Anti-Knight grid of interest / Weak links in AK, AN and NC

[newman-iknewit]

I'm sure other grids are known which defeat SE with anti-knight or other constraints, but thought I would share this one.

jovi_al (of the CTC discord server and LMD, among other places), found this anti-knight grid which SukakuExplainer rates at 11.8:

31.....5424.....36.............................................18.....7552.....68

I pointed out that either of the 5s in the bottom rows could be removed (or one of the 6s), and we both re-ran it:

java -Xrs -Xmx500m -cp SukakuExplainer.jar diuf.sudoku.test.serate --isAntiKnight=1 31.....5424.....36.............................................18.....75.2.....68
20.0/12.6/2.9

[1to9only]

The 12.6 rating is quite a Nested Forcing Chains (+ Dynamic Forcing Chains) ED=10.5 + 2.1 for chains with 4097-6144 (total) nodes. The 12.6 solving step is a: Contradiction Forcing Chain (w/5859 nodes). I have not rated this further as it's occupying my computer for too long!!

If you have memory to spare, increase the maximum java heap size, use: -Xmx2g or -Xmx4g To use all cpu cores, to speed up rating, use: --threads=0

To output the solution path when rating, use: --after="%i %r, %s" If the command is in a batch file, you have to double-up the % char, e.g: --after="%%i %%r, %%s" Pipe the output to a file.

java.exe -Xrs -Xmx4g -cp SukakuExplainer.jar diuf.sudoku.test.serate --isAntiKnight=1 --threads=0 --after="%i %r, %s" --input=puzzle.txt >output.txt

[newman-iknewit]

I have a new computer coming in the next month, I'll give it a try then :)

[1to9only]

31.....5424.....36.............................................18.....7552.....68 ED=11.8/2.9/2.9

31.....5424.....36.............................................18.....7.52.....68 at least ED=12.5
31.....5424.....36.............................................18.....75.2.....68 at least ED=12.6

31.....5424.....36.............................................18.....7552......8 ED=12.2/12.2/2.9

Removing the other 6 (at r2c9) results in SE reporting that the grid has multiple solutions.

[sscg13]

.9....6..3.....2......4...8..........5..............1...2............7.9.6...8... is at least 12.3

Immediately after the 12.3 step, it stalled for more than 30 minutes (whereas the 12.3 step only took a couple of minutes) and I forcibly ended the program.

In fact, .9....6..3.....2..........8..........5..............1...2............7.9.6...8... also has a unique solution (but SE stalls on the first > 10 step)

[1to9only]

.9....6..3.....2......4...8..........5..............1...2............7.9.6...8... ED=12.4/1.2/1.2

Solution Path:

Click to show.

