## Minimal NC Thermo

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Minimal NC Thermo

This is believed to be minimal in terms of cell coverage (4 givens is minimal for NC, we haven't checked that none of the 4 given grids can convert to a thermo but it seems very unlikely):

Code: Select all
`+-------+-------+-------+| . . . | . . . | . . . || . . . | . . . | . . . || . . . | . . . | . . . |+-------+-------+-------+| . . . | . . . | . . . || . . 9 | 7 5 . | . . . || . . . | . 3 1 | . . . |+-------+-------+-------+| . . . | . . . | . . . || . . . | . . . | . . . || . . . | . . . | . . . |+-------+-------+-------+......................................975........31.............................. non-consecutive thermo, r6c6<r6c5<r5c5<r5c4<r5c3 (digits are forced)`

I've had this running for a few days on rangsk's fork of SE:

Code: Select all
`................................6.....975........31.............................. 1.2, Hidden Single: r4c6: 6 in block..............................4.6.....975........31.............................. 1.2, Hidden Single: r4c4: 4 in block..............................426.....975........31.............................. 1.2, Hidden Single: r4c5: 2 in block..............................426.....9758.......31.............................. 1.2, Hidden Single: r5c6: 8 in block..............................426.....9758......931.............................. 1.0, Hidden Single: r6c4: 9 in block..............................426.....9758......931.............................. 2.5, 9: Cells r4c7,r4c8,r4c9 on value(s) 8..............................426.....9758......931.............................. 8.8, Contradiction Forcing Chain: r6c2.5 on ==> r5c1.4 both on & off..............................426.....9758......931.............................. 10.2, Contradiction Forcing Chain: r5c8.3 on ==> r4c2.3 both on & off..............................426.....9758......931.............................. 10.2, Region Forcing Chains: 2 in block ==> r6c8.2 off..............................426.....9758......931.............................. 10.1, Region Forcing Chains: 3 in row ==> r6c7.4 off..............................426.....9758......931.............................. 9.4, Contradiction Forcing Chain: r5c9.3 on ==> r6c3.5 both on & off..............................426.....9758......931.............................. 9.2, Contradiction Forcing Chain: r5c2.4 on ==> r4c2.8 both on & off..............................426.....9758......931.............................. 9.2, Contradiction Forcing Chain: r5c1.4 on ==> r6c1.2 both on & off..............................426.....9758......931.............................. 2.6, Pointing: Cells r6c1,r6c2,r6c3: 4 in block and row..............................426.....9758......931.............................. 9.0, Region Forcing Chains: 2 in block ==> r6c3.6 off..............................426.....9758......931.............................. 9.3, Contradiction Forcing Chain: r6c8.7 on ==> r4c7.8 both on & off..............................426.....9758......931.............................. 10.0, Double Forcing Chain: r6c8.5 on & off ==> r4c8.1 off..............................426.....9758......931.............................. 10.0, Region Forcing Chains: 7 in row ==> r6c1.5 off..............................426.....9758......931.............................. 9.5, Region Forcing Chains: 3 in row ==> r4c9.5 off..............................426.....9758......931.............................. 10.2, Contradiction Forcing Chain: r4c2.7 on ==> r5c1.6 both on & off..............................426.....9758......931.............................. 10.2, Contradiction Forcing Chain: r4c1.7 on ==> r5c2.6 both on & off..............................426.....9758......931.............................. 10.2, Region Forcing Chains: 5 in block ==> r5c8.6 off..............................426.....9758......931.............................. 9.0, Region Forcing Chains: 2 in row ==> r4c8.3 off..............................426.....9758......931.............................. 9.0, Contradiction Forcing Chain: r4c9.8 on ==> r6c7.7 both on & off..............................426.....9758......931.............................. 9.0, Contradiction Forcing Chain: r4c7.8 on ==> r6c7.7 both on & off..............................426.....9758......931.............................. 2.6, Pointing: Cells r6c7,r6c8,r6c9: 8 in block and row..............................426.....9758......931.............................. 7.0, Forcing Chain: r4c1.1 off..............................426.....9758......931.............................. 9.0, Contradiction Forcing Chain: r5c1.2 on ==> r6c3.5 both on & off..............................426.....9758......931.............................. 8.8, Region Forcing Chains: 3 in block ==> r4c2.3 off..............................426.....9758......931.............................. 8.9, Contradiction Forcing Chain: r7c1.3 on ==> r6c3.2 both on & off..............................426.....9758......931.............................. 9.0, Contradiction Forcing Chain: r4c2.1 on ==> r5c1.3 both on & off..............................426.....9758......931.............................. 9.1, Region Forcing Chains: 1 in block ==> r7c3.1 off..............................426.....9758......931.............................. 9.1, Region Forcing Chains: 1 in block ==> r3c3.2 off..............................426.....9758......931.............................. 9.4, Region Forcing Chains: 3 in block ==> r6c3.7 off..............................426.....9758......931.............................. 9.6, Region Forcing Chains: 1 in block ==> r3c9.2 off..............................426.....9758......931.............................. 12.5, Contradiction Forcing Chain: r7c2.3 on ==> r2c2.1 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r2c5.6 on ==> r2c7.9 both on & off..............................426.....9758......931.............................. 12.7, Contradiction Forcing Chain: r8c6.5 on ==> r3c9.8 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r8c5.7 on ==> r6c9.6 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r2c5.8 on ==> r3c8.5 both on & off..............................426.....9758......931.............................. 