Analysis of xx-HardestSudokusThread-00206-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...2....871......9..6.9.5....8.6...5.....23...4....6....9.3..5.4....1........7... initial

Autosolve

position: ...2....871......9..6.9.5....8.6...5.....23...4....6....9.3..5.4....1........7... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

See Appendix: Full HDP Chains for full list of HDP chains.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:01:04.077356

The following important HDP chains were detected:

* DIS # H1: 1,7 # E5: 1,7 => CTR => E5: 4,5,8
* DIS # H1: 1,7 + E5: 4,5,8 # E5: 5,8 => CTR => E5: 4
* DIS # H1: 1,7 + E5: 4,5,8 + E5: 4 # A1: 3,5 => CTR => A1: 9
* PRF # H1: 1,7 + E5: 4,5,8 + E5: 4 + A1: 9 => SOL
* STA H1: 1,7
* CNT   4 HDP CHAINS /  66 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

...2....871......9..6.9.5....8.6...5.....23...4....6....9.3..5.4....1........7... initial
...2....871......9..6.9.5....8.6...5.....23...4....6....9.3..5.4....1........7... autosolve
935216478714385269826794513278163945691542387543879621169438752457921836382657194 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
E1: 1,7
D3: 1,7
F3: 3,4
G2: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,D3: 1.. / E1 = 1  =>  3 pairs (_) / D3 = 1  =>  3 pairs (_)
E8,E9: 2.. / E8 = 2  =>  4 pairs (_) / E9 = 2  =>  5 pairs (_)
C1,C2: 4.. / C1 = 4  =>  6 pairs (_) / C2 = 4  => 11 pairs (_)
H1,H2: 6.. / H1 = 6  =>  5 pairs (_) / H2 = 6  =>  5 pairs (_)
A5,B5: 6.. / A5 = 6  =>  4 pairs (_) / B5 = 6  =>  4 pairs (_)
F1,H1: 6.. / F1 = 6  =>  5 pairs (_) / H1 = 6  =>  5 pairs (_)
E1,D3: 7.. / E1 = 7  =>  3 pairs (_) / D3 = 7  =>  3 pairs (_)
A3,B3: 8.. / A3 = 8  =>  5 pairs (_) / B3 = 8  =>  5 pairs (_)
H5,H6: 8.. / H5 = 8  =>  6 pairs (_) / H6 = 8  =>  4 pairs (_)
A1,B1: 9.. / A1 = 9  =>  5 pairs (_) / B1 = 9  =>  5 pairs (_)
F4,F6: 9.. / F4 = 9  =>  6 pairs (_) / F6 = 9  =>  8 pairs (_)
D8,D9: 9.. / D8 = 9  =>  4 pairs (_) / D9 = 9  =>  4 pairs (_)
* DURATION: 0:00:12.048611  START: 00:30:25.269093  END: 00:30:37.317704 2017-05-01
* CP COUNT: (12)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:01:03.667972  START: 00:31:07.187809  END: 00:32:10.855781 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH xx-HardestSudokusThread-00206-base-pr-002.dot
* REASONING
* DIS # H1: 1,7 # E5: 1,7 => CTR => E5: 4,5,8
* DIS # H1: 1,7 + E5: 4,5,8 # E5: 5,8 => CTR => E5: 4
* DIS # H1: 1,7 + E5: 4,5,8 + E5: 4 # A1: 3,5 => CTR => A1: 9
* PRF # H1: 1,7 + E5: 4,5,8 + E5: 4 + A1: 9 => SOL
* STA H1: 1,7
* CNT   4 HDP CHAINS /  66 HYP OPENED

Header Info

HardestSudokusThread-00206,coloin,92829,96694,,,,4956,1010

Solution

position: 935216478714385269826794513278163945691542387543879621169438752457921836382657194 solved
Solution

