c2} - b1n4{r1c2 r2c1} - c6n4{r2 r8} - c8n4{r8 .} ==> r5c7≠4
t-whip[5]: b4n4{r5c3 r6c3} - c1n4{r5 r2} - c6n4{r2 r8} - r7n4{c4 c9} - r1n4{c9 .} ==> r5c4≠4
whip[1]: r5n4{c3 .} ==> r6c3≠4
whip[6]: r6n4{c6 c7} - r3n4{c7 c2} - r1n4{c2 c9} - r8n4{c9 c8} - c8n7{r8 r9} - r9c2{n7 .} ==> r2c6≠4
whip[5]: b6n4{r4c9 r6c7} - r3n4{c7 c2} - b2n4{r3c5 r1c4} - r9n4{c4 c8} - r2n4{c8 .} ==> r4c5≠4
EL14c30-OR4-whip[6]: c1n4{r5 r2} - c1n5{r2 r4} - r4c6{n5 n8} - OR4{{n8r4c4 n2r5c9 n5r4c4 | n1r1c3}} - b7n1{r7c3 r8c1} - c1n7{r8 .} ==> r5c1≠2The end is easy, in Z6 (and could probably be shortened):
- Code: Select all
hidden-single-in-a-row ==> r5c9=2
naked-pairs-in-a-column: c1{r2 r5}{n4 n5} ==> r4c1≠5
whip[1]: r4n5{c6 .} ==> r5c4≠5
z-chain[5]: c9n8{r7 r9} - r9c6{n8 n5} - c4n5{r9 r4} - b5n4{r4c4 r6c6} - r8n4{c6 .} ==> r7c9≠4
z-chain[6]: b5n5{r4c4 r4c6} - r4n8{c6 c7} - c7n1{r4 r8} - b7n1{r8c1 r7c3} - r7n4{c3 c5} - b2n4{r3c5 .} ==> r4c4≠4
hidden-single-in-a-block ==> r6c6=4
whip[1]: r8n4{c9 .} ==> r9c8≠4
biv-chain[4]: r9c8{n3 n7} - b7n7{r9c2 r8c1} - b7n1{r8c1 r7c3} - b8n1{r7c5 r9c5} ==> r9c5≠3
whip[2]: c5n3{r3 r4} - b6n3{r4c7 .} ==> r3c7≠3
biv-chain[2]: c6n3{r8 r2} - b3n3{r2c8 r1c9} ==> r8c9≠3
z-chain[3]: b3n3{r1c9 r2c8} - r9n3{c8 c4} - b5n3{r5c4 .} ==> r4c9≠3
z-chain[3]: b6n3{r6c7 r4c8} - c5n3{r4 r3} - c6n3{r2 .} ==> r8c7≠3
whip[1]: c7n3{r6 .} ==> r4c8≠3
z-chain[3]: b2n4{r1c4 r3c5} - c5n3{r3 r4} - b5n9{r4c5 .} ==> r1c4≠9
z-chain[3]: r1n9{c3 c9} - b3n3{r1c9 r2c8} - r2c6{n3 .} ==> r2c2≠9
z-chain[3]: r1c4{n4 n3} - b3n3{r1c9 r2c8} - r2n4{c8 .} ==> r1c3≠4, r1c2≠4
biv-chain[4]: r1n4{c4 c9} - c9n3{r1 r9} - r9c8{n3 n7} - r9c2{n7 n4} ==> r9c4≠4
biv-chain[3]: r7c3{n1 n4} - r9n4{c2 c5} - b8n1{r9c5 r7c5} ==> r7c9≠1
biv-chain[4]: c9n3{r1 r9} - r9c8{n3 n7} - c2n7{r9 r4} - c2n2{r4 r1} ==> r1c2≠3
z-chain[4]: r3n3{c2 c5} - r4c5{n3 n9} - r4c8{n9 n4} - r2n4{c8 .} ==> r3c2≠4
S2-tte