12.4, Contradiction Forcing Chain: r7c3.3 on ==> r7c6.4 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r7c8.9 on ==> r9c3.3 both on & off..............................426.....9758......931.............................. 12.7, Contradiction Forcing Chain: r8c3.7 on ==> r1c7.9 both on & off..............................426.....9758......931.............................. 12.4, Contradiction Forcing Chain: r7c1.8 on ==> r8c9.3 both on & off..............................426.....9758......931.............................. 12.4, Contradiction Forcing Chain: r3c1.7 on ==> r1c2.6 both on & off..............................426.....9758......931.............................. 12.8, Contradiction Forcing Chain: r8c6.3 on ==> r3c5.8 both on & off..............................426.....9758......931.............................. 12.5, Contradiction Forcing Chain: r9c5.4 on ==> r5c2.3 both on & off..............................426.....9758......931.............................. 12.5, Contradiction Forcing Chain: r3c8.8 on ==> r1c4.8 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r3c2.6 on ==> r2c1.5 both on & off..............................426.....9758......931.............................. 12.5, Region Forcing Chains: 4 in column ==> r7c8.4 off..............................426.....9758......931.............................. 12.4, Contradiction Forcing Chain: r3c7.2 on ==> r7c7.6 both on & off..............................426.....9758......931.............................. 12.6, Region Forcing Chains: 5 in column ==> r7c7.6 off..............................426.....9758......931.............................. 12.6, Region Forcing Chains: 5 in column ==> r7c9.6 off..............................426.....9758......931.............................. 12.5, Contradiction Forcing Chain: r6c8.6 on ==> r2c4.8 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r8c8.8 on ==> r6c2.6 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r7c2.8 on ==> r9c6.5 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r4c1.3 on ==> r8c7.4 both on & off..............................426.....9758......931.............................. 2.5, 3: Cells r5c1,r5c2 on value(s) 2,4..............................426.....9758......931.............................. 2.5, 2: Cells r5c7,r5c8,r5c9 on value(s) 1,3..............................426.....9758......931.............................. 2.4, Cell r5c8 on value(s) 3..............................426.....9758......931.............................. 2.6, Pointing: Cells r6c1,r6c2,r6c3: 2 in block and row..............................426.....9758......931.............................. 3.0, Naked Pair: Cells r4c1,r4c2: 5,8 in block..............................426.....9758......931.............................. 2.6, Pointing: Cells r4c1,r4c2: 5 in block and row..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r2c1.8 on ==> r2c8.9 both on & off..............................426.....9758......931.............................. 12.5, Contradiction Forcing Chain: r3c7.4 on ==> r2c7.1 both on & off..............................426.....9758......931.............................. 12.7, Contradiction Forcing Chain: r8c4.2 on ==> r1c4.1 both on & off..............................426.....9758......931.............................. 12.7, Contradiction Forcing Chain: r2c6.2 on ==> r6c2.7 both on & off..............................426.....9758......931.............................. 12.2, Region Forcing Chains: 8 in block ==> r2c3.7 off..............................426.....9758......931.............................. 12.4, Contradiction Forcing Chain: r1c2.5 on ==> r7c6.3 both on & off..............................426.....9758......931.............................. 12.5, Contradiction Forcing Chain: r2c2.5 on ==> r8c9.3 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r3c7.3 on ==> r5c9.1 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r8c5.8 on ==> r9c3.8 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r1c2.3 on ==> r1c6.9 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r3c2.4 on ==> r8c4.1 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r1c1.8 on ==> r8c1.6 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r9c2.5 on ==> r2c8.2 both on & off..............................426.....9758......931.............................. 12.7, Contradiction Forcing Chain: r8c8.4 on ==> r6c7.7 both on & off..............................426.....9758......931.............................. 12.5, Contradiction Forcing Chain: r9c8.8 on ==> r8c4.6 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r3c1.6 on ==> r1c2.7 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r2c3.1 on ==> r2c1.7 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r2c6.4 on ==> r2c4.5 both on & off..............................426.....9758......931.............................. 12.2, Contradiction Forcing Chain: r1c6.7 on ==> r8c8.6 both on & off..............................426.....9758......931.............................. 12.7, Contradiction Forcing Chain: r2c7.8 on ==> r8c2.5 both on & off..............................426.....9758......931.............................. 12.7, Contradiction Forcing Chain: r1c6.9 on ==> r1c8.7 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r1c7.4 on ==> r3c3.4 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r7c2.6 on ==> r8c2.2 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r1c7.3 on ==> r9c5.8 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r2c7.6 on ==> r8c4.1 both on & off..............................426.....9758......931.............................. 12.5, Contradiction Forcing Chain: r2c6.3 on ==> r9c3.7 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r2c8.2 on ==> r7c7.2 both on & off..............................426.....9758......931.............................. 12.8, Contradiction Forcing Chain: r2c2.7 on ==> r2c6.9 both on & off..............................426.....9758......931.............................. 12.6, Contradiction Forcing Chain: r8c1.8 on ==> r1c3.4 both on & off..............................426.....9758......931.............................. 