1.2, Hidden Single: r7c8: 8 in block: r7c8=8 1.2, Hidden Single: r6c7: 8 in block: r6c7=8 2.9, General Intersection: Cells r1c1,r3c1,r3c2 on value 2 in block 1: r5c1<>2 2.9, General Intersection: Cells r4c3,r5c3,r6c2,r6c3 on value 3 in block 4: r8c3<>3 2.9, General Intersection: Cells r7c2,r8c2,r9c3 on value 3 in block 7: r7c4<>3 2.9, General Intersection: Cells r1c1,r1c3,r2c3 on value 5 in block 1: r1c5<>5 2.9, General Intersection: Cells r2c3,r3c1,r3c3 on value 6 in block 1: r4c3<>6 2.9, General Intersection: Cells r7c9,r8c8 on value 6 in block 9: r6c9<>6, r5c8<>6, r7c6<>6 2.9, General Intersection: Cells r7c4,r7c6,r9c4 on value 7 in block 8: r6c4<>7 2.9, General Intersection: Cells r4c4,r4c5,r5c4 on value 8 in block 5: r2c4<>8, r4c2<>8 2.9, General Intersection: Cells r1c4,r1c5,r2c5 on value 8 in block 2: r1c3<>8 2.9, General Intersection: Cells r2c5,r2c6,r3c4,r3c6 on value 9 in block 2: r4c6<>9 2.9, General Intersection: Cells r2c8,r3c7,r3c8 on value 9 in block 3: r3c6<>9, r5c8<>9 2.9, General Intersection: Cells r4c7,r4c8,r5c7 on value 9 in block 6: r4c5<>9 2.9, General Intersection: Cells r5c7,r7c7,r9c7 on value 4 in column 7: r7c6<>4 2.9, General Intersection: Cells r7c4,r8c4,r8c6,r9c4 on value 4 in block 8: r8c2<>4 4.3, Grouped 2 Strong links 201: Cell r4c3,r4c1,r7c1,r7c4 on value 9: r5c5<>9 9.0, Double Forcing Chain (w/3 nodes): r6c9.5 on & off ==> r8c5.5 off: r8c5<>5 9.0, Double Forcing Chain (w/3 nodes): r3c4.9 on & off ==> r4c4.9 off: r4c4<>9 9.0, Double Forcing Chain (w/3 nodes): r4c5.8 on & off ==> r4c1.8 off: r4c1<>8 9.0, Region Forcing Chains (w/3 nodes): 6 in column ==> r4c5.6 off: r4c5<>6 9.1, Double Forcing Chain (w/5 nodes): r4c9.6 on & off ==> r5c6.6 off: r5c6<>6 9.4, Region Forcing Chains (w/14 nodes): 5 in block ==> r8c6.5 off: r8c6<>5 9.6, Double Forcing Chain (w/29 nodes): r4c5.1 on & off ==> r3c4.1 off: r3c4<>1 10.6, Contradiction Forcing Chain (w/163 nodes): r9c1.5 on ==> r9c4.1 both on & off: r9c1<>5 10.9, Contradiction Forcing Chain (w/438 nodes): r4c5.1 on ==> r6c3.3 both on & off: r4c5<>1 11.3, Contradiction Forcing Chain (w/370 nodes): r4c8.4 on ==> r8c6.4 both on & off: r4c8<>4 12.1, Contradiction Forcing Chain (w/946 nodes): r2c5.1 on ==> r3c6.2 both on & off: r2c5<>1 12.1, Contradiction Forcing Chain (w/986 nodes): r8c8.5 on ==> r8c3.8 both on & off: r8c8<>5 12.2, Contradiction Forcing Chain (w/1254 nodes): r6c9.4 on ==> r9c5.9 both on & off: r6c9<>4 12.3, Double Forcing Chain (w/1617 nodes): r4c9.4 on & off ==> r5c1.4 off: r5c1<>4 10.8, Double Forcing Chain (w/12 nodes): r6c9.5 on & off ==> r2c8.5 off: r2c8<>5 10.0, Contradiction Forcing Chain (w/126 nodes): r1c9.4 on ==> r5c6.3 both on & off: r1c9<>4 10.9, Double Forcing Chain (w/16 nodes): r9c1.9 on & off ==> r9c4.9 off: r9c4<>9 12.0, Contradiction Forcing Chain (w/576 nodes): r8c8.4 on ==> r5c8.2 both on & off: r8c8<>4 12.2, Contradiction Forcing Chain (w/1130 nodes): r8c4.5 on ==> r5c8.2 both on & off: r8c4<>5 2.9, General Intersection: Cells r8c1,r8c3 on value 5 in row 8: r9c3<>5 10.9, Double Forcing Chain (w/13 nodes): r9c1.9 on & off ==> r6c5.9 off: r6c5<>9 10.2, Contradiction Forcing Chain (w/209 nodes): r6c6.2 on ==> r8c4.4 both on & off: r6c6<>2 10.2, Region Forcing Chains (w/41 nodes): 9 in column ==> r5c1.9 off: r5c1<>9 11.6, Region Forcing Chains (w/169 nodes): 9 in block ==> r2c5.5 off: r2c5<>5 12.2, Double Forcing Chain (w/1472 nodes): r2c2.7 on & off ==> r5c3.7 off: r5c3<>7 12.4, Contradiction Forcing Chain (w/2214 nodes): r4c4.2 on ==> r3c6.1 both on & off: r4c4<>2 11.2, Double Forcing Chain (w/39 nodes): r4c7.9 on & off ==> r2c9.5 off: r2c9<>5 12.2, Region Forcing Chains (w/1160 nodes): 4 in block ==> r6c3.4 off: r6c3<>4 10.7, Contradiction Forcing Chain (w/229 nodes): r8c1.4 on ==> r3c3.1 both on & off: r8c1<>4 12.0, Contradiction Forcing Chain (w/621 nodes): r4c9.4 on ==> r8c5.3 both on & off: r4c9<>4 2.9, General Intersection: Cells r5c7,r5c8,r5c9 on value 4 in block 6: r5c3<>4 12.2, Contradiction Forcing Chain (w/1381 nodes): r1c5.3 on ==> r5c8.7 both on & off: r1c5<>3 11.4, Contradiction Forcing Chain (w/413 nodes): r5c6.2 on ==> r7c4.5 both on & off: r5c6<>2 11.4, Contradiction Forcing Chain (w/394 nodes): r3c4.2 on ==> r6c4.9 both on & off: r3c4<>2 11.5, Contradiction Forcing Chain (w/538 nodes): r4c4.3 on ==> r2c8.7 both on & off: r4c4<>3 12.1, Contradiction Forcing Chain (w/859 nodes): r9c4.3 on ==> r2c9.1 both on & off: r9c4<>3 12.0, Region Forcing Chains (w/659 nodes): 4 in block ==> r7c4.4 off: r7c4<>4 12.2, Contradiction Forcing Chain (w/1100 nodes): r4c4.6 on ==> r3c6.5 both on & off: r4c4<>6 11.3, Contradiction Forcing Chain (w/378 nodes): r1c5.1 on ==> r6c1.7 both on & off: r1c5<>1 2.9, General Intersection: Cells r5c5,r7c5,r8c5,r9c5 on value 1 in column 5: r7c4<>1 11.1, Contradiction Forcing Chain (w/188 nodes): r2c2.1 on ==> r6c3.3 both on & off: r2c2<>1 9.3, Cell Forcing Chains (w/12 nodes): r1c5 ==> r4c4.1 off: r4c4<>1 10.9, Double Forcing Chain (w/72 nodes): r2c3.8 on & off ==> r4c5.8 off: r4c5<>8 2.9, General Intersection: Cells r4c4,r5c4 on value 8 in block 5: r1c4<>8 2.9, General Intersection: Cells r1c5,r2c5 on value 8 in block 2: r2c3<>8 8.3, Region Forcing Chains (w/10 nodes): 8 in block ==> r8c1.1 off: r8c1<>1 10.2, Region Forcing Chains (w/44 nodes): 2 in block ==> r8c4.3 off: r8c4<>3 10.2, Contradiction Forcing Chain (w/237 nodes): r9c4.4 on ==> r4c4.8 both on & off: r9c4<>4 2.9, General Intersection: Cells r8c4,r8c6 on value 4 in block 8: r8c3<>4 9.0, Double Forcing Chain (w/3 nodes): r4c4.4 on & off ==> r4c1.4 off: r4c1<>4 10.0, Contradiction Forcing Chain (w/124 nodes): r2c2.4 on ==> r9c9.2 both on & off: r2c2<>4 2.9, General Intersection: Cells r1c1,r1c3 on value 4 in block 1: r1c8<>4 10.0, Contradiction Forcing Chain (w/125 nodes): r8c6.3 on ==> r7c7.5 both on & off: r8c6<>3 2.9, General Intersection: Cells r7c5,r7c6,r8c5,r9c5 on value 3 in block 8: r5c5<>3 9.7, Cell Forcing Chains (w/42 nodes): r9c4 ==> r2c4.7 off: r2c4<>7 10.1, Contradiction Forcing Chain (w/137 nodes): r8c4.1 on ==> r9c4.5 both on & off: r8c4<>1 10.1, Contradiction Forcing Chain (w/162 nodes): r4c6.7 on ==> r4c1.2 both on & off: r4c6<>7 10.4, Region Forcing Chains (w/65 nodes): 3 in block ==> r7c2.4 off: r7c2<>4 2.9, General Intersection: Cells r4c2,r6c2 on value 4 in column 2: r6c1<>4 9.9, Region Forcing Chains (w/85 nodes): 4 in row ==> r4c2.1 off: r4c2<>1 10.1, Contradiction Forcing Chain (w/180 nodes): r4c1.9 on ==> r9c9.3 both on & off: r4c1<>9 10.2, Contradiction Forcing Chain (w/210 nodes): r4c6.4 on ==> r7c5.9 both on & off: r4c6<>4 9.3, Double Forcing Chain (w/12 nodes): r6c4.2 on & off ==> r9c3.1 off: r9c3<>1 9.3, Region Forcing Chains (w/12 nodes): 2 in block ==> r8c6.1 off: r8c6<>1 9.0, Double Forcing Chain (w/4 nodes): r3c7.1 on & off ==> r7c1.1 off: r7c1<>1 9.0, Double Forcing Chain (w/4 nodes): r3c7.1 on & off ==> r9c1.1 off: r9c1<>1 9.5, Cell Forcing Chains (w/18 nodes): r8c5 ==> r4c5.3 off: r4c5<>3 9.0, Contradiction Forcing Chain (w/20 nodes): r4c2.7 on ==> r6c9.5 both on & off: r4c2<>7 9.6, Double Forcing Chain (w/26 nodes): r8c2.3 on & off ==> r9c7.3 off: r9c7<>3 2.9, General Intersection: Cells r3c7,r4c7,r5c7,r7c7 on value 3 in column 7: r5c8<>3 9.5, Double Forcing Chain (w/22 nodes): r4c7.9 on & off ==> r7c6.9 off: r7c6<>9 9.6, Double Forcing Chain (w/30 nodes): r8c2.3 on & off ==> r7c6.3 off: r7c6<>3 2.9, General Intersection: Cells r7c5,r8c5,r9c5 on value 3 in block 8: r6c5<>3 9.4, Double Forcing Chain (w/15 nodes): r2c5.9 on & off ==> r6c5.7 off: r6c5<>7 9.5, Cell Forcing Chains (w/18 nodes): r2c4 ==> r7c5.5 off: r7c5<>5 9.3, Region Forcing Chains (w/12 nodes): 5 in row ==> r4c6.5 off: r4c6<>5 9.5, Cell Forcing Chains (w/18 nodes): r2c4 ==> r9c5.5 off: r9c5<>5 2.9, General Intersection: Cells r4c5,r6c5 on value 5 in column 5: r6c6<>5 2.9, General Intersection: Cells r6c5,r6c9 on value 5 in row 6: r7c7<>5 9.1, Double Forcing Chain (w/6 nodes): r7c4.5 on & off ==> r6c5.5 on: r6c5<>6, r6c5=5 2.9, General Intersection: Cells r5c5,r7c5,r8c5 on value 6 in column 5: r7c4<>6 9.3, Double Forcing Chain (w/10 nodes): r7c5.9 on & off ==> r9c3.9 off: r9c3<>9 2.9, General Intersection: Cells r7c1,r9c1 on value 9 in block 7: r6c1<>9 9.0, Double Forcing Chain (w/3 nodes): r7c4.9 on & off ==> r5c4.9 off: r5c4<>9 9.3, Double Forcing Chain (w/10 nodes): r8c3.8 on & off ==> r7c4.7 off: r7c4<>7 7.5, TUVWXYZ-Wing 1419: Cells r5c5,r7c4,r7c5,r7c6,r8c5,r9c5,r4c5 on value 7: r5c6<>7 6.3, VWXYZ-Wing 2413: Cells r3c7,r5c7,r7c7,r9c7,r5c6 on values 3,9: r4c7<>5 9.1, Double Forcing Chain (w/5 nodes): r9c4.1 on & off ==> r8c5.1 off: r8c5<>1 2.9, General Intersection: Cells r8c2,r8c3 on value 1 in row 8: r7c2<>1 4.0, Hidden Triplet: Cells r8c1,r8c2,r8c3: 1,5,8 in block: r8c2<>3 2.9, General Intersection: Cells r7c2,r9c3 on value 3 in block 7: r5c3<>3 2.9, General Intersection: Cells r4c3,r6c2,r6c3 on value 3 in block 4: r6c4<>3 2.9, General Intersection: Cells r8c5,r8c8 on value 3 in row 8: r7c7<>3 2.9, General Intersection: Cells r3c7,r4c7,r5c7 on value 3 in column 7: r4c9<>3 5.6, WXYZ-Wing 138: Cells r7c6,r9c4,r9c7,r7c7 on value 1: r9c9<>1 6.3, VWXYZ-Wing 1412: Cells r3c7,r5c7,r7c7,r9c7,r5c6 on value 3: r3c6<>3 9.2, Contradiction Forcing Chain (w/41 nodes): r3c4.7 on ==> r3c8.9 both on & off: r3c4<>7 9.2, Contradiction Forcing Chain (w/42 nodes): r6c4.2 on ==> r4c6.3 both on & off: r6c4<>2 2.9, General Intersection: Cells r4c5,r5c5 on value 2 in block 5: r9c5<>2 2.9, General Intersection: Cells r8c4,r8c6 on value 2 in block 8: r8c8<>2 3.0, Generalized Naked Pair: Cells r8c5,r8c8: 3,6 in row: r8c6<>6 2.9, General Intersection: Cells r7c5,r8c5 on value 6 in block 8: r5c5<>6 9.2, Contradiction Forcing Chain (w/46 nodes): r7c5.9 on ==> r6c3.9 both on & off: r7c5<>9 9.0, Region Forcing Chains (w/21 nodes): 3 in row ==> r9c8.4 off: r9c8<>4 9.2, Contradiction Forcing Chain (w/47 nodes): r4c2.2 on ==> r7c6.5 both on & off: r4c2<>2 2.3, Naked Single: r4c2: 4: r4c2=4 9.2, Contradiction Forcing Chain (w/42 nodes): r4c1.6 on ==> r9c5.1 both on & off: r4c1<>6 9.2, Contradiction Forcing Chain (w/48 nodes): r9c5.3 on ==> r4c6.1 both on & off: r9c5<>3 3.4, Hidden Pair: Cells r7c5,r8c5: 3,6 in block: r7c5<>1 2.9, General Intersection: Cells r9c4,r9c5 on value 1 in block 8: r9c7<>1 4.0, Skyscraper 011: Cell r6c2,r7c2,r7c5,r8c5 on value 3: r6c6<>3 5.6, WXYZ-Wing 138: Cells r5c6,r6c4,r6c6,r7c5 on value 6: r8c5<>6, r5c4<>6, r6c3<>6 1.2, Hidden Single: r7c5: 6 in block: r7c5=6 1.2, Hidden Single: r8c5: 3 in block: r8c5=3 1.2, Hidden Single: r7c2: 3 in block: r7c2=3 1.2, Hidden Single: r8c8: 6 in block: r8c8=6 3.4, Hidden Pair: Cells r9c8,r9c9: 2,3 in block: r9c9<>4,5, r9c8<>5 2.9, General Intersection: Cells r7c9,r9c7 on value 5 in block 9: r7c6<>5 2.3, Naked Single: r7c6: 7: r7c6=7 2.9, General Intersection: Cells r7c4,r9c4 on value 5 in block 8: r1c4<>5, r3c4<>5, r2c4<>5 2.9, General Intersection: Cells r1c4,r1c5,r2c5 on value 7 in block 2: r1c3<>7 6.4, VWXYZ-Wing 139: Cells r2c5,r4c5,r5c5,r9c5,r2c2 on value 7: r3c3<>7 5.6, WXYZ-Wing 137: Cells r4c1,r6c1,r6c2,r3c3 on value 6: r3c1<>6, r5c3<>6 6.6, UVWXYZ-Wing 1313: Cells r6c1,r6c2,r6c4,r6c6,r6c9,r5c6 on value 3: r4c8<>3, r5c7<>3, r5c9<>3 2.9, General Intersection: Cells r5c4,r5c6 on value 3 in row 5: r4c6<>3 2.9, General Intersection: Cells r1c6,r5c6 on value 3 in column 6: r3c7<>3 1.5, Hidden Single: r4c7: 3 in column: r4c7=3 1.2, Hidden Single: r6c3: 3 in block: r6c3=3 2.0, Direct Hidden Pair: Cells r6c4,r6c6: 4,9 in row: r6c4<>6, r6c6<>6, r6c1=6 1.2, Hidden Single: r4c6: 6 in block: r4c6=6 1.2, Hidden Single: r2c4: 6 in block: r2c4=6 1.2, Hidden Single: r3c3: 6 in block: r3c3=6 1.2, Hidden Single: r5c9: 6 in block: r5c9=6 2.9, General Intersection: Cells r5c4,r5c5 on value 1 in block 5: r5c1<>1, r5c3<>1 2.9, General Intersection: Cells r4c1,r4c3 on value 1 in block 4: r3c1<>1 2.9, General Intersection: Cells r5c7,r5c8 on value 4 in block 6: r7c7<>4 2.0, Direct Hidden Pair: Cells r7c9,r9c7: 4,5 in block: r7c9<>1, r7c7=1 2.9, General Intersection: Cells r4c8,r5c7 on value 9 in block 6: r3c8<>9, r5c6<>9 2.3, Naked Single: r5c6: 3: r5c6=3 2.9, General Intersection: Cells r2c8,r3c7 on value 9 in block 3: r2c5<>9 1.5, Hidden Single: r9c5: 9 in column: r9c5=9 1.2, Hidden Single: r7c1: 9 in block: r7c1=9 1.2, Hidden Single: r9c4: 1 in block: r9c4=1 1.2, Hidden Single: r5c5: 1 in block: r5c5=1 1.2, Hidden Single: r4c1: 1 in block: r4c1=1 1.2, Hidden Single: r6c2: 2 in block: r6c2=2 1.2, Hidden Single: r4c5: 2 in block: r4c5=2 1.2, Hidden Single: r5c8: 2 in block: r5c8=2 1.2, Hidden Single: r5c7: 4 in block: r5c7=4 1.2, Hidden Single: r4c8: 9 in block: r4c8=9 1.2, Hidden Single: r3c7: 9 in block: r3c7=9 1.0, Hidden Single: r9c7: 5 in column: r9c7=5 1.2, Hidden Single: r2c6: 9 in block: r2c6=9 1.2, Hidden Single: r1c6: 1 in block: r1c6=1 1.2, Hidden Single: r3c6: 5 in block: r3c6=5 1.2, Hidden Single: r1c4: 2 in block: r1c4=2 1.2, Hidden Single: r3c1: 2 in block: r3c1=2 1.2, Hidden Single: r3c4: 3 in block: r3c4=3 1.2, Hidden Single: r2c9: 1 in block: r2c9=1 1.2, Hidden Single: r3c2: 1 in block: r3c2=1 1.0, Hidden Single: r3c8: 7 in row: r3c8=7 1.2, Hidden Single: r2c8: 4 in block: r2c8=4 1.2, Hidden Single: r5c3: 9 in block: r5c3=9 1.2, Hidden Single: r6c4: 9 in block: r6c4=9 1.2, Hidden Single: r6c6: 4 in block: r6c6=4 1.0, Hidden Single: r8c6: 2 in column: r8c6=2 1.0, Hidden Single: r6c9: 7 in row: r6c9=7 1.0, Hidden Single: r4c9: 5 in block: r4c9=5 1.2, Hidden Single: r1c8: 5 in block: r1c8=5 1.0, Hidden Single: r1c9: 3 in block: r1c9=3 1.0, Hidden Single: r9c8: 3 in column: r9c8=3 1.2, Hidden Single: r2c3: 5 in block: r2c3=5 1.2, Hidden Single: r8c3: 1 in block: r8c3=1 1.2, Hidden Single: r8c1: 5 in block: r8c1=5 1.2, Hidden Single: r8c2: 8 in block: r8c2=8 1.0, Hidden Single: r2c2: 7 in column: r2c2=7 1.0, Hidden Single: r2c5: 8 in row: r2c5=8 1.0, Hidden Single: r1c5: 7 in block: r1c5=7 1.0, Hidden Single: r8c4: 4 in row: r8c4=4 1.0, Hidden Single: r7c4: 5 in block: r7c4=5 1.0, Hidden Single: r7c9: 4 in row: r7c9=4 1.0, Hidden Single: r9c9: 2 in block: r9c9=2 1.2, Hidden Single: r1c1: 8 in block: r1c1=8 1.0, Hidden Single: r1c3: 4 in block: r1c3=4 1.2, Hidden Single: r5c1: 7 in block: r5c1=7 1.0, Hidden Single: r4c3: 8 in block: r4c3=8 1.0, Hidden Single: r9c1: 4 in column: r9c1=4 1.0, Hidden Single: r9c3: 7 in block: r9c3=7 1.0, Hidden Single: r4c4: 7 in row: r4c4=7 1.0, Hidden Single: r5c4: 8 in block: r5c4=8 ED=12.4/1.2/1.2

