.
As usual, the first thing I do is, find the rating.
In the present case, one has W=7 but gW=6.
As expected for a puzzle with this high SER, W or gW, the simplest-first resolution path is rather long:
- Code: Select all
t-whip[4]: r4n8{c9 c6} - r5c4{n8 n4} - c5n4{r5 r1} - c5n8{r1 .} ==> r3c9≠8
whip[5]: r8n1{c5 c8} - c9n1{r9 r4} - b6n8{r4c9 r5c8} - c5n8{r5 r1} - b3n8{r1c8 .} ==> r3c5≠1
z-chain[4]: c5n1{r2 r8} - r8n5{c5 c8} - c7n5{r7 r3} - c7n2{r3 .} ==> r2c7≠1
z-chain[5]: r2n7{c4 c6} - r2n9{c6 c8} - r2n1{c8 c5} - b8n1{r8c5 r7c4} - c4n7{r7 .} ==> r2c4≠6
whip[5]: r8n5{c5 c8} - r8n1{c8 c5} - r2c5{n1 n2} - r1n2{c6 c3} - r1n5{c3 .} ==> r3c5≠5
t-whip[6]: r4c2{n5 n2} - r5n2{c2 c5} - r4c6{n2 n8} - b8n8{r9c6 r7c4} - b8n1{r7c4 r8c5} - r2c5{n1 .} ==> r2c2≠5
t-whip[6]: r4c6{n2 n8} - b8n8{r9c6 r7c4} - c4n7{r7 r2} - c4n1{r2 r3} - b3n1{r3c9 r2c8} - r2n9{c8 .} ==> r2c6≠2
g-whip[6]: b8n1{r8c5 r7c4} - b8n8{r7c4 r789c6} - r4n8{c6 c9} - r5c8{n8 n9} - c9n9{r6 r3} - c9n1{r3 .} ==> r8c8≠1
singles ==> r8c8=5, r8c5=1
whip[1]: b8n5{r9c6 .} ==> r1c6≠5, r2c6≠5, r3c6≠5
naked-pairs-in-a-column: c7{r4 r7}{n1 n6} ==> r3c7≠6, r3c7≠1, r2c7≠6
naked-pairs-in-a-row: r2{c5 c7}{n2 n5} ==> r2c3≠5, r2c3≠2, r2c2≠2, r2c1≠5, r2c1≠2
whip[1]: b1n2{r3c3 .} ==> r7c3≠2
whip[1]: b1n5{r3c3 .} ==> r7c3≠5, r9c3≠5
naked-pairs-in-a-block: b7{r7c3 r9c3}{n1 n3} ==> r9c2≠3, r9c1≠3, r7c2≠3, r7c1≠3
whip[1]: b7n3{r9c3 .} ==> r1c3≠3, r2c3≠3, r3c3≠3
naked-single ==> r2c3=6
whip[1]: b1n3{r2c2 .} ==> r2c6≠3, r2c8≠3
naked-pairs-in-a-row: r3{c3 c7}{n2 n5} ==> r3c6≠2, r3c5≠2
naked-single ==> r3c5=8
biv-chain[3]: r1c4{n6 n4} - r5c4{n4 n8} - c8n8{r5 r1} ==> r1c8≠6
biv-chain[3]: c8n6{r7 r3} - r3c4{n6 n1} - r2n1{c4 c8} ==> r7c8≠1
biv-chain[3]: r1c6{n3 n2} - r4c6{n2 n8} - c9n8{r4 r1} ==> r1c9≠3
biv-chain[3]: c8n6{r7 r3} - r1c9{n6 n8} - r1c8{n8 n3} ==> r7c8≠3
biv-chain[3]: r9c3{n1 n3} - r7n3{c3 c9} - b9n7{r7c9 r9c9} ==> r9c9≠1
biv-chain[3]: r6c9{n9 n6} - r1c9{n6 n8} - b6n8{r4c9 r5c8} ==> r5c8≠9
singles ==> r6c9=9, r6c2=3, r2c2=8, r2c1=3, r6c1=6, r5c2=9