12.4, Contradiction Forcing Chain: r8c2.5 on ==> r3c4.8 both on & off..............................426.....9758......931.............................. 12.4, Contradiction Forcing Chain: r3c1.9 on ==> r8c8.2 both on & off..............................426.....9758......931.............................. 12.4, Contradiction Forcing Chain: r7c2.5 on ==> r8c2.7 both on & off..............................426.....9758......931.............................. 11.8, Contradiction Forcing Chain: r3c2.3 on ==> r8c2.2 both on & off..............................426.....9758......931.............................. 12.3, Contradiction Forcing Chain: r3c1.8 on ==> r9c2.1 both on & off..............................426.....9758......931.............................. 12.3, Contradiction Forcing Chain: r6c2.2 on ==> r7c4.3 both on & off..............................426.....9758......931.............................. 11.2, Contradiction Forcing Chain: r6c1.7 on ==> r7c7.8 both on & off..............................426.....9758......931.............................. 7.0, Forcing Chain: r5c2.6 off..............................426.....9758......931.............................. 8.3, Region Forcing Chains: 6 in block ==> r4c2.8 off...........................8..426.....9758......931.............................. 1.2, Hidden Single: r4c1: 8 in block...........................85.426.....9758......931.............................. 1.2, Hidden Single: r4c2: 5 in block...........................85.426.....9758......931.............................. 12.1, Contradiction Forcing Chain: r8c1.6 on ==> r1c3.4 both on & off...........................85.426.....9758......931.............................. 12.3, Contradiction Forcing Chain: r9c2.3 on ==> r4c9.3 both on & off...........................85.426.....9758......931.............................. 12.3, Contradiction Forcing Chain: r2c2.3 on ==> r8c5.1 both on & off...........................85.426.....9758......931.............................. 12.3, Contradiction Forcing Chain: r7c2.7 on ==> r3c4.6 both on & off...........................85.426.....9758......931.............................. 12.1, Contradiction Forcing Chain: r6c1.6 on ==> r8c7.5 both on & off...........................85.426.....9758......931.............................. 2.4, Cell r6c1 on value(s) 3...........................85.426....39758......931.............................. 1.2, Hidden Single: r5c2: 3 in block...........................85.426....39758......931.............................. 12.3, Contradiction Forcing Chain: r2c1.4 on ==> r2c9.2 both on & off...........................85.426....39758......931.............................. 12.3, Contradiction Forcing Chain: r7c3.2 on ==> r3c4.1 both on & off...........................85.426....39758......931.............................. 12.4, Contradiction Forcing Chain: r3c3.1 on ==> r1c8.7 both on & off...........................85.426....39758......931.............................. 12.3, Contradiction Forcing Chain: r2c8.8 on ==> r3c8.1 both on & off...........................85.426....39758......931.............................. 12.2, Contradiction Forcing Chain: r7c8.7 on ==> r3c4.1 both on & off...........................85.426....39758......931.............................. 12.2, Contradiction Forcing Chain: r1c1.6 on ==> r9c3.5 both on & off...........................85.426....39758......931.............................. 12.2, Contradiction Forcing Chain: r1c8.8 on ==> r2c7.3 both on & off...........................85.426....39758......931.............................. 10.8, Contradiction Forcing Chain: r8c2.7 on ==> r9c6.5 both on & off...........................85.426....39758......931.............................. 11.6, Contradiction Forcing Chain: r9c2.7 on ==> r2c6.9 both on & off...........................85.426....39758......931.............................. 11.5, Contradiction Forcing Chain: r7c1.6 on ==> r2c4.8 both on & off...........................85.426....39758......931.............................. 12.0, Contradiction Forcing Chain: r8c3.1 on ==> r8c2.4 both on & off...........................85.426....39758......931.............................. 11.5, Contradiction Forcing Chain: r9c1.6 on ==> r8c8.1 both on & off...........................85.426....39758......931.............................. 10.8, Contradiction Forcing Chain: r2c8.4 on ==> r1c5.6 both on & off...........................85.426....39758......931.............................. 11.3, Contradiction Forcing Chain: r1c3.1 on ==> r7c4.1 both on & off...........................85.426....39758......931.............................. 11.4, Contradiction Forcing Chain: r1c2.7 on ==> r1c4.6 both on & off...........................85.426....39758......931.............................. 10.8, Contradiction Forcing Chain: r9c8.4 on ==> r2c5.1 both on & off...........................85.426....39758......931.............................. 11.3, Cell Forcing Chains: r6c8 ==> r1c8.4 off...........................85.426....39758......931.............................. 11.2, Contradiction Forcing Chain: r6c9.7 on ==> r9c2.9 both on & off...........................85.426....39758......931.............................. 7.0, Forcing Chain: r5c7.6 off...........................85.426....39758......931.............................. 8.2, Cell Forcing Chains: r5c7 ==> r4c9.1 off...........................85.426....39758......931.............................. 8.2, Cell Forcing Chains: r5c7 ==> r5c9.4 off...........................85.426....39758......931.............................. 8.2, Cell Forcing Chains: r6c9 ==> r6c7.8 off...........................85.426....39758......931.............................. 10.4, Contradiction Forcing Chain: r7c9.5 on ==> r3c7.6 both on & off...........................85.426....39758......931.............................. 11.3, Contradiction Forcing Chain: r7c7.5 on ==> r1c6.5 both on & off...........................85.426....39758......931.............................. 10.8, Contradiction Forcing Chain: r6c2.6 on ==> r8c5.1 both on & off...........................85.426...639758......931.............................. 