.9....6..3.....2..........8..........5..............1...2............7.9.6...8... ED=12.4/1.2/1.2

Solution Path:

Click to show.

1.2, Hidden Single: r7c8: 8 in block: r7c8=8 1.2, Hidden Single: r6c7: 8 in block: r6c7=8 2.9, General Intersection: Cells r1c1,r3c1,r3c2 on value 2 in block 1: r5c1<>2 2.9, General Intersection: Cells r4c3,r5c3,r6c2,r6c3 on value 3 in block 4: r8c3<>3 2.9, General Intersection: Cells r7c2,r8c2,r9c3 on value 3 in block 7: r7c4<>3 2.9, General Intersection: Cells r1c1,r1c3,r2c3 on value 5 in block 1: r1c5<>5 2.9, General Intersection: Cells r2c3,r3c1,r3c3 on value 6 in block 1: r3c5<>6, r4c3<>6 2.9, General Intersection: Cells r7c9,r8c8 on value 6 in block 9: r6c9<>6, r5c8<>6, r7c6<>6 2.9, General Intersection: Cells r7c4,r7c6,r9c4 on value 7 in block 8: r6c4<>7 2.9, General Intersection: Cells r4c4,r4c5,r5c4 on value 8 in block 5: r2c4<>8, r4c2<>8 2.9, General Intersection: Cells r1c4,r1c5,r2c5 on value 8 in block 2: r1c3<>8 2.9, General Intersection: Cells r2c8,r3c7,r3c8 on value 9 in block 3: r3c6<>9, r5c8<>9 2.9, General Intersection: Cells r4c7,r4c8,r5c7 on value 9 in block 6: r4c5<>9 4.3, Grouped 2 Strong links 201: Cell r4c3,r4c1,r7c1,r7c4 on value 9: r5c5<>9 9.0, Double Forcing Chain (w/3 nodes): r6c9.5 on & off ==> r8c5.5 off: r8c5<>5 9.0, Double Forcing Chain (w/3 nodes): r4c5.8 on & off ==> r4c1.8 off: r4c1<>8 9.0, Region Forcing Chains (w/3 nodes): 6 in column ==> r4c5.6 off: r4c5<>6 9.1, Double Forcing Chain (w/5 nodes): r4c9.6 on & off ==> r5c6.6 off: r5c6<>6 9.4, Region Forcing Chains (w/14 nodes): 5 in block ==> r8c6.5 off: r8c6<>5 11.0, Double Forcing Chain (w/17 nodes): r6c5.9 on & off ==> r6c5.9 off: r6c5<>9 11.0, Double Forcing Chain (w/20 nodes): r8c6.1 on & off ==> r3c4.1 off: r3c4<>1 11.0, Double Forcing Chain (w/22 nodes): r2c8.9 on & off ==> r4c4.9 off: r4c4<>9 11.1, Double Forcing Chain (w/27 nodes): r9c3.9 on & off ==> r5c1.9 off: r5c1<>9 12.0, Double Forcing Chain (w/621 nodes): r7c4.6 on & off ==> r6c5.6 off: r6c5<>6 2.9, General Intersection: Cells r5c5,r7c5,r8c5 on value 6 in column 5: r7c4<>6 12.2, Contradiction Forcing Chain (w/1384 nodes): r9c1.5 on ==> r7c6.7 both on & off: r9c1<>5 12.3, Contradiction Forcing Chain (w/1834 nodes): r4c4.2 on ==> r3c6.7 both on & off: r4c4<>2 12.4, Double Forcing Chain (w/2095 nodes): r9c3.5 on & off ==> r8c8.5 off: r8c8<>5 12.4, Double Forcing Chain (w/2817 nodes): r2c2.7 on & off ==> r5c3.7 off: r5c3<>7 12.4, Contradiction Forcing Chain (w/2852 nodes): r7c9.3 on ==> r4c8.4 both on & off: r7c9<>3 11.8, Double Forcing Chain (w/266 nodes): r4c8.3 on & off ==> r4c8.3 off: r4c8<>3 12.3, Contradiction Forcing Chain (w/1925 nodes): r4c4.6 on ==> r8c6.4 both on & off: r4c4<>6 12.3, Double Forcing Chain (w/2005 nodes): r9c3.3 on & off ==> r8c4.3 off: r8c4<>3 11.8, Contradiction Forcing Chain (w/274 nodes): r6c6.2 on ==> r3c7.1 both on & off: r6c6<>2 12.3, Double Forcing Chain (w/1688 nodes): r9c3.3 on & off ==> r5c5.3 off: r5c5<>3 12.3, Contradiction Forcing Chain (w/1863 nodes): r1c5.3 on ==> r2c5.8 both on & off: r1c5<>3 11.7, Double Forcing Chain (w/198 nodes): r8c8.3 on & off ==> r9c4.3 off: r9c4<>3 12.0, Double Forcing Chain (w/617 nodes): r4c3.3 on & off ==> r6c5.3 off: r6c5<>3 9.2, Double Forcing Chain (w/7 nodes): r7c6.3 on & off ==> r7c6.3 off: r7c6<>3 11.0, Double Forcing Chain (w/17 nodes): r5c5.7 on & off ==> r5c5.7 off: r5c5<>7 12.2, Contradiction Forcing Chain (w/1172 nodes): r7c5.5 on ==> r6c9.5 both on & off: r7c5<>5 12.3, Region Forcing Chains (w/1538 nodes): 9 in row ==> r5c7.3 off: r5c7<>3 12.3, Contradiction Forcing Chain (w/1989 nodes): r5c4.4 on ==> r1c1.7 both on & off: r5c4<>4 12.4, Contradiction Forcing Chain (w/2226 nodes): r2c5.1 on ==> r7c2.3 both on & off: r2c5<>1 12.4, Contradiction Forcing Chain (w/2328 nodes): r9c3.3 on ==> r1c4.7 both on & off: r9c3<>3 2.9, General Intersection: Cells r7c2,r8c2 on value 3 in block 7: r6c2<>3 12.2, Contradiction Forcing Chain (w/1405 nodes): r4c4.1 on ==> r8c8.6 both on & off: r4c4<>1 12.0, Contradiction Forcing Chain (w/750 nodes): r1c5.1 on ==> r4c6.6 both on & off: r1c5<>1 12.2, Cell Forcing Chains (w/1110 nodes): r6c6 ==> r8c4.5 off: r8c4<>5 2.9, General Intersection: Cells r8c1,r8c3 on value 5 in row 8: r9c3<>5 12.2, Contradiction Forcing Chain (w/1111 nodes): r8c1.1 on ==> r3c7.1 both on & off: r8c1<>1 12.0, Region Forcing Chains (w/649 nodes): 2 in block ==> r1c4.8 off: r1c4<>8 2.9, General Intersection: Cells r1c5,r2c5 on value 8 in block 2: r2c3<>8, r4c5<>8 8.3, Region Forcing Chains (w/10 nodes): 8 in block ==> r8c1.4 off: r8c1<>4 12.2, Cell Forcing Chains (w/1135 nodes): r8c6 ==> r3c5.1 off: r3c5<>1 12.0, Region Forcing Chains (w/733 nodes): 6 in row ==> r5c5.4 off: r5c5<>4 12.0, Double Forcing Chain (w/746 nodes): r4c6.1 on & off ==> r7c5.1 off: r7c5<>1 12.2, Contradiction Forcing Chain (w/1222 nodes): r7c5.9 on ==> r7c6.5 both on & off: r7c5<>9 9.0, Double Forcing Chain (w/4 nodes): r7c1.9 on & off ==> r4c1.9 off: r4c1<>9 11.9, Region Forcing Chains (w/407 nodes): 2 in column ==> r3c1.1 off: r3c1<>1 11.5, Double Forcing Chain (w/106 nodes): r4c6.1 on & off ==> r5c3.1 off: r5c3<>1 11.8, Double Forcing Chain (w/265 nodes): r6c3.9 on & off ==> r4c5.3 off: r4c5<>3 9.0, Double Forcing Chain (w/4 nodes): r5c3.3 on & off ==> r5c8.3 off: r5c8<>3 11.1, Double Forcing Chain (w/29 nodes): r6c5.4 on & off ==> r6c5.4 off: r6c5<>4 11.4, Region Forcing Chains (w/87 nodes): 4 in row ==> r7c6.4 off: r7c6<>4 11.5, Double Forcing Chain (w/126 nodes): r7c6.9 on & off ==> r6c1.9 off: r6c1<>9 2.9, General Intersection: Cells r4c3,r5c3,r6c3 on value 9 in block 4: r9c3<>9 11.4, Region Forcing Chains (w/89 nodes): 8 in block ==> r5c1.4 off: r5c1<>4 11.6, Cell Forcing Chains (w/159 nodes): r4c8 ==> r2c5.5 off: r2c5<>5 11.6, Region Forcing Chains (w/177 nodes): 3 in row ==> r4c8.4 off: r4c8<>4 11.7, Double Forcing Chain (w/213 nodes): r6c9.5 on & off ==> r2c6.7 off: r2c6<>7 11.6, Double Forcing Chain (w/129 nodes): r5c1.1 on & off ==> r7c4.1 off: r7c4<>1 11.8, Region Forcing Chains (w/345 nodes): 3 in row ==> r7c6.9 off: r7c6<>9 11.3, Double Forcing Chain (w/56 nodes): r4c8.9 on & off ==> r5c4.9 off: r5c4<>9 11.8, Region Forcing Chains (w/308 nodes): 6 in column ==> r6c3.4 off: r6c3<>4 11.5, Double Forcing Chain (w/106 nodes): r1c4.7 on & off ==> r9c5.5 off: r9c5<>5 9.3, Double Forcing Chain (w/12 nodes): r9c4.5 on & off ==> r6c6.5 off: r6c6<>5 2.9, General Intersection: Cells r6c5,r6c9 on value 5 in row 6: r7c7<>5 12.2, Contradiction Forcing Chain (w/1317 nodes): r4c6.1 on ==> r3c5.3 both on & off: r4c6<>1 12.2, Double Forcing Chain (w/1413 nodes): r4c4.4 on & off ==> r4c4.4 off: r4c4<>4 11.4, Region Forcing Chains (w/78 nodes): 7 in block ==> r4c4.3 off: r4c4<>3 11.5, Double Forcing Chain (w/100 nodes): r3c5.9 on & off ==> r2c8.7 off: r2c8<>7 11.4, Region Forcing Chains (w/76 nodes): 7 in column ==> r4c6.7 off: r4c6<>7 11.2, Double Forcing Chain (w/47 nodes): r5c3.4 on & off ==> r5c3.4 off: r5c3<>4 11.6, Double Forcing Chain (w/162 nodes): r6c1.4 on & off ==> r2c2.4 off: r2c2<>4 11.7, Cell Forcing Chains (w/198 nodes): r5c6 ==> r5c4.3 off: r5c4<>3 12.3, Contradiction Forcing Chain (w/1602 nodes): r2c2.1 on ==> r3c7.5 both on & off: r2c2<>1 9.0, Double Forcing Chain (w/4 nodes): r9c5.1 on & off ==> r4c5.1 off: r4c5<>1 2.9, General Intersection: Cells r5c4,r5c5 on value 1 in block 5: r5c1<>1 11.4, Region Forcing Chains (w/82 nodes): 6 in row ==> r6c4.2 off: r6c4<>2 11.5, Cell Forcing Chains (w/125 nodes): r7c5 ==> r3c4.9 off: r3c4<>9 10.0, Contradiction Forcing Chain (w/114 nodes): r7c4.4 on ==> r4c3.3 both on & off: r7c4<>4 11.4, Double Forcing Chain (w/72 nodes): r5c5.1 on & off ==> r8c5.4 off: r8c5<>4 11.5, Region Forcing Chains (w/121 nodes): 4 in block ==> r6c9.4 off: r6c9<>4 12.1, Contradiction Forcing Chain (w/803 nodes): r5c3.8 on ==> r3c1.7 both on & off: r5c3<>8 10.1, Contradiction Forcing Chain (w/136 nodes): r5c1.6 on ==> r2c2.7 both on & off: r5c1<>6 6.6, UVWXYZ-Wing 1419: Cells r3c2,r4c2,r6c2,r7c2,r8c2,r5c1 on value 8: r8c1<>8 2.3, Naked Single: r8c1: 5: r8c1=5 12.2, Cell Forcing Chains (w/1349 nodes): r5c3 ==> r5c9.3 off: r5c9<>3 12.0, Region Forcing Chains (w/519 nodes): 4 in row ==> r6c2.4 off: r6c2<>4 11.4, Region Forcing Chains (w/441 nodes): 3 in row ==> r6c3.7 off: r6c3<>7 10.1, Contradiction Forcing Chain (w/145 nodes): r4c6.3 on ==> r4c8.6 both on & off: r4c6<>3 4.3, Grouped Skyscraper 111: Cell r4c7,r4c3,r5c3,r5c6 on value 3: r3c7<>3 9.7, Cell Forcing Chains (w/42 nodes): r5c3 ==> r4c3.3 off: r4c3<>3 2.9, General Intersection: Cells r4c7,r4c9 on value 3 in row 4: r6c9<>3 3.6, Generalized Naked Triplet: Cells r6c2,r6c5,r6c9: 2,5,7 in row: r6c1<>7 9.7, Cell Forcing Chains (w/43 nodes): r6c6 ==> r3c8.4 off: r3c8<>4 9.8, Contradiction Forcing Chain (w/64 nodes): r4c8.7 on ==> r4c1.2 both on & off: r4c8<>7 9.9, Contradiction Forcing Chain (w/71 nodes): r4c9.7 on ==> r5c6.7 both on & off: r4c9<>7 10.1, Contradiction Forcing Chain (w/167 nodes): r9c4.5 on ==> r4c1.2 both on & off: r9c4<>5 2.9, General Intersection: Cells r7c4,r7c6 on value 5 in block 8: r7c9<>5 9.9, Contradiction Forcing Chain (w/74 nodes): r4c9.6 on ==> r2c5.7 both on & off: r4c9<>6 9.2, Double Forcing Chain (w/8 nodes): r5c9.6 on & off ==> r5c3.6 off: r5c3<>6 9.0, Double Forcing Chain (w/3 nodes): r3c4.6 on & off ==> r6c4.6 off: r6c4<>6 9.8, Cell Forcing Chains (w/64 nodes): r2c6 ==> r9c5.1 off: