Analysis of xx-ph-00254514-12_12_03-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ........1..2..3.4..5.16......3..2.7..2.5..8..6...8......9.....3.4...9..72...4..9. initial

Autosolve

position: ........1..2..3.4..5.16......3..2.7..2.5..8..6...8......9...4.3.4...9..72...4..9. 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: 0:00:39.237473

The following important HDP chains were detected:

* DIS # E5: 1,9 # I3: 2,8 => CTR => I3: 9
* DIS # E5: 1,9 + I3: 9 # I4: 5 => CTR => I4: 4,6
* DIS # E5: 1,9 + I3: 9 + I4: 4,6 # A4: 1,9 => CTR => A4: 5,8
* DIS # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 # B4: 1,9 => CTR => B4: 8
* DIS # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 # F5: 4,7 => CTR => F5: 6
* PRF # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 + F5: 6 # C1: 7,8 => SOL
* STA # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 + F5: 6 + C1: 7,8
* CNT   6 HDP CHAINS /  31 HYP OPENED

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

Details

Positions

........1..2..3.4..5.16......3..2.7..2.5..8..6...8......9.....3.4...9..72...4..9. initial
........1..2..3.4..5.16......3..2.7..2.5..8..6...8......9...4.3.4...9..72...4..9. autosolve
467925381912873645358164729583412976721596834694387152179258463845639217236741598 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
E4: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,B2: 1.. / A2 = 1  =>  1 pairs (_) / B2 = 1  =>  3 pairs (_)
D1,E1: 2.. / D1 = 2  =>  2 pairs (_) / E1 = 2  =>  1 pairs (_)
I3,I6: 2.. / I3 = 2  =>  2 pairs (_) / I6 = 2  =>  2 pairs (_)
E5,D6: 3.. / E5 = 3  =>  2 pairs (_) / D6 = 3  =>  2 pairs (_)
A8,B9: 3.. / A8 = 3  =>  2 pairs (_) / B9 = 3  =>  1 pairs (_)
E5,H5: 3.. / E5 = 3  =>  2 pairs (_) / H5 = 3  =>  2 pairs (_)
B9,D9: 3.. / B9 = 3  =>  1 pairs (_) / D9 = 3  =>  2 pairs (_)
B1,B9: 3.. / B1 = 3  =>  2 pairs (_) / B9 = 3  =>  1 pairs (_)
E5,E8: 3.. / E5 = 3  =>  2 pairs (_) / E8 = 3  =>  2 pairs (_)
A4,C6: 5.. / A4 = 5  =>  1 pairs (_) / C6 = 5  =>  1 pairs (_)
D4,F5: 6.. / D4 = 6  =>  1 pairs (_) / F5 = 6  =>  4 pairs (_)
A4,B4: 8.. / A4 = 8  =>  5 pairs (_) / B4 = 8  =>  1 pairs (_)
* DURATION: 0:00:08.144366  START: 02:15:34.912601  END: 02:15:43.056967 2020-10-28
* CP COUNT: (12)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:39.013379  START: 02:15:47.733017  END: 02:16:26.746396 2020-10-28
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00254514-12_12_03-base-pr-002.dot
* REASONING
* DIS # E5: 1,9 # I3: 2,8 => CTR => I3: 9
* DIS # E5: 1,9 + I3: 9 # I4: 5 => CTR => I4: 4,6
* DIS # E5: 1,9 + I3: 9 + I4: 4,6 # A4: 1,9 => CTR => A4: 5,8
* DIS # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 # B4: 1,9 => CTR => B4: 8
* DIS # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 # F5: 4,7 => CTR => F5: 6
* PRF # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 + F5: 6 # C1: 7,8 => SOL
* STA # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 + F5: 6 + C1: 7,8
* CNT   6 HDP CHAINS /  31 HYP OPENED

Header Info

254514;12_12_03;dob;23;11.40;1.20;1.20

Solution

position: 467925381912873645358164729583412976721596834694387152179258463845639217236741598 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 # E5: 1,9 => UNS
* INC # E5: 3,7 => UNS
* INC # A4: 1,9 => UNS
* INC # B4: 1,9 => UNS
* INC # G4: 1,9 => UNS
* CNT   5 HDP CHAINS /   5 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E5: 1,9 => UNS
* INC # E5: 3,7 => UNS
* INC # A4: 1,9 => UNS
* INC # B4: 1,9 => UNS
* INC # G4: 1,9 => UNS
* CNT   5 HDP CHAINS /   5 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E5: 1,9 => UNS
* INC # E5: 3,7 => UNS
* INC # A4: 1,9 => UNS
* INC # B4: 1,9 => UNS
* INC # G4: 1,9 => UNS
* INC # E5: 1,9 # E1: 5,7 => UNS
* INC # E5: 1,9 # E1: 2 => UNS
* INC # E5: 1,9 # G2: 5,7 => UNS
* INC # E5: 1,9 # G2: 6,9 => UNS
* INC # E5: 1,9 # E7: 5,7 => UNS
* INC # E5: 1,9 # E7: 2 => UNS
* INC # E5: 1,9 # D1: 4,8 => UNS
* INC # E5: 1,9 # F1: 4,8 => UNS
* INC # E5: 1,9 # A3: 4,8 => UNS
* INC # E5: 1,9 # C3: 4,8 => UNS
* DIS # E5: 1,9 # I3: 2,8 => CTR => I3: 9
* INC # E5: 1,9 + I3: 9 # H7: 2,8 => UNS
* INC # E5: 1,9 + I3: 9 # H8: 2,8 => UNS
* INC # E5: 1,9 + I3: 9 # F5: 4,6 => UNS
* INC # E5: 1,9 + I3: 9 # F5: 7 => UNS
* INC # E5: 1,9 + I3: 9 # I4: 4,6 => UNS
* DIS # E5: 1,9 + I3: 9 # I4: 5 => CTR => I4: 4,6
* INC # E5: 1,9 + I3: 9 + I4: 4,6 # F5: 4,6 => UNS
* INC # E5: 1,9 + I3: 9 + I4: 4,6 # F5: 7 => UNS
* DIS # E5: 1,9 + I3: 9 + I4: 4,6 # A4: 1,9 => CTR => A4: 5,8
* DIS # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 # B4: 1,9 => CTR => B4: 8
* INC # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 # A5: 1,9 => UNS
* INC # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 # A5: 4,7 => UNS
* DIS # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 # F5: 4,7 => CTR => F5: 6
* PRF # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 + F5: 6 # C1: 7,8 => SOL
* STA # E5: 1,9 + I3: 9 + I4: 4,6 + A4: 5,8 + B4: 8 + F5: 6 + C1: 7,8
* CNT  30 HDP CHAINS /  31 HYP OPENED