1.2, Hidden Single: r5c1: 6 in block...........................851426...639758......931.............................. 1.2, Hidden Single: r4c3: 1 in block...........................851426...639758....7.931.............................. 1.2, Hidden Single: r6c2: 7 in block...........................851426...639758....7.931.............................. 2.4, Cell r5c9 on value(s) 1,2...........................851426...639758.4..7.931.............................. 2.0, Direct Hidden Pair: Cells r5c7,r5c9: 1,2 in block...........................851426...639758.4..7.931.8............................ 2.0, Direct Hidden Pair: Cells r6c7,r6c9: 5,6 in block...........................851426...639758.4..7.931.8............................ 12.1, Contradiction Forcing Chain: r1c5.4 on ==> r2c5.9 both on & off...........................851426...639758.4..7.931.8............................ 11.5, Contradiction Forcing Chain: r8c9.4 on ==> r3c9.5 both on & off...........................851426...639758.4..7.931.8............................ 11.6, Contradiction Forcing Chain: r8c3.4 on ==> r8c7.9 both on & off...........................851426...639758.4..7.931.8............................ 12.2, Contradiction Forcing Chain: r3c8.7 on ==> r7c3.7 both on & off...........................851426...639758.4..7.931.8............................ 12.2, Contradiction Forcing Chain: r8c7.5 on ==> r8c9.8 both on & off...........................851426...639758.4..7.931.8............................ 12.2, Contradiction Forcing Chain: r2c4.3 on ==> r2c3.6 both on & off...........................851426...639758.4..7.931.8............................ 12.1, Contradiction Forcing Chain: r2c3.5 on ==> r3c3.3 both on & off...........................851426...639758.4..7.931.8............................ 11.5, Contradiction Forcing Chain: r8c3.6 on ==> r9c9.1 both on & off...........................851426...639758.4..7.931.8............................ 11.5, Contradiction Forcing Chain: r9c4.6 on ==> r7c2.4 both on & off...........................851426...639758.4..7.931.8............................ 12.1, Contradiction Forcing Chain: r9c3.2 on ==> r8c5.4 both on & off...........................851426...639758.4..7.931.8............................ 12.2, Contradiction Forcing Chain: r2c7.1 on ==> r2c4.5 both on & off...........................851426...639758.4..7.931.8............................ 12.1, Contradiction Forcing Chain: r2c4.2 on ==> r3c9.4 both on & off...........................851426...639758.4..7.931.8............................ 10.9, Contradiction Forcing Chain: r2c5.7 on ==> r6c1.4 both on & off...........................851426...639758.4..7.931.8............................ 11.5, Contradiction Forcing Chain: r1c4.6 on ==> r1c2.2 both on & off...........................851426...639758.4..7.931.8............................ 11.5, Contradiction Forcing Chain: r3c8.6 on ==> r9c3.7 both on & off...........................851426...639758.4..7.931.8............................ 12.0, Contradiction Forcing Chain: r1c8.7 on ==> r9c9.5 both on & off...........................851426...639758.4..7.931.8............................ 11.6, Contradiction Forcing Chain: r2c9.5 on ==> r8c1.1 both on & off...........................851426...639758.4..7.931.8............................ 12.0, Contradiction Forcing Chain: r2c8.7 on ==> r2c2.2 both on & off...........................851426...639758.4..7.931.8............................ 12.0, Contradiction Forcing Chain: r2c6.5 on ==> r8c8.9 both on & off...........................851426...639758.4..7.931.8............................ 10.6, Contradiction Forcing Chain: r3c6.9 on ==> r1c4.2 both on & off...........................851426...639758.4..7.931.8............................ 11.3, Contradiction Forcing Chain: r3c5.4 on ==> r1c8.9 both on & off...........................851426...639758.4..7.931.8............................ 11.4, Contradiction Forcing Chain: r1c8.5 on ==> r3c9.8 both on & off...........................851426...639758.4..7.931.8............................ 11.4, Contradiction Forcing Chain: r8c1.4 on ==> r7c4.6 both on & off...........................851426...639758.4..7.931.8............................ 11.4, Contradiction Forcing Chain: r8c2.4 on ==> r6c9.6 both on & off...........................851426...639758.4..7.931.8............................ 11.5, Contradiction Forcing Chain: r7c3.4 on ==> r9c8.2 both on & off...........................851426...639758.4..7.931.8............................ 11.4, Contradiction Forcing Chain: r2c1.2 on ==> r2c7.5 both on & off...........................851426...639758.4..7.931.8............................ 11.5, Contradiction Forcing Chain: r2c7.7 on ==> r8c7.6 both on & off...........................851426...639758.4..7.931.8............................ 11.5, Contradiction Forcing Chain: r2c7.9 on ==> r7c3.5 both on & off...........................851426...639758.4..7.931.8............................ 11.3, Contradiction Forcing Chain: r1c1.5 on ==> r7c3.5 both on & off...........................851426...639758.4..7.931.8............................ 11.5, Contradiction Forcing Chain: r1c5.6 on ==> r9c6.5 both on & off...........................851426...639758.4..7.931.8............................ 10.9, Contradiction Forcing Chain: r1c3.5 on ==> r7c8.2 both on & off...........................851426...639758.4..7.931.8............................ 10.8, Contradiction Forcing Chain: r3c3.3 on ==> r8c7.4 both on & off...........................851426...639758.4..7.931.8............................ 11.3, Contradiction Forcing Chain: r2c5.9 on ==> r2c1.3 both on & off...........................851426...639758.4..7.931.8............................ 10.8, Contradiction Forcing Chain: r1c9.5 on ==> r8c1.9 both on & off...........................851426...639758.4..7.931.8............................ 10.0, Contradiction Forcing Chain: r8c7.3 on ==> r2c2.8 both on & off...........................851426...639758.4..7.931.8............................ 10.8, Contradiction Forcing Chain: r2c8.1 on ==> r9c9.6 both on & off...........................851426...639758.4..7.931.8............................ 