r9c5<>1 2.9, General Intersection: Cells r8c4,r8c5,r8c6,r9c4 on value 1 in block 8: r8c2<>1 9.9, Cell Forcing Chains (w/66 nodes): r8c5 ==> r5c4.7 off: r5c4<>7 10.0, Contradiction Forcing Chain (w/107 nodes): r7c9.1 on ==> r3c5.4 both on & off: r7c9<>1 9.6, Region Forcing Chains (w/28 nodes): 5 in row ==> r4c9.4 off: r4c9<>4 9.7, Contradiction Forcing Chain (w/38 nodes): r9c9.4 on ==> r9c5.2 both on & off: r9c9<>4 9.7, Contradiction Forcing Chain (w/44 nodes): r9c7.4 on ==> r9c5.2 both on & off: r9c7<>4 2.9, General Intersection: Cells r7c7,r7c9,r8c8,r9c8 on value 4 in block 9: r5c8<>4 9.2, Contradiction Forcing Chain (w/41 nodes): r5c9.7 on ==> r7c7.3 both on & off: r5c9<>7 9.5, Double Forcing Chain (w/18 nodes): r9c7.5 on & off ==> r9c9.5 off: r9c9<>5 9.0, Double Forcing Chain (w/3 nodes): r6c9.5 on & off ==> r3c7.5 off: r3c7<>5 2.9, General Intersection: Cells r3c4,r3c5,r3c6,r3c8 on value 5 in row 3: r2c6<>5 9.6, Contradiction Forcing Chain (w/25 nodes): r3c5.3 on ==> r7c7.1 both on & off: r3c5<>3 2.9, General Intersection: Cells r7c5,r8c5,r9c5 on value 3 in column 5: r8c6<>3 9.7, Region Forcing Chains (w/43 nodes): 2 in block ==> r4c5.4 off: r4c5<>4 9.7, Region Forcing Chains (w/39 nodes): 2 in row ==> r3c6.4 off: r3c6<>4 9.7, Region Forcing Chains (w/47 nodes): 4 in row ==> r3c4.4 off: r3c4<>4 9.8, Region Forcing Chains (w/52 nodes): 2 in row ==> r9c9.3 off: r9c9<>3 9.9, Region Forcing Chains (w/81 nodes): 4 in column ==> r3c3.4 off: r3c3<>4 9.9, Region Forcing Chains (w/91 nodes): 5 in block ==> r4c7.4 off: r4c7<>4 2.9, General Intersection: Cells r5c7,r5c9 on value 4 in block 6: r5c6<>4 9.9, Region Forcing Chains (w/70 nodes): 9 in column ==> r2c4.5 off: r2c4<>5 9.6, Double Forcing Chain (w/27 nodes): r3c7.4 on & off ==> r2c3.4 off: r2c3<>4 9.8, Cell Forcing Chains (w/52 nodes): r3c7 ==> r1c9.1 off: r1c9<>1 9.5, Double Forcing Chain (w/17 nodes): r4c7.5 on & off ==> r2c9.5 off: r2c9<>5 9.5, Double Forcing Chain (w/20 nodes): r6c9.5 on & off ==> r4c1.6 off: r4c1<>6 2.9, General Intersection: Cells r6c1,r6c3 on value 6 in block 4: r6c6<>6 2.9, General Intersection: Cells r4c6,r5c4,r5c5 on value 6 in block 5: r3c4<>6 2.9, General Intersection: Cells r2c4,r2c6 on value 6 in block 2: r2c3<>6 9.6, Double Forcing Chain (w/26 nodes): r6c6.9 on & off ==> r3c3.1 off: r3c3<>1 9.7, Region Forcing Chains (w/36 nodes): 5 in block ==> r2c3.7 off: r2c3<>7 9.9, Double Forcing Chain (w/80 nodes): r3c8.3 on & off ==> r1c4.3 off: r1c4<>3 9.9, Contradiction Forcing Chain (w/68 nodes): r8c6.4 on ==> r2c6.6 both on & off: r8c6<>4 9.7, Region Forcing Chains (w/33 nodes): 1 in row ==> r5c5.2 off: r5c5<>2 5.7, Grouped 3-String Kite 2121: Cell r5c8,r5c6,r4c5,r9c5,r8c4,r8c8 on value 2: r6c9<>2 1.5, Hidden Single: r6c2: 2 in row: r6c2=2 7.1, Forcing Chain (w/6 nodes): r4c5.7 off: r4c5<>7 9.0, Double Forcing Chain (w/22 nodes): r4c8.6 on & off ==> r4c8.5 off: r4c8<>5 9.2, Contradiction Forcing Chain (w/43 nodes): r3c6.7 on ==> r1c4.5 both on & off: r3c6<>7 9.0, Double Forcing Chain (w/3 nodes): r9c4.7 on & off ==> r3c4.7 off: r3c4<>7 9.3, Region Forcing Chains (w/9 nodes): 7 in row ==> r1c3.7 off: r1c3<>7 9.8, Region Forcing Chains (w/53 nodes): 4 in row ==> r4c3.1 off: r4c3<>1 9.7, Region Forcing Chains (w/48 nodes): 1 in block ==> r4c1.7 off: r4c1<>7 9.9, Contradiction Forcing Chain (w/84 nodes): r1c4.4 on ==> r5c6.2 both on & off: r1c4<>4 10.0, Contradiction Forcing Chain (w/106 nodes): r6c6.9 on ==> r3c2.4 both on & off: r6c6<>9 2.9, General Intersection: Cells r6c3,r6c4 on value 9 in row 6: r4c3<>9 2.0, Direct Hidden Pair: Cells r5c3,r6c3: 3,9 in block: r6c3<>6, r6c1=6 1.2, Hidden Single: r3c3: 6 in block: r3c3=6 1.5, Hidden Single: r2c4: 6 in column: r2c4=6 2.9, General Intersection: Cells r4c1,r4c2,r4c3 on value 4 in block 4: r4c6<>4 3.2, X-Wing: Cells r4c6,r4c8,r8c6,r8c8: 6 in 2 columns and 2 rows: r8c5<>6 4.3, Grouped 2 Strong links 101: Cell r1c4,r2c5,r6c5,r6c9 on value 7: r1c9<>7 5.6, WXYZ-Wing 238: Cells r7c5,r7c7,r7c9,r8c5 on values 1,3: r7c1<>4, r7c2<>4, r9c7<>1 6.6, UVWXYZ-Wing 2313: Cells r1c9,r4c9,r5c9,r6c9,r7c9,r5c8 on values 2,7: r2c9<>4 2.9, General Intersection: Cells r1c8,r1c9,r2c8,r3c7 on value 4 in block 3: r1c6<>4 9.0, Contradiction Forcing Chain (w/23 nodes): r1c4.1 on ==> r2c3.1 both on & off: r1c4<>1 2.9, General Intersection: Cells r1c6,r2c6,r3c6 on value 1 in block 2: r8c6<>1 9.1, Cell Forcing Chains (w/32 nodes): r9c5 ==> r3c8.3 off: r3c8<>3 2.9, General Intersection: Cells r1c8,r1c9 on value 3 in block 3: r1c6<>3 9.2, Cell Forcing Chains (w/33 nodes): r8c8 ==> r9c5.4 off: r9c5<>4 9.3, Region Forcing Chains (w/51 nodes): 7 in column ==> r1c1.7 off: r1c1<>7 9.0, Double Forcing Chain (w/3 nodes): r3c2.1 on & off ==> r2c3.1 off: r2c3<>1 2.3, Naked Single: r2c3: 5: r2c3=5 2.9, General Intersection: Cells r3c4,r3c6,r3c8 on value 5 in row 3: r4c6<>5 3.0, Generalized Naked Pair: Cells r4c6,r4c8: 6,9 in row: r4c7<>9, r3c8<>9, r5c6<>9 2.9, General Intersection: Cells r2c8,r3c7 on value 9 in block 3: r2c5<>9 3.0, Generalized Naked Pair: Cells r4c7,r9c7: 3,5 in column: r7c7<>3 4.0, Hidden Triplet: Cells r4c8,r5c7,r5c9: 4,6,9 in block: r5c9<>2 3.0, Generalized Naked Pair: Cells r5c9,r7c9: 4,6 in column: r1c9<>4 3.2, X-Wing: Cells r4c5,r4c9,r9c5,r9c9: 2 in 2 columns and 2 rows: r9c8<>2 5.6, WXYZ-Wing 137: Cells r7c7,r9c7,r9c8,r8c5 on value 3: r8c8<>3, r9c5<>3 3.4, Hidden Pair: Cells r9c7,r9c8: 3,5 in block: r9c8<>4 2.9, General Intersection: Cells r9c1,r9c3,r9c4 on value 4 in row 9: r8c2<>4 4.0, Hidden Triplet: Cells r5c5,r7c5,r8c5: 1,3,6 in column: r7c5<>4 1.7, Direct Pointing: Cells r8c4,r9c4: 4 of block in column: r6c4<>4, r6c6=4 2.9, General Intersection: Cells r2c5,r2c8 on value 4 in row 2: r3c7<>4 2.9, General Intersection: Cells r1c8,r2c8 on value 4 in block 3: r8c8<>4 3.0, Generalized Naked Pair: Cells r8c6,r8c8: 2,6 in row: r8c4<>2 2.9, General Intersection: Cells r1c4,r3c4 on value 2 in column 4: r1c6<>2, r3c6<>2 4.2, XY-Wing: Cells r4c6,r2c6,r5c5 on value 1: r3c6<>1 3.8, Swordfish: Cells r4c1,r7c1,r3c2,r4c2,r7c2,r3c7,r7c7: 1 in 3 rows and 3 columns: r1c1<>1, r9c1<>1 5.6, WXYZ-Wing 137: Cells r8c2,r8c3,r8c5,r1c3 on value 1: r9c3<>1 6.6, UVWXYZ-Wing 2313: Cells r3c1,r3c2,r3c4,r3c6,r3c8,r1c3 on values 1,4: r1c1<>4, r3c5<>7 6.4, VWXYZ-Wing 139: Cells r2c2,r2c5,r2c6,r2c9,r3c5 on value 4: r1c5<>4 6.8, Bidirectional Y-Cycle (w/12 nodes): r2c9,r2c6,r4c6,r5c5,r8c5,r8c2,r2c2: r2c5<>7 2.9, General Intersection: Cells r1c4,r1c5,r1c6 on value 7 in block 2: r1c8<>7 6.6, UVWXYZ-Wing 1210: Cells r2c5,r3c5,r4c5,r6c5,r9c5,r4c4 on value 7: r5c6<>7 6.6, Bidirectional Y-Cycle (w/6 nodes): r5c6,r5c8,r3c8,r3c6: r3c4<>5 4.0, Skyscraper 011: Cell r3c6,r3c8,r9c8,r9c7 on value 5: r7c6<>5 1.2, Hidden Single: r7c4: 5 in block: r7c4=5 1.5, Hidden Single: r7c1: 9 in row: r7c1=9 1.2, Hidden Single: r5c3: 9 in block: r5c3=9 1.2, Hidden Single: r6c3: 3 in block: r6c3=3 1.2, Hidden Single: r5c6: 3 in block: r5c6=3 1.2, Hidden Single: r3c4: 3 in block: r3c4=3 1.2, Hidden Single: r1c4: 2 in block: r1c4=2 1.2, Hidden Single: r3c1: 2 in block: r3c1=2 1.2, Hidden Single: r4c5: 2 in block: r4c5=2 1.2, Hidden Single: r6c5: 5 in block: r6c5=5 1.2, Hidden Single: r4c4: 7 in block: r4c4=7 1.2, Hidden Single: r2c2: 7 in block: r2c2=7 1.2, Hidden Single: r1c1: 8 in block: r1c1=8 1.2, Hidden Single: r2c5: 8 in block: r2c5=8 1.2, Hidden Single: r3c5: 4 in block: r3c5=4 1.2, Hidden Single: r1c3: 4 in block: r1c3=4 1.0, Hidden Single: r3c2: 1 in block: r3c2=1 1.2, Hidden Single: r2c6: 9 in block: r2c6=9 1.2, Hidden Single: r1c6: 1 in block: r1c6=1 1.2, Hidden Single: r3c6: 5 in block: r3c6=5 1.0, Hidden Single: r1c5: 7 in block: r1c5=7 1.2, Hidden Single: r2c9: 1 in block: r2c9=1 1.0, Hidden Single: r2c8: 4 in row: r2c8=4 1.2, Hidden Single: r3c8: 7 in block: r3c8=7 1.0, Hidden Single: r3c7: 9 in row: r3c7=9 1.2, Hidden Single: r4c1: 1 in block: r4c1=1 1.2, Hidden Single: r4c2: 4 in block: r4c2=4 1.2, Hidden Single: r5c1: 7 in block: r5c1=7 1.0, Hidden Single: r4c3: 8 in block: r4c3=8 1.0, Hidden Single: r9c1: 4 in column: r9c1=4 1.2, Hidden Single: r5c4: 8 in block: r5c4=8 1.2, Hidden Single: r5c5: 1 in block: r5c5=1 1.2, Hidden Single: r4c6: 6 in block: r4c6=6 1.0, Hidden Single: r6c4: 9 in block: r6c4=9 1.0, Hidden Single: r6c9: 7 in row: r6c9=7 1.2, Hidden Single: r5c8: 2 in block: r5c8=2 1.2, Hidden Single: r5c9: 6 in block: r5c9=6 1.0, Hidden Single: r5c7: 4 in row: r5c7=4 1.2, Hidden Single: r4c8: 9 in block: r4c8=9 1.2, Hidden Single: r8c3: 1 in block: r8c3=1 1.0, Hidden Single: r9c3: 7 in column: r9c3=7 1.2, Hidden Single: r7c2: 3 in block: r7c2=3 1.0, Hidden Single: r8c2: 8 in block: r8c2=8 1.2, Hidden Single: r9c4: 1 in block: r9c4=1 1.0, Hidden Single: r8c4: 4 in column: r8c4=4 1.2, Hidden Single: r8c6: 2 in block: r8c6=2 1.0, Hidden Single: r7c6: 7 in column: r7c6=7 1.2, Hidden Single: r8c5: 3 in block: r8c5=3 1.0, Hidden Single: r8c8: 6 in row: r8c8=6 1.2, Hidden Single: r7c5: 6 in block: r7c5=6 1.0, Hidden Single: r9c5: 9 in block: r9c5=9 1.2, Hidden Single: r7c7: 1 in block: r7c7=1 1.0, Hidden Single: r7c9: 4 in row: r7c9=4 1.2, Hidden Single: r9c9: 2 in block: r9c9=2 1.2, Hidden Single: r9c8: 3 in block: r9c8=3 1.0, Hidden Single: r9c7: 5 in block: r9c7=5 1.0, Hidden Single: r4c7: 3 in column: r4c7=3 1.0, Hidden Single: r4c9: 5 in block: r4c9=5 1.0, Hidden Single: r1c8: 5 in column: r1c8=5 1.0, Hidden Single: r1c9: 3 in block: r1c9=3 ED=12.4/1.2/1.2

