Analysis of xx-ph-00000464-141-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ....5.7.......9.3..8.2....6..81.4...6.4.....1.1..2.....6......85....39......7..5. initial

Autosolve

position: ....5.7.......9.3..8.2....6..81.4...6.4.....1.1..2.....6......85....39..8...7..5. 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: 0:00:29.387754

The following important HDP chains were detected:

* DIS # A3: 1,7 # H8: 4,7 => CTR => H8: 1,2,6
* PRF # A3: 1,7 + H8: 1,2,6 # G9: 3,4 => SOL
* STA # A3: 1,7 + H8: 1,2,6 + G9: 3,4
* CNT   2 HDP CHAINS /  31 HYP OPENED

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

Details

Positions

....5.7.......9.3..8.2....6..81.4...6.4.....1.1..2.....6......85....39......7..5. initial
....5.7.......9.3..8.2....6..81.4...6.4.....1.1..2.....6......85....39..8...7..5. autosolve
123456789456789132789231546278164395634597821915328674367945218542813967891672453 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
F3: 1,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F7,F9: 2.. / F7 = 2  =>  2 pairs (_) / F9 = 2  =>  3 pairs (_)
D1,E3: 3.. / D1 = 3  =>  2 pairs (_) / E3 = 3  =>  3 pairs (_)
D7,F7: 5.. / D7 = 5  =>  2 pairs (_) / F7 = 5  =>  5 pairs (_)
C3,G3: 5.. / C3 = 5  =>  2 pairs (_) / G3 = 5  =>  2 pairs (_)
C1,C2: 6.. / C1 = 6  =>  2 pairs (_) / C2 = 6  =>  1 pairs (_)
H8,G9: 6.. / H8 = 6  =>  2 pairs (_) / G9 = 6  =>  5 pairs (_)
D2,F3: 7.. / D2 = 7  => 10 pairs (_) / F3 = 7  =>  1 pairs (_)
H1,G2: 8.. / H1 = 8  =>  3 pairs (_) / G2 = 8  =>  1 pairs (_)
D8,E8: 8.. / D8 = 8  =>  1 pairs (_) / E8 = 8  =>  3 pairs (_)
* DURATION: 0:00:05.343129  START: 21:43:17.507939  END: 21:43:22.851068 2020-10-25
* CP COUNT: (9)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:29.208297  START: 21:43:24.966084  END: 21:43:54.174381 2020-10-25
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00000464-141-base-pr-002.dot
* REASONING
* DIS # A3: 1,7 # H8: 4,7 => CTR => H8: 1,2,6
* PRF # A3: 1,7 + H8: 1,2,6 # G9: 3,4 => SOL
* STA # A3: 1,7 + H8: 1,2,6 + G9: 3,4
* CNT   2 HDP CHAINS /  31 HYP OPENED

Header Info

464;141;elev;22;11.40;1.20;1.20

Solution

position: 123456789456789132789231546278164395634597821915328674367945218542813967891672453 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 # A3: 1,7 => UNS
* INC # C3: 1,7 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 1,7 => UNS
* INC # C3: 1,7 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 1,7 => UNS
* INC # C3: 1,7 => UNS
* INC # A3: 1,7 # A2: 1,7 => UNS
* INC # A3: 1,7 # C2: 1,7 => UNS
* INC # A3: 1,7 # A7: 1,7 => UNS
* INC # A3: 1,7 # A7: 2,3,4,9 => UNS
* INC # A3: 1,7 # D1: 3,4 => UNS
* INC # A3: 1,7 # D1: 6,8 => UNS
* INC # A3: 1,7 # F1: 1,8 => UNS
* INC # A3: 1,7 # F1: 6 => UNS
* INC # A3: 1,7 # E2: 1,8 => UNS
* INC # A3: 1,7 # E2: 4,6 => UNS
* INC # A3: 1,7 # I2: 4,5 => UNS
* INC # A3: 1,7 # I2: 2 => UNS
* INC # A3: 1,7 # G6: 4,5 => UNS
* INC # A3: 1,7 # G6: 3,6,8 => UNS
* INC # A3: 1,7 # I1: 4,9 => UNS
* INC # A3: 1,7 # I1: 2 => UNS
* INC # A3: 1,7 # H6: 4,9 => UNS
* INC # A3: 1,7 # H6: 6,7,8 => UNS
* INC # A3: 1,7 # H7: 4,7 => UNS
* DIS # A3: 1,7 # H8: 4,7 => CTR => H8: 1,2,6
* INC # A3: 1,7 + H8: 1,2,6 # H7: 4,7 => UNS
* INC # A3: 1,7 + H8: 1,2,6 # H7: 1,2 => UNS
* INC # A3: 1,7 + H8: 1,2,6 # B8: 4,7 => UNS
* INC # A3: 1,7 + H8: 1,2,6 # B8: 2 => UNS
* INC # A3: 1,7 + H8: 1,2,6 # I6: 4,7 => UNS
* INC # A3: 1,7 + H8: 1,2,6 # I6: 3,5,9 => UNS
* INC # A3: 1,7 + H8: 1,2,6 # G7: 3,4 => UNS
* PRF # A3: 1,7 + H8: 1,2,6 # G9: 3,4 => SOL
* STA # A3: 1,7 + H8: 1,2,6 + G9: 3,4
* CNT  30 HDP CHAINS /  31 HYP OPENED