10.8, Contradiction Forcing Chain: r2c4.5 on ==> r9c1.5 both on & off...........................851426...639758.4..7.931.8............................ 2.6, Pointing: Cells r1c4,r1c6: 5 in block and row...........................851426...639758.4..7.931.8............................ 10.9, Contradiction Forcing Chain: r1c9.2 on ==> r8c2.6 both on & off...........................851426...639758.4..7.931.8............................ 10.9, Contradiction Forcing Chain: r1c4.8 on ==> r3c7.6 both on & off...........................851426...639758.4..7.931.8............................ 9.6, Region Forcing Chains: 7 in column ==> r1c5.1 off...........................851426...639758.4..7.931.8............................ 10.8, Contradiction Forcing Chain: r8c4.3 on ==> r2c8.5 both on & off...........................851426...639758.4..7.931.8............................ 11.1, Contradiction Forcing Chain: r7c4.6 on ==> r1c8.6 both on & off...........................851426...639758.4..7.931.8............................ 10.5, Contradiction Forcing Chain: r8c4.1 on ==> r7c3.8 both on & off...........................851426...639758.4..7.931.8............................ 10.8, Contradiction Forcing Chain: r2c2.4 on ==> r9c8.6 both on & off...........................851426...639758.4..7.931.8............................ 10.6, Contradiction Forcing Chain: r1c3.2 on ==> r2c7.3 both on & off...........................851426...639758.4..7.931.8............................ 10.8, Contradiction Forcing Chain: r8c7.6 on ==> r1c5.8 both on & off...........................851426...639758.4..7.931.8............................ 10.7, Contradiction Forcing Chain: r2c9.3 on ==> r8c8.6 both on & off...........................851426...639758.4..7.931.8............................ 9.2, Region Forcing Chains: 4 in column ==> r9c9.4 off...........................851426...639758.4..7.931.8............................ 9.5, Contradiction Forcing Chain: r2c7.4 on ==> r9c7.6 both on & off...........................851426...639758.4..7.931.8............................ 2.6, Pointing: Cells r1c9,r2c9,r3c9: 4 in block and column...........................851426...639758.4..7.931.8............................ 9.9, Contradiction Forcing Chain: r9c7.3 on ==> r9c8.1 both on & off...........................851426...639758.4..7.931.8............................ 10.6, Contradiction Forcing Chain: r7c7.3 on ==> r9c6.2 both on & off...........................851426...639758.4..7.931.8............................ 10.6, Contradiction Forcing Chain: r9c7.6 on ==> r8c4.5 both on & off...........................851426...639758.4..7.931.8............................ 10.4, Contradiction Forcing Chain: r3c9.5 on ==> r3c7.7 both on & off...........................851426...639758.4..7.931.8............................ 10.5, Contradiction Forcing Chain: r2c8.6 on ==> r3c2.1 both on & off...........................851426...639758.4..7.931.8............................ 10.4, Contradiction Forcing Chain: r1c9.9 on ==> r3c8.2 both on & off...........................851426...639758.4..7.931.8............................ 10.4, Contradiction Forcing Chain: r8c8.7 on ==> r1c9.4 both on & off...........................851426...639758.4..7.931.8............................ 10.5, Contradiction Forcing Chain: r3c7.5 on ==> r3c9.7 both on & off...........................851426...639758.4..7.931.8............................ 10.6, Contradiction Forcing Chain: r1c7.1 on ==> r9c3.6 both on & off...........................851426...639758.4..7.931.8............................ 10.7, Contradiction Forcing Chain: r1c7.9 on ==> r6c1.2 both on & off...........................851426...639758.4..7.931.8............................ 10.7, Contradiction Forcing Chain: r1c3.4 on ==> r3c2.1 both on & off...........................851426...639758.4..7.931.8............................ 10.6, Contradiction Forcing Chain: r8c1.2 on ==> r8c9.5 both on & off...........................851426...639758.4..7.931.8............................ 10.8, Contradiction Forcing Chain: r8c7.2 on ==> r1c7.7 both on & off...........................851426...639758.4..7.931.8............................ 10.8, Contradiction Forcing Chain: r4c9.7 on ==> r8c3.3 both on & off...........................851426.7.639758.4..7.931.8............................ 1.2, Hidden Single: r4c8: 7 in block...........................851426.7.639758.4..7.931.8............................ 9.2, Contradiction Forcing Chain: r2c9.9 on ==> r2c3.8 both on & off...........................851426.7.639758.4..7.931.8............................ 9.4, Contradiction Forcing Chain: r3c9.9 on ==> r3c2.2 both on & off...........................851426.7.639758.4..7.931.8............................ 10.0, Contradiction Forcing Chain: r9c9.2 on ==> r2c9.4 both on & off...........................851426.7.639758.4..7.931.8............................ 10.0, Contradiction Forcing Chain: r8c9.2 on ==> r9c3.6 both on & off...........................851426.7.639758.4..7.931.8............................ 10.6, Contradiction Forcing Chain: r7c9.2 on ==> r8c4.5 both on & off...........................851426.7.639758.4..7.931.8............................ 9.3, Contradiction Forcing Chain: r8c9.9 on ==> r1c7.7 both on & off...........................851426.7.639758.4..7.931.8............................ 9.9, Contradiction Forcing Chain: r3c7.1 on ==> r7c9.8 both on & off...........................851426.7.639758.4..7.931.8............................ 10.1, Contradiction Forcing Chain: r1c8.2 on ==> r8c8.5 both on & off...........................851426.7.639758.4..7.931.8............................ 9.9, Contradiction Forcing Chain: r8c8.1 on ==> r9c5.7 both on & off...........................851426.7.639758.4..7.931.8............................ 10.2, Contradiction Forcing Chain: r8c8.3 on ==> r7c2.1 both on & off...........................851426.7.639758.4..7.931.8............................ 9.7, Contradiction Forcing Chain: r8c7.1 on ==> r7c9.7 both on & off...........................851426.7.639758.4..7.931.8............................ 