[newman-iknewit]

ryokousha of the CTC Discord has found a minimal anti-knight grid:

................1.....................2.......3.4.......5.6.......7.........8.... ED=??

SE manages a few eliminations up to a 9.7 and then stalls. We noticed in exploring the code that weak links specific to the variant aren't actually being used by SE in chains (just in generalized subsets/pointing/that sort of thing) so it's not clear how meaningful the SE rating even is at this point.

[1to9only]

................1.....................2.......3.4.......5.6.......7.........8.... ED=12.5/12.4/2.9

Solution Path:

Click to show.

2.9, General Intersection: Cells r4c4,r4c6,r6c6 on value 2 in block 5: r4c7<>2, r3c6<>2 2.9, General Intersection: Cells r4c1,r4c2,r5c1 on value 4 in block 4: r2c1<>4 2.9, General Intersection: Cells r8c6,r9c6 on value 4 in block 8: r1c6<>4, r8c8<>4, r3c6<>4, r2c6<>4, r9c8<>4 2.9, General Intersection: Cells r1c5,r2c5,r3c5 on value 4 in block 2: r2c3<>4, r2c7<>4 2.9, General Intersection: Cells r4c1,r4c2,r5c1 on value 5 in block 4: r2c1<>5 2.9, General Intersection: Cells r8c6,r9c6 on value 5 in block 8: r4c6<>5, r6c6<>5, r1c6<>5, r8c8<>5, r3c6<>5, r5c6<>5, r2c6<>5, r9c8<>5 2.9, General Intersection: Cells r4c4,r4c5,r5c5 on value 5 in block 5: r4c7<>5, r2c5<>5 2.9, General Intersection: Cells r4c4,r4c6,r6c6 on value 6 in block 5: r4c7<>6, r3c6<>6 2.9, General Intersection: Cells r6c7,r6c8,r6c9 on value 5 in row 6: r4c8<>5, r4c9<>5, r5c7<>5, r5c8<>5, r5c9<>5 3.4, Hidden Pair: Cells r8c6,r9c6: 4,5 in block: r8c6<>1,2,3,9, r9c6<>1,2,3,9 2.9, General Intersection: Cells r7c6,r8c5,r9c4 on value 2 in block 8: r9c7<>2 2.9, General Intersection: Cells r7c6,r8c5,r9c4 on value 3 in block 8: r9c7<>3 2.9, General Intersection: Cells r8c5,r8c7,r8c8,r8c9 on value 3 in row 8: r7c7<>3 2.9, General Intersection: Cells r4c6,r5c6,r6c6,r7c6 on value 1 in column 6: r5c5<>1 8.4, Region Forcing Chains (w/14 nodes): 1 in column ==> r4c4.9 off: r4c4<>9 8.4, Region Forcing Chains (w/14 nodes): 1 in column ==> r5c4.9 off: r5c4<>9 8.4, Region Forcing Chains (w/14 nodes): 1 in block ==> r8c5.9 off: r8c5<>9 8.8, Cell Forcing Chains (w/11 nodes): r5c4 ==> r5c2.8 off: r5c2<>8 9.0, Region Forcing Chains (w/20 nodes): 1 in block ==> r6c6.8 off: r6c6<>8 9.0, Region Forcing Chains (w/20 nodes): 1 in block ==> r5c1.8 off: r5c1<>8 9.0, Double Forcing Chain (w/3 nodes): r9c3.3 on & off ==> r2c5.3 off: r2c5<>3 9.0, Double Forcing Chain (w/3 nodes): r7c1.7 on & off ==> r5c8.7 off: r5c8<>7 9.1, Double Forcing Chain (w/5 nodes): r2c9.4 on & off ==> r9c9.4 off: r9c9<>4 9.1, Region Forcing Chains (w/6 nodes): 4 in block ==> r8c9.4 off: r8c9<>4 9.2, Double Forcing Chain (w/7 nodes): r6c1.8 on & off ==> r4c4.8 off: r4c4<>8 2.9, General Intersection: Cells r4c6,r5c4,r5c6 on value 8 in block 5: r5c8<>8 9.2, Double Forcing Chain (w/8 nodes): r9c4.9 on & off ==> r5c5.9 off: r5c5<>9 9.2, Double Forcing Chain (w/8 nodes): r9c4.9 on & off ==> r6c6.9 off: r6c6<>9 9.3, Cell Forcing Chains (w/9 nodes): r9c6 ==> r2c9.5 off: r2c9<>5 9.3, Double Forcing Chain (w/11 nodes): r2c4.8 on & off ==> r3c3.8 off: r3c3<>8 9.4, Double Forcing Chain (w/13 nodes): r5c6.8 on & off ==> r4c2.8 off: r4c2<>8 9.5, Contradiction Forcing Chain (w/18 nodes): r1c1.4 on ==> r5c8.4 both on & off: r1c1<>4 9.5, Contradiction Forcing Chain (w/24 nodes): r8c1.4 on ==> r1c8.4 both on & off: r8c1<>4 9.5, Contradiction Forcing Chain (w/24 nodes): r9c1.4 on ==> r1c8.4 both on & off: r9c1<>4 9.7, Region Forcing Chains (w/40 nodes): 9 in row ==> r7c7.9 off: r7c7<>9 11.0, Double Forcing Chain (w/19 nodes): r6c3.8 on & off ==> r6c3.9 off: r6c3<>9 11.2, Double Forcing Chain (w/44 nodes): r4c2.5 on & off ==> r3c3.7 off: r3c3<>7 11.2, Double Forcing Chain (w/45 nodes): r7c6.9 on & off ==> r9c3.9 off: r9c3<>9 11.4, Double Forcing Chain (w/70 nodes): r1c8.4 on & off ==> r5c5.3 off: r5c5<>3 2.9, General Intersection: Cells r4c4,r4c5,r4c6,r5c6 on value 3 in block 5: r4c8<>3 10.9, Double Forcing Chain (w/16 nodes): r9c3.4 on & off ==> r3c1.4 off: r3c1<>4 11.4, Region Forcing Chains (w/88 nodes): 4 in column ==> r7c1.9 off: r7c1<>9 11.6, Region Forcing Chains (w/183 nodes): 2 in block ==> r2c4.2 off: r2c4<>2 11.8, Cell Forcing Chains (w/258 nodes): r4c2 ==> r1c2.5 off: r1c2<>5 2.9, General Intersection: Cells r2c2,r3c2,r4c2 on value 5 in column 2: r3c4<>5 9.1, Double Forcing Chain (w/5 nodes): r4c4.5 on & off ==> r4c5.5 off: r4c5<>5 11.4, Region Forcing Chains (w/73 nodes): 8 in block ==> r2c4.8 off: r2c4<>8 12.3, Contradiction Forcing Chain (w/1818 nodes): r5c7.8 on ==> r2c2.2 both on & off: r5c7<>8 12.3, Cell Forcing Chains (w/1875 nodes): r5c5 ==> r1c5.5 off: r1c5<>5 12.2, Double Forcing Chain (w/1504 nodes): r7c1.4 on & off ==> r5c1.7 off: r5c1<>7 12.4, Contradiction Forcing Chain (w/2190 nodes): r1c4.8 on ==> r6c8.7 both on & off: r1c4<>8 2.9, General Intersection: Cells r1c6,r2c6,r3c4,r3c6 on value 8 in block 2: r4c6<>8 2.9, General Intersection: Cells r5c4,r5c6 on value 8 in block 5: r5c9<>8 12.4, Double Forcing Chain (w/3050 nodes): r7c1.4 on & off ==> r5c1.5 off: r5c1<>5 1.5, Hidden Single: r5c5: 5 in row: r5c5=5 2.9, General Intersection: Cells r1c4,r2c4 on value 5 in block 2: r2c2<>5 2.9, General Intersection: Cells r6c8,r6c9 on value 5 in block 6: r8c9<>5 2.9, General Intersection: Cells r4c5,r4c6,r5c6,r6c6 on value 7 in block 5: r2c6<>7 11.9, Double Forcing Chain (w/406 nodes): r8c2.1 on & off ==> r8c2.1 off: r8c2<>1 12.0, Double Forcing Chain (w/722 nodes): r4c2.7 on & off ==> r3c1.7 off: r3c1<>7 12.2, Double Forcing Chain (w/1331 nodes): r4c3.8 on & off ==> r7c1.8 off: r7c1<>8 12.3, Contradiction Forcing Chain (w/1752 nodes): r7c8.9 on ==> r2c5.7 both on & off: r7c8<>9 12.4, Contradiction Forcing Chain (w/2228 nodes): r9c7.4 on ==> r8c9.8 both on & off: r9c7<>4 12.3, Double Forcing Chain (w/2017 nodes): r4c6.9 on & off ==> r5c7.9 off: r5c7<>9 12.4, Contradiction Forcing Chain (w/2097 nodes): r4c2.4 on ==> r3c7.9 both on & off: r4c2<>4 2.9, General Intersection: Cells r4c1,r5c1 on value 4 in block 4: r7c1<>4 2.9, General Intersection: Cells r7c7,r7c8,r7c9 on value 4 in row 7: r8c7<>4, r5c8<>4 11.1, Region Forcing Chains (w/29 nodes): 7 in row ==> r4c7.7 off: r4c7<>7 10.8, Contradiction Forcing Chain (w/345 nodes): r2c4.9 on ==> r3c9.7 both on & off: r2c4<>9 12.2, Region Forcing Chains (w/1191 nodes): 9 in row ==> r6c8.9 off: r6c8<>9 12.0, Region Forcing Chains (w/710 nodes): 9 in column ==> r4c6.9 off: r4c6<>9 2.9, General Intersection: Cells r4c5,r5c6,r6c5 on value 9 in block 5: r3c5<>9 12.5, Double Forcing Chain (w/3286 nodes): r9c4.9 on & off ==> r7c9.9 off: r7c9<>9 12.5, Region Forcing Chains (w/4006 nodes): 6 in column ==> r2c2.7 off: r2c2<>7 11.4, Region Forcing Chains (w/94 nodes): 7 in block ==> r6c1.7 off: r6c1<>7 11.9, Region Forcing Chains (w/508 nodes): 1 in column ==> r9c1.9 off: r9c1<>9 12.1, Double Forcing Chain (w/781 nodes): r8c8.2 on & off ==> r8c8.2 off: r8c8<>2 12.3, Region Forcing Chains (w/1790 nodes): 7 in row ==> r1c7.7 off: r1c7<>7 12.3, Region Forcing Chains (w/1833 nodes): 7 in row ==> r3c7.7 off: r3c7<>7 12.5, Double Forcing Chain (w/3109 nodes): r6c6.7 on & off ==> r5c7.7 off: r5c7<>7 12.4, Double Forcing Chain (w/2386 nodes): r6c6.7 on & off ==> r5c9.7 off: r5c9<>7 10.9, Double Forcing Chain (w/13 nodes): r9c1.7 on & off ==> r4c1.7 off: r4c1<>7 11.9, Cell Forcing Chains (w/433 nodes): r4c6 ==> r4c4.1 off: r4c4<>1 12.0, Double Forcing Chain (w/718 nodes): r3c8.7 on & off ==> r7c1.1 off: r7c1<>1 12.1, Region Forcing Chains (w/820 nodes): 3 in block ==> r2c4.3 off: r2c4<>3 12.1, Region Forcing Chains (w/807 nodes): 7 in column ==> r6c9.9 off: r6c9<>9 12.2, Region Forcing Chains (w/1380 nodes): 7 in column ==> r8c7.2 off: r8c7<>2 12.2, Region Forcing Chains (w/1168 nodes): 3 in block ==> r3c5.3 off: r3c5<>3 12.3, Contradiction Forcing Chain (w/1803 nodes): r8c9.2 on ==> r9c2.1 both on & off: r8c9<>2 12.2, Region Forcing Chains (w/1503 nodes): 6 in row ==> r6c8.6 off: r6c8<>6 12.4, Region Forcing Chains (w/2077 nodes): 6 in column ==> r6c9.6 off: r6c9<>6 12.1, Region Forcing Chains (w/897 nodes): 4 in block ==> r5c1.6 off: r5c1<>6 12.5, Double Forcing Chain (w/3355 nodes): r4c2.6 on & off ==> r3c1.6 off: r3c1<>6 12.3, Double Forcing Chain (w/2040 nodes): r4c2.6 on & off ==> r4c2.6 off: r4c2<>6 12.3, Cell Forcing Chains (w/1961 nodes): r6c5 ==> r4c5.9 off: r4c5<>9 12.3, Region Forcing Chains (w/1637 nodes): 1 in block ==> r1c5.9 off: r1c5<>9 12.3, Region Forcing Chains (w/1614 nodes): 1 in row ==> r2c1.7 off: r2c1<>7 12.0, Cell Forcing Chains (w/523 nodes): r6c5 ==> r6c7.9 off: r6c7<>9 12.2, Region Forcing Chains (w/1149 nodes): 9 in row ==> r2c2.9 off: r2c2<>9 12.0, Region Forcing Chains (w/529 nodes): 2 in column ==> r6c5.1 off: r6c5<>1 2.3, Naked Single: r6c5: 9: r6c5=9 12.0, Double Forcing Chain (w/534 nodes): r2c9.7 on & off ==> r4c6.7 off: r4c6<>7 9.3, Double Forcing Chain (w/11 nodes): r6c6.7 on & off ==> r3c5.7 off: r3c5<>7 11.2, Region Forcing Chains (w/40 nodes): 7 in row ==> r4c2.7 off: r4c2<>7 11.3, Region Forcing Chains (w/58 nodes): 1 in block ==> r9c3.1 off: r9c3<>1 11.5, Double Forcing Chain (w/115 nodes): r1c3.4 on & off ==> r4c9.7 off: r4c9<>7 11.6, Double Forcing Chain (w/160 nodes): r7c8.4 on & off ==> r7c1.2 off: r7c1<>2 6.6, UVWXYZ-Wing 1519: Cells r5c1,r5c2,r5c7,r5c8,r5c9,r7c1 on value 3: r7c8<>3 11.8, Region Forcing Chains (w/321 nodes): 2 in block ==> r2c7.5 off: r2c7<>5 1.5, Hidden Single: r2c4: 5 in row: r2c4=5 1.5, Hidden Single: r4c2: 5 in column: r4c2=5 2.9, General Intersection: Cells r4c1,r4c3,r5c1,r5c2 on value 9 in block 4: r3c1<>9 11.7, Double Forcing Chain (w/244 nodes): r5c1.4 on & off ==> r3c3.9 off: r3c3<>9 12.0, Region Forcing Chains (w/600 nodes): 3 in column ==> r3c8.6 off: r3c8<>6 12.0, Region Forcing Chains (w/654 nodes): 1 in column ==> r5c2.1 off: r5c2<>1 12.2, Contradiction Forcing Chain (w/1349 nodes): r8c7.9 on ==> r1c8.9 both on & off: r8c7<>9 12.1, Contradiction Forcing Chain (w/828 nodes): r9c2.9 on ==> r7c7.1 both on & off: r9c2<>9 11.6, Cell Forcing Chains (w/137 nodes): r5c2 ==> r8c8.9 off: r8c8<>9 11.6, Cell Forcing Chains (w/138 nodes): r7c1 ==> r9c1.6 off: r9c1<>6 11.9, Cell Forcing Chains (w/420 nodes): r7c4 ==> r8c9.9 off: r8c9<>9 2.9, General Intersection: Cells r9c7,r9c8,r9c9 on value 9 in block 9: r9c4<>9 2.9, General Intersection: Cells r7c4,r7c6 on value 9 in block 8: r7c2<>9 11.7, Contradiction Forcing Chain (w/236 nodes): r2c3.9 on ==> r9c2.2 both on & off: r2c3<>9 12.0, Region Forcing Chains (w/590 nodes): 1 in column ==> r9c3.7 off: r9c3<>7 2.9, General Intersection: Cells r7c1,r9c1 on value 7 in block 7: r1c1<>7 9.1, Double Forcing Chain (w/5 nodes): r4c5.7 on & off ==> r4c8.7 off: r4c8<>7 2.9, General Intersection: Cells r6c7,r6c8,r6c9 on value 7 in block 6: r6c6<>7 10.0, Contradiction Forcing Chain (w/128 nodes): r4c3.8 on ==> r8c8.6 both on & off: r4c3<>8 11.4, Double Forcing Chain (w/93 nodes): r4c3.1 on & off ==> r4c3.1 off: r4c3<>1 11.2, Region Forcing Chains (w/48 nodes): 2 in block ==> r1c3.6 off: r1c3<>6 11.4, Cell Forcing Chains (w/81 nodes): r5c2 ==> r5c1.9 off: r5c1<>9 10.8, Double Forcing Chain (w/10 nodes): r4c6.1 on & off ==> r4c5.1 off: r4c5<>1 12.1, Contradiction Forcing Chain (w/792 nodes): r1c1.6 on ==> r2c3.3 both on & off: r1c1<>6 11.0, Double Forcing Chain (w/18 nodes): r9c4.1 on & off ==> r3c4.1 off: r3c4<>1 10.6, Contradiction Forcing Chain (w/189 nodes): r1c1.1 on ==> r2c1.6 both on & off: r1c1<>1 11.4, Cell Forcing Chains (w/87 nodes): r1c3 ==> r9c1.1 off: r9c1<>1 11.6, Region Forcing Chains (w/143 nodes): 3 in block ==> r1c3.3 off: r1c3<>3 11.3, Cell Forcing Chains (w/262 nodes): r5c1 ==> r5c9.4 off: r5c9<>4 11.6, Region Forcing Chains (w/151 nodes): 2 in column ==> r1c7.5 off: r1c7<>5 11.6, Region Forcing Chains (w/159 nodes): 3 in row ==> r5c4.1 off: r5c4<>1 2.3, Naked Single: r5c4: 8: r5c4=8 2.9, General Intersection: Cells r4c6,r5c6,r6c6 on value 1 in block 5: r7c6<>1 11.7, Double Forcing Chain (w/201 nodes): r3c1.1 on & off ==> r6c7.8 off: r6c7<>8 11.5, Region Forcing Chains (w/109 nodes): 3 in block ==> r9c9.5 off: r9c9<>5 2.9, General Intersection: Cells r8c7,r9c7 on value 5 in block 9: r3c7<>5 11.5, Cell Forcing Chains (w/113 nodes): r8c2 ==> r2c7.2 off: r2c7<>2 11.6, Region Forcing Chains (w/135 nodes): 2 in column ==> r1c6.2 off: r1c6<>2 9.9, Contradiction Forcing Chain (w/71 nodes): r1c1.3 on ==> r1c7.9 both on & off: r1c1<>3 9.9, Double Forcing Chain (w/88 nodes): r9c3.3 on & off ==> r3c1.3 off: r3c1<>3 11.6, Region Forcing Chains (w/168 nodes): 8 in row ==> r2c3.8 off: r2c3<>8 11.3, Double Forcing Chain (w/54 nodes): r1c5.1 on & off ==> r1c3.4 off: r1c3<>4 11.6, Cell Forcing Chains (w/149 nodes): r2c2 ==> r3c2.6 off: r3c2<>6 11.6, Double Forcing Chain (w/167 nodes): r7c8.4 on & off ==> r1c2.8 off: r1c2<>8 11.6, Double Forcing Chain (w/188 nodes): r1c2.2 on & off ==> r9c1.2 off: r9c1<>2 3.0, Generalized Naked Pair: Cells r7c1,r9c1: 3,7 in block: r2c1<>3, r9c3<>3 11.4, Cell Forcing Chains (w/94 nodes): r8c9 ==> r8c7.1 off: r8c7<>1 10.4, Double Forcing Chain (w/68 nodes): r8c1.8 on & off ==> r3c2.8 off: r3c2<>8 11.2, Double Forcing Chain (w/42 nodes): r9c4.2 on & off ==> r8c9.1 off: r8c9<>1 5.7, Grouped 3 Strong links 3012: Cell r1c4,r3c5,r8c5,r8c1,r7c2,r1c2 on value 1: r1c3<>1, r3c3<>1 7.1, Forcing Chain (w/6 nodes): r2c2.8 off: r2c2<>8 2.9, General Intersection: Cells r7c2,r8c2 on value 8 in column 2: r8c1<>8 10.9, Contradiction Forcing Chain (w/508 nodes): r3c8.7 on ==> r4c7.4 both on & off: r3c8<>7 11.8, Region Forcing Chains (w/266 nodes): 1 in block ==> r6c1.1 off: r6c1<>1 11.3, Double Forcing Chain (w/57 nodes): r2c1.9 on & off ==> r1c8.8 off: r1c8<>8 11.4, Double Forcing Chain (w/73 nodes): r4c7.8 on & off ==> r7c7.8 off: r7c7<>8 2.9, General Intersection: Cells r1c7,r2c7,r3c7,r4c7 on value 8 in column 7: r3c9<>8 11.4, Double Forcing Chain (w/76 nodes): r4c4.6 on & off ==> r9c7.7 off: r9c7<>7 11.5, Double Forcing Chain (w/98 nodes): r3c6.7 on & off ==> r1c9.8 off: r1c9<>8 11.6, Double Forcing Chain (w/150 nodes): r9c2.6 on & off ==> r2c9.2 off: r2c9<>2 11.6, Region Forcing Chains (w/136 nodes): 1 in block ==> r1c6.7 off: r1c6<>7 11.6, Region Forcing Chains (w/142 nodes): 3 in row ==> r4c9.3 off: r4c9<>3 11.6, Cell Forcing Chains (w/162 nodes): r8c2 ==> r4c8.6 off: r4c8<>6 11.1, Cell Forcing Chains (w/32 nodes): r6c3 ==> r8c1.6 off: r8c1<>6 10.1, Double Forcing Chain (w/31 nodes): r8c1.2 on & off ==> r8c2.2 off: r8c2<>2 10.6, Region Forcing Chains (w/153 nodes): 9 in block ==> r1c2.9 off: r1c2<>9 11.5, Region Forcing Chains (w/587 nodes): 9 in column ==> r4c9.6 off: r4c9<>6 2.9, General Intersection: Cells r5c7,r5c8,r5c9 on value 6 in block 6: r5c2<>6 11.0, Region Forcing Chains (w/538 nodes): 1 in block ==> r2c6.9 off: r2c6<>9 10.8, Contradiction Forcing Chain (w/376 nodes): r2c9.6 on ==> r8c2.6 both on & off: r2c9<>6 11.3, Double Forcing Chain (w/51 nodes): r9c4.3 on & off ==> r3c6.3 off: r3c6<>3 11.3, Contradiction Forcing Chain (w/334 nodes): r9c9.2 on ==> r7c9.3 both on & off: r9c9<>2 11.3, Double Forcing Chain (w/50 nodes): r5c8.3 on & off ==> r2c6.2 off: r2c6<>2 4.3, Grouped Skyscraper 111: Cell r2c1,r2c5,r8c5,r8c1 on value 2: r1c1<>2, r3c1<>2 9.1, Region Forcing Chains (w/5 nodes): 1 in row ==> r8c1.1 off: r8c1<>1 9.8, Cell Forcing Chains (w/55 nodes): r9c2 ==> r9c8.6 off: r9c8<>6 9.9, Region Forcing Chains (w/81 nodes): 2 in row ==> r3c7.4 off: r3c7<>4 10.5, Double Forcing Chain (w/113 nodes): r9c4.1 on & off ==> r7c8.2 off: r7c8<>2 6.6, UVWXYZ-Wing 1313: Cells r7c8,r8c6,r8c7,r8c8,r8c9,r7c1 on value 3: r7c9<>3 11.2, Region Forcing Chains (w/229 nodes): 2 in column ==> r4c1.6 off: r4c1<>6 9.9, Region Forcing Chains (w/79 nodes): 3 in block ==> r6c7.2 off: r6c7<>2 9.9, Cell Forcing Chains (w/86 nodes): r9c2 ==> r9c9.6 off: r9c9<>6 10.7, Contradiction Forcing Chain (w/239 nodes): r3c8.3 on ==> r2c5.7 both on & off: r3c8<>3 10.9, Cell Forcing Chains (w/410 nodes): r8c9 ==> r2c9.8 off: r2c9<>8 11.2, Region Forcing Chains (w/216 nodes): 7 in row ==> r4c7.9 off: r4c7<>9 10.6, Region Forcing Chains (w/129 nodes): 7 in block ==> r3c8.9 off: r3c8<>9 11.4, Cell Forcing Chains (w/406 nodes): r4c7 ==> r4c8.4 off: r4c8<>4 9.0, Double Forcing Chain (w/3 nodes): r1c8.4 on & off ==> r3c9.4 off: r3c9<>4 12.0, Region Forcing Chains (w/520 nodes): 3 in row ==> r1c8.3 off: r1c8<>3 9.9, Region Forcing Chains (w/69 nodes): 3 in row ==> r3c7.9 off: r3c7<>9 9.5, Contradiction Forcing Chain (w/24 nodes): r1c4.9 on ==> r8c2.9 both on & off: r1c4<>9 10.1, Double Forcing Chain (w/28 nodes): r4c1.1 on & off ==> r5c1.1 off: r5c1<>1 2.3, Naked Single: r5c1: 4: r5c1=4 9.4, Contradiction Forcing Chain (w/90 nodes): r3c9.7 on ==> r2c3.3 both on & off: r3c9<>7 3.2, X-Wing: Cells r3c2,r5c2,r3c6,r5c6: 7 in 2 rows and 2 columns: r1c2<>7 9.7, Contradiction Forcing Chain (w/39 nodes): r7c7.7 on ==> r2c5.4 both on & off: r7c7<>7 10.7, Contradiction Forcing Chain (w/215 nodes): r8c9.6 on ==> r3c8.5 both on & off: r8c9<>6 9.5, Cell Forcing Chains (w/18 nodes): r8c9 ==> r8c8.8 off: r8c8<>8 6.4, VWXYZ-Wing 1311: Cells r6c6,r7c4,r7c6,r8c5,r8c8 on value 6: r5c8<>6 9.0, Cell Forcing Chains (w/20 nodes): r8c9 ==> r4c9.8 off: r4c9<>8 10.8, Region Forcing Chains (w/287 nodes): 6 in row ==> r1c7.6 off: r1c7<>6 10.8, Region Forcing Chains (w/349 nodes): 7 in row ==> r1c5.2 off: r1c5<>2 11.3, Region Forcing Chains (w/56 nodes): 8 in column ==> r1c6.8 off: r1c6<>8 2.9, General Intersection: Cells r2c6,r3c6 on value 8 in block 2: r3c8<>8 2.9, General Intersection: Cells r1c7,r2c7,r3c7 on value 8 in block 3: r4c7<>8 6.6, UVWXYZ-Wing 1416: Cells r1c6,r4c6,r5c6,r6c6,r7c6,r4c5 on value 3: r2c6<>3 8.4, Cell Forcing Chains (w/16 nodes): r8c5 ==> r2c1.8 off: r2c1<>8 6.4, VWXYZ-Wing 2310: Cells r2c1,r4c1,r6c1,r8c1,r6c3 on values 1,8: r1c1<>9 9.4, Contradiction Forcing Chain (w/90 nodes): r1c7.4 on ==> r2c7.7 both on & off: r1c7<>4 9.6, Region Forcing Chains (w/25 nodes): 3 in column ==> r2c9.9 off: r2c9<>9 9.5, Contradiction Forcing Chain (w/126 nodes): r6c8.7 on ==> r2c2.2 both on & off: r6c8<>7 2.9, General Intersection: Cells r6c7,r6c9 on value 7 in block 6: r7c9<>7 6.6, UVWXYZ-Wing 1313: Cells r4c7,r4c8,r4c9,r5c8,r6c8,r8c7 on value 3: r3c7<>3, r5c7<>3 2.9, General Intersection: Cells r4c7,r5c8,r5c9 on value 3 in block 6: r3c9<>3 2.9, General Intersection: Cells r3c3,r3c4 on value 3 in row 3: r1c4<>3 9.3, Contradiction Forcing Chain (w/52 nodes): r2c7.7 on ==> r1c6.3 both on & off: r2c7<>7 1.5, Hidden Single: r6c7: 7 in column: r6c7=7 9.2, Cell Forcing Chains (w/48 nodes): r5c6 ==> r4c6.3 off: r4c6<>3 9.4, Contradiction Forcing Chain (w/70 nodes): r1c8.5 on ==> r4c4.6 both on & off: r1c8<>5 9.5, Region Forcing Chains (w/111 nodes): 3 in block ==> r1c9.6 off: r1c9<>6 10.5, Double Forcing Chain (w/101 nodes): r2c1.9 on & off ==> r3c4.6 off: r3c4<>6 2.9, General Intersection: Cells r1c4,r1c6,r2c6 on value 6 in block 2: r1c8<>6 1.5, Hidden Single: r8c8: 6 in column: r8c8=6 6.4, VWXYZ-Wing 139: Cells r6c3,r8c2,r8c3,r9c3,r6c1 on value 6: r4c3<>6 1.2, Hidden Single: r6c1: 6 in block: r6c1=6 3.0, Generalized Naked Pair: Cells r4c3,r5c2: 7,9 in block: r4c1<>9 4.0, Hidden Triplet: Cells r2c3,r3c3,r9c3: 3,4,6 in column: r2c3<>7 5.6, WXYZ-Wing 137: Cells r6c6,r7c4,r8c5,r3c4 on value 3: r1c5<>3, r9c4<>3 7.2, Forcing Chain (w/8 nodes): r2c9.3 off: r2c9<>3 7.3, Forcing Chain (w/10 nodes): r3c2.9 off: r3c2<>9 8.9, Cell Forcing Chains (w/13 nodes): r7c6 ==> r5c6.3 off: r5c6<>3 2.9, General Intersection: Cells r4c4,r4c5 on value 3 in block 5: r4c7<>3 2.3, Naked Single: r4c7: 4: r4c7=4 6.4, VWXYZ-Wing 1310: Cells r4c8,r4c9,r5c8,r6c8,r8c7 on value 3: r9c8<>3 1.5, Hidden Single: r5c8: 3 in column: r5c8=3 6.6, UVWXYZ-Wing 1312: Cells r1c1,r1c3,r2c1,r3c1,r3c2,r3c5 on value 2: r2c5<>2 2.9, General Intersection: Cells r2c1,r2c2 on value 2 in row 2: r1c2<>2 3.0, Generalized Naked Pair: Cells r2c5,r2c9: 4,7 in row: r2c2<>4 7.1, Forcing Chain (w/6 nodes): r7c6.2 off: r7c6<>2 2.9, General Intersection: Cells r7c7,r7c9 on value 2 in row 7: r6c9<>2, r9c8<>2 2.9, General Intersection: Cells r4c6,r6c6 on value 2 in column 6: r4c4<>2 8.4, Cell Forcing Chains (w/14 nodes): r4c6 ==> r3c8.2 off: r3c8<>2 9.0, Cell Forcing Chains (w/19 nodes): r7c8 ==> r1c8.4 off: r1c8<>4 6.6, UVWXYZ-Wing 1314: Cells r1c8,r4c8,r6c8,r7c8,r9c8,r8c6 on value 5: r8c7<>5 1.2, Hidden Single: r9c7: 5 in block: r9c7=5 1.2, Hidden Single: r8c6: 5 in block: r8c6=5 1.2, Hidden Single: r9c6: 4 in block: r9c6=4 1.2, Hidden Single: r8c2: 4 in block: r8c2=4 1.2, Hidden Single: r3c3: 4 in block: r3c3=4 1.2, Hidden Single: r2c3: 3 in block: r2c3=3 1.2, Hidden Single: r1c5: 4 in block: r1c5=4 1.2, Hidden Single: r2c9: 4 in block: r2c9=4 1.2, Hidden Single: r4c5: 3 in block: r4c5=3 1.2, Hidden Single: r5c6: 7 in block: r5c6=7 1.2, Hidden Single: r2c5: 7 in block: r2c5=7 1.2, Hidden Single: r3c2: 7 in block: r3c2=7 1.2, Hidden Single: r4c3: 7 in block: r4c3=7 1.2, Hidden Single: r5c2: 9 in block: r5c2=9 1.2, Hidden Single: r7c2: 8 in block: r7c2=8 1.2, Hidden Single: r7c6: 3 in block: r7c6=3 1.2, Hidden Single: r3c4: 3 in block: r3c4=3 1.2, Hidden Single: r9c1: 3 in block: r9c1=3 1.2, Hidden Single: r7c1: 7 in block: r7c1=7 1.2, Hidden Single: r7c4: 9 in block: r7c4=9 1.2, Hidden Single: r7c8: 4 in block: r7c8=4 1.2, Hidden Single: r8c9: 8 in block: r8c9=8 1.2, Hidden Single: r4c8: 8 in block: r4c8=8 1.2, Hidden Single: r2c6: 8 in block: r2c6=8 1.2, Hidden Single: r6c3: 8 in block: r6c3=8 1.0, Hidden Single: r4c1: 1 in block: r4c1=1 1.2, Hidden Single: r1c2: 1 in block: r1c2=1 1.2, Hidden Single: r2c2: 6 in block: r2c2=6 1.0, Hidden Single: r9c2: 2 in column: r9c2=2 1.2, Hidden Single: r2c1: 2 in block: r2c1=2 1.0, Hidden Single: r2c7: 9 in row: r2c7=9 1.2, Hidden Single: r1c3: 9 in block: r1c3=9 1.2, Hidden Single: r3c5: 1 in block: r3c5=1 1.0, Hidden Single: r8c5: 2 in column: r8c5=2 1.0, Hidden Single: r9c4: 1 in block: r9c4=1 1.2, Hidden Single: r1c4: 2 in block: r1c4=2 1.0, Hidden Single: r4c4: 6 in column: r4c4=6 1.2, Hidden Single: r1c6: 6 in block: r1c6=6 1.0, Hidden Single: r3c6: 9 in block: r3c6=9 1.2, Hidden Single: r3c9: 6 in block: r3c9=6 1.2, Hidden Single: r3c7: 2 in block: r3c7=2 1.2, Hidden Single: r1c7: 8 in block: r1c7=8 1.2, Hidden Single: r3c1: 8 in block: r3c1=8 1.0, Hidden Single: r1c1: 5 in block: r1c1=5 1.0, Hidden Single: r8c1: 9 in column: r8c1=9 1.0, Hidden Single: r3c8: 5 in row: r3c8=5 1.2, Hidden Single: r1c9: 3 in block: r1c9=3 1.0, Hidden Single: r1c8: 7 in block: r1c8=7 1.2, Hidden Single: r6c6: 1 in block: r6c6=1 1.0, Hidden Single: r4c6: 2 in block: r4c6=2 1.0, Hidden Single: r4c9: 9 in row: r4c9=9 1.2, Hidden Single: r6c8: 2 in block: r6c8=2 1.0, Hidden Single: r9c8: 9 in column: r9c8=9 1.0, Hidden Single: r6c9: 5 in row: r6c9=5 1.2, Hidden Single: r5c7: 6 in block: r5c7=6 1.0, Hidden Single: r5c9: 1 in block: r5c9=1 1.2, Hidden Single: r8c3: 1 in block: r8c3=1 1.0, Hidden Single: r9c3: 6 in block: r9c3=6 1.0, Hidden Single: r8c7: 3 in row: r8c7=3 1.0, Hidden Single: r7c7: 1 in column: r7c7=1 1.0, Hidden Single: r7c9: 2 in row: r7c9=2 1.0, Hidden Single: r9c9: 7 in block: r9c9=7 ED=12.5/12.4/2.9