See section Deep Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # G1: 1,7 => UNS
* INC # H1: 1,7 => UNS
* INC # E5: 1,7 => UNS
* INC # E6: 1,7 => UNS
* INC # H3: 1,7 => UNS
* INC # I3: 1,7 => UNS
* INC # D4: 1,7 => UNS
* INC # D5: 1,7 => UNS
* INC # D6: 1,7 => UNS
* INC # F1: 3,4 => UNS
* INC # D2: 3,4 => UNS
* INC # F2: 3,4 => UNS
* INC # H3: 3,4 => UNS
* INC # I3: 3,4 => UNS
* INC # F4: 3,4 => UNS
* INC # F4: 9 => UNS
* INC # H2: 2,4 => UNS
* INC # H3: 2,4 => UNS
* INC # I3: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # C2: 3,5 => UNS
* INC # G4: 2,4 => UNS
* INC # G7: 2,4 => UNS
* INC # G9: 2,4 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 1,7 => UNS
* INC # H1: 1,7 => UNS
* INC # E5: 1,7 => UNS
* INC # E6: 1,7 => UNS
* INC # H3: 1,7 => UNS
* INC # I3: 1,7 => UNS
* INC # D4: 1,7 => UNS
* INC # D5: 1,7 => UNS
* INC # D6: 1,7 => UNS
* INC # F1: 3,4 => UNS
* INC # D2: 3,4 => UNS
* INC # F2: 3,4 => UNS
* INC # H3: 3,4 => UNS
* INC # I3: 3,4 => UNS
* INC # F4: 3,4 => UNS
* INC # F4: 9 => UNS
* INC # H2: 2,4 => UNS
* INC # H3: 2,4 => UNS
* INC # I3: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # C2: 3,5 => UNS
* INC # G4: 2,4 => UNS
* INC # G7: 2,4 => UNS
* INC # G9: 2,4 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 1,7 => UNS
* INC # H1: 1,7 => UNS
* INC # E5: 1,7 => UNS
* INC # E6: 1,7 => UNS
* INC # H3: 1,7 => UNS
* INC # I3: 1,7 => UNS
* INC # D4: 1,7 => UNS
* INC # D5: 1,7 => UNS
* INC # D6: 1,7 => UNS
* INC # F1: 3,4 => UNS
* INC # D2: 3,4 => UNS
* INC # F2: 3,4 => UNS
* INC # H3: 3,4 => UNS
* INC # I3: 3,4 => UNS
* INC # F4: 3,4 => UNS
* INC # F4: 9 => UNS
* INC # H2: 2,4 => UNS
* INC # H3: 2,4 => UNS
* INC # I3: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # C2: 3,5 => UNS
* INC # G4: 2,4 => UNS
* INC # G7: 2,4 => UNS
* INC # G9: 2,4 => UNS
* INC # G1: 1,7 # E5: 1,7 => UNS
* INC # G1: 1,7 # E6: 1,7 => UNS
* INC # G1: 1,7 # H3: 1,7 => UNS
* INC # G1: 1,7 # I3: 1,7 => UNS
* INC # G1: 1,7 # D4: 1,7 => UNS
* INC # G1: 1,7 # D5: 1,7 => UNS
* INC # G1: 1,7 # D6: 1,7 => UNS
* INC # G1: 1,7 # F1: 3,4 => UNS
* INC # G1: 1,7 # D2: 3,4 => UNS
* INC # G1: 1,7 # F2: 3,4 => UNS
* INC # G1: 1,7 # H3: 3,4 => UNS
* INC # G1: 1,7 # I3: 3,4 => UNS
* INC # G1: 1,7 # F4: 3,4 => UNS
* INC # G1: 1,7 # F4: 9 => UNS
* INC # G1: 1,7 # H3: 1,7 => UNS
* INC # G1: 1,7 # I3: 1,7 => UNS
* INC # G1: 1,7 # G4: 1,7 => UNS
* INC # G1: 1,7 # G7: 1,7 => UNS
* INC # G1: 1,7 # H2: 2,4 => UNS
* INC # G1: 1,7 # H3: 2,4 => UNS
* INC # G1: 1,7 # I3: 2,4 => UNS
* INC # G1: 1,7 # C2: 2,4 => UNS
* INC # G1: 1,7 # C2: 3,5 => UNS
* INC # G1: 1,7 # G4: 2,4 => UNS
* INC # G1: 1,7 # G7: 2,4 => UNS
* INC # G1: 1,7 # G9: 2,4 => UNS
* INC # G1: 1,7 => UNS
* INC # H1: 1,7 # A1: 3,5 => UNS
* INC # H1: 1,7 # B1: 3,5 => UNS
* INC # H1: 1,7 # C6: 3,5 => UNS
* INC # H1: 1,7 # C8: 3,5 => UNS
* INC # H1: 1,7 # C9: 3,5 => UNS
* INC # H1: 1,7 # A9: 2,8 => UNS
* INC # H1: 1,7 # A9: 1,3,5,6 => UNS
* INC # H1: 1,7 # B8: 2,8 => UNS
* INC # H1: 1,7 # B9: 2,8 => UNS
* DIS # H1: 1,7 # E5: 1,7 => CTR => E5: 4,5,8
* INC # H1: 1,7 + E5: 4,5,8 # D2: 5,8 => UNS
* INC # H1: 1,7 + E5: 4,5,8 # D2: 3 => UNS
* DIS # H1: 1,7 + E5: 4,5,8 # E5: 5,8 => CTR => E5: 4
* DIS # H1: 1,7 + E5: 4,5,8 + E5: 4 # A1: 3,5 => CTR => A1: 9
* PRF # H1: 1,7 + E5: 4,5,8 + E5: 4 + A1: 9 => SOL
* STA H1: 1,7
* CNT  66 HDP CHAINS /  66 HYP OPENED