10.2, Contradiction Forcing Chain: r3c9.8 on ==> r8c8.6 both on & off...........................851426.7.639758.4..7.931.8............................ 9.4, Contradiction Forcing Chain: r7c9.9 on ==> r9c8.3 both on & off...........................851426.7.639758.4..7.931.8............................ 9.3, Contradiction Forcing Chain: r9c7.1 on ==> r7c8.3 both on & off...........................851426.7.639758.4..7.931.8............................ 9.4, Contradiction Forcing Chain: r2c7.3 on ==> r9c8.3 both on & off...........................85142637.639758.4..7.931.8............................ 1.5, Hidden Single: r4c7: 3 in column...........................851426379639758.4..7.931.8............................ 1.0, Hidden Single: r4c9: 9 in row...........................851426379639758.42.7.931.8............................ 1.2, Hidden Single: r5c9: 2 in block...........................851426379639758142.7.931.8............................ 1.0, Hidden Single: r5c7: 1 in row...........................851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r3c8.5 on ==> r3c9.3 both on & off...........................851426379639758142.7.931.8............................ 2.6, Pointing: Cells r2c7,r2c8: 5 in block and row...........................851426379639758142.7.931.8............................ 9.3, Contradiction Forcing Chain: r3c1.3 on ==> r9c4.5 both on & off...........................851426379639758142.7.931.8............................ 9.3, Contradiction Forcing Chain: r1c3.3 on ==> r2c3.8 both on & off...........................851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r2c2.2 on ==> r2c3.4 both on & off...........................851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r2c3.8 on ==> r3c2.2 both on & off...........................851426379639758142.7.931.8............................ 9.2, Contradiction Forcing Chain: r2c9.6 on ==> r3c2.8 both on & off...........................851426379639758142.7.931.8............................ 9.2, Contradiction Forcing Chain: r1c2.8 on ==> r1c5.9 both on & off...........................851426379639758142.7.931.8............................ 9.3, Contradiction Forcing Chain: r3c1.2 on ==> r8c6.4 both on & off...........................851426379639758142.7.931.8............................ 9.3, Contradiction Forcing Chain: r2c1.7 on ==> r8c3.8 both on & off...........................851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r3c5.7 on ==> r3c8.9 both on & off...........................851426379639758142.7.931.8............................ 9.2, Contradiction Forcing Chain: r2c2.1 on ==> r1c7.6 both on & off...........................851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r1c2.9 on ==> r2c8.9 both on & off...........................851426379639758142.7.931.8............................ 9.2, Contradiction Forcing Chain: r1c1.3 on ==> r3c3.7 both on & off...........................851426379639758142.7.931.8............................ 2.6, Pointing: Cells r2c1,r2c3: 3 in block and row...........................851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r9c8.5 on ==> r1c8.6 both on & off...........................851426379639758142.7.931.8............................ 9.0, Cell Forcing Chains: r7c8 ==> r7c7.2 off...........................851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r8c9.6 on ==> r9c8.1 both on & off...........................851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r9c7.2 on ==> r8c8.5 both on & off...........................851426379639758142.7.931.8............................ 2.6, Pointing: Cells r7c8,r8c8,r9c8: 2 in block and column...........................851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r7c8.5 on ==> r1c8.6 both on & off...........................851426379639758142.7.931.8............................ 9.2, Contradiction Forcing Chain: r1c1.2 on ==> r1c6.5 both on & off...........................851426379639758142.7.931.8............................ 9.2, Contradiction Forcing Chain: r8c2.2 on ==> r8c3.5 both on & off...........................851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r2c9.4 on ==> r9c6.3 both on & off...............2...........851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r2c7.2 off ==> r8c6.4 both on & off...............25..........851426379639758142.7.931.8............................ 1.2, Hidden Single: r2c8: 5 in block...............25..........851426379639758142.7.931.8............................ 2.6, Pointing: Cells r1c2,r3c2: 2 in block and column...............25..........851426379639758142.7.931.8............................ 2.8, Claiming: Cells r7c8,r8c8,r9c8: 6 in column and block...............25..........851426379639758142.7.931.8............................ 8.4, Region Forcing Chains: 3 in block ==> r9c1.4 off...............25..........851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r3c9.7 on ==> r1c4.5 both on & off...............25..........851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r8c1.5 on ==> r8c9.7 both on & off...............25..........851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r9c1.5 on ==> r8c1.7 both on & off...............25..........851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r7c1.4 on ==> r9c9.5 both on & off...............25..........851426379639758142.7.931.8............................ 9.1, Cell Forcing Chains: r8c8 ==> r9c8.6 off...............25..........851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r9c4.5 on ==> r7c1.5 both on & off...............25..........851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r8c1.1 on ==> r7c1.5 both on & off...............25..........851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r1c6.4 on ==> r8c9.1 both on & off...............25..........851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r3c3.6 on ==> r2c1.9 both on & off...............25..........851426379639758142.7.931.8............................ 9.2, Contradiction Forcing Chain: r1c9.7 on ==> r2c2.8 both on & off...............25..........851426379639758142.7.931.8............................ 