[sscg13]

Someone has released a fork where weak links are added for anti-knight, anti-king, and nonconsecutive

https://github.com/dclamage/SukakuExplainer/releases/tag/v1.18.0-rangsk

[SudokuMonster]

Thanks for the continued interest and updates from everyone. Unfortunately I have very little time to dedicate for this project at the moment but I'm hoping this may change soon.

The fork is really interesting but I didn't have time to checks or do tests (Although it appears to be a good job!!) to do a pull request. There was also also a pull request from a user a few months ago about a very small bug which I also didn't look into!

[1to9only]

@sscg13, thanks for link. There is a newer version: v1.18.1-rangsk - updated ratings (only took a few minutes for each puzzle!):

31.....5424.....36.............................................18.....7552.....68 ED=9.8/2.9/2.9
31.....5424.....36.............................................18.....7.52.....68 ED=10.1/10.1/2.9
31.....5424.....36.............................................18.....75.2.....68 ED=10.6/10.6/2.9
31.....5424.....36.............................................18.....7552......8 ED=9.9/9.9/2.9

.9....6..3.....2......4...8..........5..............1...2............7.9.6...8... ED=10.1/1.2/1.2
.9....6..3.....2..........8..........5..............1...2............7.9.6...8... ED=11.3/1.2/1.2

................1.....................2.......3.4.......5.6.......7.........8.... ED=10.7/10.7/2.9

Above SE ratings are from dclamage's SukakuExplainer.

[SudokuMonster]

commit #1fb47ce fixes weak links in AK, AN and NC