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Minimal Anti-Knight Found

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Minimal Anti-Knight Found

Postby mith » Tue Sep 07, 2021 3:44 pm

ryokousha over on the CTC Discord was able to find this anti-knight grid with 8 givens (which is of course a trivial lower bound):

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................1.....................2.......3.4.......5.6.......7.........8.... anti-knight
mith
 
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Postby 1to9only » Wed Sep 08, 2021 4:56 pm

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

Solution Path: Show
Code: Select all
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
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Re: Minimal Anti-Knight Found

Postby mith » Wed Sep 08, 2021 6:56 pm

Nice, I wasn't expecting it to be that low (as if 12.5 is low, heh) so I didn't leave it running long.
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Re: Minimal Anti-Knight Found

Postby 1to9only » Mon Sep 13, 2021 6:27 am

From: https://github.com/SudokuMonster/SukakuExplainer/issues/108#issuecomment-917696960
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

There is a later version: v1.18.1-rangsk - this rated (only took a few minutes!) the 8-clues Anti-Knight sudoku as ED=10.7/10.7/2.9.
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Re: Minimal Anti-Knight Found

Postby mith » Mon Sep 13, 2021 3:27 pm

Yep, we were discussing it elsewhere yesterday. Those weak links make a big difference!
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Re: Minimal Anti-Knight Found

Postby mith » Thu Sep 16, 2021 8:43 pm

Code: Select all
1.........2.........3.......6.4.........5.........6.....9...7.........8.........9  ED=12.2/12.2/2.9 (anti-knight)
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Re: Minimal Anti-Knight Found

Postby tarek » Wed Sep 22, 2021 11:18 am

Sukaku Explainer repository files have been updated and currently have a version number 1.18.0 and incorporates these changes which addresses the links issue

I haven't released it as we are looking at an issue which I would like to sore prior to an official release but you can build a functional executable if required
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Re: Minimal Anti-Knight Found

Postby mith » Thu Jan 13, 2022 9:07 pm

Just a quick update on this. A while ago, rangsk (also from CTC Discord) and I found another three 8c anti-knight puzzles, and yesterday rangsk and ryokousha were able to show that in fact these are the only four such puzzles. Here they are in minlex form:

Code: Select all
................1.....................2.......3.4.......5.6.......7.........8.... anti-knight, ryokousha
..........................................1.....2.3.4...5.6.7.......8............ anti-knight, rangsk
..........................................1.....2.3.....4.5.6.7.....8............ anti-knight, mith
..........................................1.....2.3.....4.5.6.7.......8.......... anti-knight, mith
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Re: Minimal Anti-Knight Found

Postby mith » Tue Feb 01, 2022 10:21 pm

Today we were messing around with a further restriction: anti-knight where givens may only be placed on the edges of the grid. The best I was able to come up with was 10c (one example below, I found a number of them), and we believe this is minimal but haven't yet proven it conclusively. I found a 9c with 2 solutions, but only 7 distinct digits, and the best we've done with 8 distinct digits is 18 solutions. [edit]Now proven by brute force search; 18 solutions is the best with 9c 8 distinct.[/edit]

Code: Select all
+-------+-------+-------+
| . . 1 | 2 3 . | . . . |
| . . . | . . . | . . 4 |
| . . . | . . . | . . 5 |
+-------+-------+-------+
| . . . | . . . | . . 6 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| 5 . . | . . . | . . . |
| 7 . . | . . . | . . . |
| . . . | . . . | 1 8 . |
+-------+-------+-------+
..123............4........5........6..................5........7..............18.  anti-knight
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