9.2, Region Forcing Chains: 5 in column ==> r7c3.6 off...............25..........851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r7c9.7 on ==> r8c4.5 both on & off...............25..........851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r9c3.7 on ==> r8c4.5 both on & off...............25..........851426379639758142.7.931.8............................ 9.1, Contradiction Forcing Chain: r2c3.6 on ==> r9c2.6 both on & off...............25..........851426379639758142.7.931.8............................ 2.4, Cell r2c3 on value(s) 3,4...............25..........851426379639758142.7.931.8............................ 8.4, Region Forcing Chains: 5 in block ==> r7c6.5 off...............25..........851426379639758142.7.931.8............................ 9.0, Contradiction Forcing Chain: r9c3.3 on ==> r7c4.3 both on & off...............25..........851426379639758142.7.931.8............................ 8.7, Region Forcing Chains: 4 in column ==> r8c3.5 off...............25..........851426379639758142.7.931.8............................ 8.9, Region Forcing Chains: 7 in column ==> r9c5.7 off...............25..........851426379639758142.7.931.8............................ 4.3, Grouped 2 Strong links 101: Cell r3c3,r1c1,r1c5,r7c5 on value 7...............25..........851426379639758142.7.931.8............................ 2.6, Pointing: Cells r7c1,r8c1,r9c1: 7 in block and column...............25..........851426379639758142.7.931.8............................ 8.5, Region Forcing Chains: 6 in column ==> r3c4.6 off...............25..........851426379639758142.7.931.8............................ 8.3, Region Forcing Chains: 6 in block ==> r1c9.6 off...............25..........851426379639758142.7.931.8............................ 8.8, Cell Forcing Chains: r8c1 ==> r8c2.8 off...............25..........851426379639758142.7.931.8............................ 8.8, Region Forcing Chains: 4 in block ==> r9c2.8 off...............25..........851426379639758142.7.931.8............................ 2.5, 8: Cells r2c2,r3c2 on value(s) 7,9...............25..........851426379639758142.7.931.8............................ 2.6, Pointing: Cells r7c3,r8c3,r9c3: 8 in block and column...............25..........851426379639758142.7.931.8............................ 2.4, Cell r1c3 on value(s) 6,7...............25..........851426379639758142.7.931.8............................ 2.6, Pointing: Cells r1c1,r2c1: 9 in block and column...............25..........851426379639758142.7.931.8............................ 7.1, Forcing Chain: r1c1.1 off...............25..........851426379639758142.7.931.8............................ 7.1, Bidirectional Cycle: r2c2,r2c1,r2c6,r1c5,r1c3...............25..........851426379639758142.7.931.8............................ 5.5, WXYZ-Wing 126: Cells r1c3,r3c3,r7c3,r1c7 on value 8...............25..........851426379639758142.7.931.8............................ 7.1, Forcing Chain: r3c4.8 off...............25..........851426379639758142.7.931.8............................ 2.4, Cell r3c4 on value(s) 1,2...............25..........851426379639758142.7.931.8............................ 3.0, Naked Pair: Cells r2c2,r2c4: 6,8 in row...............25..........851426379639758142.7.931.8............................ 7.1, Forcing Chain: r1c5.8 off...............25..........851426379639758142.7.931.8............................ 2.5, 8: Cells r1c7,r1c9 on value(s) 7,9...............25..........851426379639758142.7.931.8............................ 2.5, 9: Cells r3c7,r3c8 on value(s) 8...............25..........851426379639758142.7.931.8............................ 2.6, Pointing: Cells r3c7,r3c8: 9 in block and row...............25..........851426379639758142.7.931.8............................ 7.0, Forcing Chain: r3c9.1 off...............25..........851426379639758142.7.931.8............................ 7.1, Forcing Chain: r3c9.6 off...............25..........851426379639758142.7.931.86........................... 1.5, Hidden Single: r6c9: 6 in column...............25..........851426379639758142.7.931586........................... 1.0, Hidden Single: r6c7: 5 in block...............25..........851426379639758142.7.931586........................... 2.4, Cell r3c9 on value(s) 3,4...............25..........851426379639758142.7.931586........................... 2.4, Cell r7c7 on value(s) 8...............25..........851426379639758142.7.931586........................... 6.3, VWXYZ-Wing 1412: Cells r3c7,r7c7,r8c7,r9c7,r3c5 on value 8...............25..........851426379639758142.7.931586........................... 6.6, UVWXYZ-Wing 1516: Cells r2c5,r3c5,r7c5,r8c5,r9c5,r7c7 on value 9...............25..........851426379639758142.7.931586........................... 7.0, Forcing Chain: r7c5.9 off...............25..........851426379639758142.7.931586........................... 7.0, Forcing Chain: r8c8.9 off...............25..........851426379639758142.7.931586........................... 7.1, Forcing Chain: r3c2.8 off..........8....25..........851426379639758142.7.931586........................... 1.2, Hidden Single: r2c2: 8 in block..6.......8....25..........851426379639758142.7.931586........................... 1.2, Hidden Single: r1c3: 6 in block..6.......8....25...7......851426379639758142.7.931586........................... 1.2, Hidden Single: r3c3: 7 in block..6.......8....25.5.7......851426379639758142.7.931586........................... 1.2, Hidden Single: r3c1: 5 in block9.6.......8....25.5.7......851426379639758142.7.931586........................... 1.2, Hidden Single: r1c1: 9 in block9.6..5....8....25.5.7......851426379639758142.7.931586........................... 1.2, Hidden Single: r1c6: 5 in block9.6..5....8....25.5.7.8....851426379639758142.7.931586........................... 1.2, Hidden Single: r3c5: 8 in block9.6..5....8.6..25.5.7.8....851426379639758142.7.931586........................... 1.2, Hidden Single: r2c4: 6 in block9.6..5....8.6.925.5.7.8....851426379639758142.7.931586........................... 1.2, Hidden Single: r2c6: 9 in block9.6.75....8.6.925.5.7.8....851426379639758142.7.931586........................... 1.2, Hidden Single: r1c5: 7 in block9.6.75....8.6.925.5.7.8.6..851426379639758142.7.931586........................... 1.2, Hidden Single: r3c7: 6 in block9.6.75....8.6.92575.7.8.6..851426379639758142.7.931586........................... 