biv-chain[3]: b3n9{r3c8 r2c8} - r2n1{c8 c4} - r3c4{n1 n6} ==> r3c8≠6
stte
So I started to look for shorter paths in gW8, using my version of François's fewer step algorithm. The best I found has 5 non-W1 steps:
1) g-whip[7]: r8c8{n5 n1} - b8n1{r8c5 r7c4} - b8n8{r7c4 r789c6} - r4n8{c6 c9} - r5c8{n8 n9} - c9n9{r6 r3} - c9n1{r3 .} ==> r8c5≠5singles ==> r8c5=1, r8c8=5
whip[1]: b8n5{r9c6 .} ==> r1c6≠5, r2c6≠5, r3c6≠5
2) whip[8]: r2n9{c8 c6} - r2n7{c6 c4} - r7c4{n7 n8} - r5n8{c4 c5} - c5n4{r5 r1} - r1n5{c5 c3} - r1n2{c3 c6} - r4c6{n2 .} ==> r5c8≠9singles ==> r6c9=9, r6c2=3, r6c1=6, r5c2=9
3) whip[8]: b6n8{r4c9 r5c8} - r5c4{n8 n4} - c5n4{r5 r1} - c5n8{r1 r3} - r1c4{n8 n6} - r3c4{n6 n1} - r3c9{n1 n3} - r1c8{n3 .} ==> r4c9≠6singles ==> r4c7=6, r7c7=1, r9c3=1
4) naked-pairs-in-a-row: r2{c5 c7}{n2 n5} ==> r2c1≠5, r2c6≠2, r2c3≠5, r2c3≠2, r2c2≠5, r2c2≠2, r2c1≠2singles ==> r2c2=8, r2c1=3, r2c3=6, r7c3=3
5) whip[6]: r2c8{n1 n9} - r3n9{c8 c6} - r2c6{n9 n7} - r9n7{c6 c9} - r9n3{c9 c8} - r3n3{c8 .} ==> r3c9≠1stte
Notice the 1st step is the same as François's.
Indeed, in my version of the algorithm (which counts as steps all the active rules, including Subsets), the first 4 steps are the only possible ones - I mean the only ones with the highest score = the highness number of candidates eliminated.
Finally, using Forcing-T&E, a 1-step solution is available:
- Code: Select all
FORCING[3]-T&E(W1) applied to trivalue candidates n1r5c8, n8r5c8 and n9r5c8 :
===> 5 values decided in the three cases: n5r8c8 n1r8c5 n6r2c3 n4r9c8 n4r7c2
===> 68 candidates eliminated in the three cases: n3r1c3 n6r1c3 n8r1c4 n2r1c5 n8r1c5 n8r1c6 n5r1c8 n6r1c8 n2r2c1 n5r2c1 n5r2c2 n2r2c3 n3r2c3 n5r2c3 n6r2c4 n1r2c5 n2r2c5 n2r2c6 n3r2c6 n5r2c6 n1r2c7 n6r2c7 n3r2c8 n5r2c8 n6r2c8 n3r3c3 n6r3c3 n8r3c4 n1r3c5 n5r3c5 n2r3c6 n5r3c6 n8r3c6 n1r3c7 n6r3c7 n1r3c8 n5r3c8 n8r3c8 n3r3c9 n8r3c9 n2r4c1 n6r4c9 n3r7c1 n8r7c1 n2r7c2 n3r7c2 n5r7c2 n8r7c2 n1r7c3 n1r7c4 n7r7c6 n5r7c7 n1r7c8 n4r7c8 n5r7c8 n1r7c9 n6r7c9 n5r8c5 n1r8c8 n3r9c1 n5r9c1 n3r9c2 n4r9c2 n5r9c3 n8r9c6 n1r9c8 n3r9c8 n5r9c8
stte