1.2, Hidden Single: r2c9: 7 in block9.6.758...8.6.92575.7.8.6..851426379639758142.7.931586........................... 1.2, Hidden Single: r1c7: 8 in block9.6.758...8.6.92575.7.8.69.851426379639758142.7.931586........................... 1.2, Hidden Single: r3c8: 9 in block9.6.758...8.6.92575.7.8.69.85142637963975814247.931586........................... 1.5, Hidden Single: r6c1: 4 in column9.6.758...8.6.92575.7.8.69.851426379639758142472931586........................... 1.0, Hidden Single: r6c3: 2 in block9.6.758...8.6.92575.7.8.69.851426379639758142472931586........................... 2.4, Cell r9c8 on value(s) 29.6.758...8.6.92575.7.8.69.851426379639758142472931586..............2............ 1.5, Hidden Single: r8c6: 2 in row9.6.758...8.6.92575.7.8369.851426379639758142472931586..............2............ 1.5, Hidden Single: r3c6: 3 in column9.6.758...8.6492575.7.8369.851426379639758142472931586..............2............ 1.2, Hidden Single: r2c5: 4 in block946.758...8.6492575.7.8369.851426379639758142472931586..............2............ 1.2, Hidden Single: r1c2: 4 in block946.758...8.649257527.8369.851426379639758142472931586..............2............ 1.2, Hidden Single: r3c2: 2 in block946.758..18.649257527.8369.851426379639758142472931586..............2............ 1.2, Hidden Single: r2c1: 1 in block946.758..183649257527.8369.851426379639758142472931586..............2............ 1.0, Hidden Single: r2c3: 3 in block9462758..183649257527.8369.851426379639758142472931586..............2............ 1.2, Hidden Single: r1c4: 2 in block9462758..18364925752718369.851426379639758142472931586..............2............ 1.0, Hidden Single: r3c4: 1 in block9462758..183649257527183694851426379639758142472931586..............2............ 1.0, Hidden Single: r3c9: 4 in row9462758..183649257527183694851426379639758142472931586..............2.....4...... 1.2, Hidden Single: r9c3: 4 in block9462758..183649257527183694851426379639758142472931586..5...........2.....4...... 1.2, Hidden Single: r7c3: 5 in block9462758..183649257527183694851426379639758142472931586..5........8..2.....4...... 1.0, Hidden Single: r8c3: 8 in column9462758..183649257527183694851426379639758142472931586..53.......8..2.....4...... 1.2, Hidden Single: r7c4: 3 in block9462758..183649257527183694851426379639758142472931586..53.4.....8..2.....4...... 1.2, Hidden Single: r7c6: 4 in block9462758..183649257527183694851426379639758142472931586..53.4.....8..2.....4..7... 1.0, Hidden Single: r9c6: 7 in column9462758..183649257527183694851426379639758142472931586..53.4.....85.2.....4..7... 1.2, Hidden Single: r8c4: 5 in block9462758..183649257527183694851426379639758142472931586..53.4.....85.2.....48.7... 1.0, Hidden Single: r9c4: 8 in column9462758..183649257527183694851426379639758142472931586..5364.....85.2.....48.7... 1.2, Hidden Single: r7c5: 6 in block9462758..183649257527183694851426379639758142472931586..5364.....85.2.....4817... 1.2, Hidden Single: r9c5: 1 in block9462758..183649257527183694851426379639758142472931586..5364.....8592.....4817... 1.0, Hidden Single: r8c5: 9 in block9462758..183649257527183694851426379639758142472931586..5364.....85924....4817... 1.2, Hidden Single: r8c7: 4 in block9462758..183649257527183694851426379639758142472931586..5364.....85924....4817..5 1.2, Hidden Single: r9c9: 5 in block9462758..183649257527183694851426379639758142472931586..5364.....859246...4817..5 1.2, Hidden Single: r8c8: 6 in block9462758..183649257527183694851426379639758142472931586..5364.....859246..64817..5 1.2, Hidden Single: r9c2: 6 in block9462758..183649257527183694851426379639758142472931586.95364.....859246..64817..5 1.2, Hidden Single: r7c2: 9 in block9462758..183649257527183694851426379639758142472931586.95364....1859246..64817..5 1.0, Hidden Single: r8c2: 1 in column9462758..183649257527183694851426379639758142472931586.953647...1859246..64817..5 1.2, Hidden Single: r7c7: 7 in block9462758..183649257527183694851426379639758142472931586.953647...1859246..648179.5 1.0, Hidden Single: r9c7: 9 in column9462758..183649257527183694851426379639758142472931586.953647..71859246..648179.5 1.2, Hidden Single: r8c1: 7 in block9462758..183649257527183694851426379639758142472931586.953647..718592463.648179.5 1.0, Hidden Single: r8c9: 3 in row94627583.183649257527183694851426379639758142472931586.953647..718592463.648179.5 1.2, Hidden Single: r1c8: 3 in block946275831183649257527183694851426379639758142472931586.953647..718592463.648179.5 1.0, Hidden Single: r1c9: 1 in block946275831183649257527183694851426379639758142472931586.953647.8718592463.648179.5 1.0, Hidden Single: r7c9: 8 in column946275831183649257527183694851426379639758142472931586.953647.87185924633648179.5 1.2, Hidden Single: r9c1: 3 in block9462758311836492575271836948514263796397581424729315862953647.87185924633648179.5 1.0, Hidden Single: r7c1: 2 in block9462758311836492575271836948514263796397581424729315862953647187185924633648179.5 1.0, Hidden Single: r7c8: 1 in row946275831183649257527183694851426379639758142472931586295364718718592463364817925 1.0, Hidden Single: r9c8: 2 in block12.8/1.2/1.2`

Has 12.8 been hit in a solve path before? I think we're in level 5 for some of these based on how long they are taking - may run it again sometime printing level and complexity.
mith

Posts: 888
Joined: 14 July 2020

### Re: Minimal NC Thermo

Finally finished, the full solve is included above. Took about 10 days altogether. 360 total steps, of which 80 are 12+, and 2 are 12.8.
mith

Posts: 888
Joined: 14 July 2020

### Re: Minimal NC Thermo

I thought about minimal NC. There is one NC in the internet with only 6 clues(all are 3). People dont talk much about minimal/maximal clues although its very interesting. Someone must make a list for each known minimal/maximal variant
High Mind

Posts: 16
Joined: 04 December 2021

### Re: Minimal NC Thermo

mith wrote:Finally finished, the full solve is included above. Took about 10 days altogether. 360 total steps, of which 80 are 12+, and 2 are 12.8.

I interes about Minimal regular NC sudoku, can it be less than 6??
High Mind

Posts: 16
Joined: 04 December 2021