Analysis of xx-ph-00000805-669-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...4...8..5...91......3...62...6...4..5..1......8...3..91....7.5....79...7......8 initial

Autosolve

position: ...4...8..5...91......3...62...6...4..5..1......8...3..91....7.5....79...7......8 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: 0:00:36.046287

The following important HDP chains were detected:

* DIS # H3: 2,4 # A2: 3,7 => CTR => A2: 4,6,8
* DIS # H3: 2,4 + A2: 4,6,8 # C2: 3,7 => CTR => C2: 2,4,6,8
* DIS # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 # C3: 2,4 => CTR => C3: 7,8,9
* PRF # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 + C3: 7,8,9 # B3: 1,8 => SOL
* STA # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 + C3: 7,8,9 + B3: 1,8
* CNT   4 HDP CHAINS /  42 HYP OPENED

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

Details

Positions

...4...8..5...91......3...62...6...4..5..1......8...3..91....7.5....79...7......8 initial
...4...8..5...91......3...62...6...4..5..1......8...3..91....7.5....79...7......8 autosolve
123456789456789123789132546217963854835241697964875231391628475548317962672594318 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
H2: 2,4
F4: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,D3: 1.. / E1 = 1  =>  2 pairs (_) / D3 = 1  =>  2 pairs (_)
H4,I6: 1.. / H4 = 1  =>  5 pairs (_) / I6 = 1  =>  5 pairs (_)
B4,H4: 1.. / B4 = 1  =>  5 pairs (_) / H4 = 1  =>  5 pairs (_)
I6,I8: 1.. / I6 = 1  =>  5 pairs (_) / I8 = 1  =>  5 pairs (_)
F1,D2: 6.. / F1 = 6  =>  3 pairs (_) / D2 = 6  =>  3 pairs (_)
E2,F3: 8.. / E2 = 8  =>  3 pairs (_) / F3 = 8  =>  3 pairs (_)
G4,G5: 8.. / G4 = 8  =>  3 pairs (_) / G5 = 8  =>  3 pairs (_)
F3,F7: 8.. / F3 = 8  =>  3 pairs (_) / F7 = 8  =>  3 pairs (_)
I1,H3: 9.. / I1 = 9  =>  3 pairs (_) / H3 = 9  =>  4 pairs (_)
D9,E9: 9.. / D9 = 9  =>  2 pairs (_) / E9 = 9  =>  2 pairs (_)
* DURATION: 0:00:07.251446  START: 08:07:15.877862  END: 08:07:23.129308 2020-11-22
* CP COUNT: (10)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:35.799809  START: 08:07:32.212634  END: 08:08:08.012443 2020-11-22
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00000805-669-base-pr-002.dot
* REASONING
* DIS # H3: 2,4 # A2: 3,7 => CTR => A2: 4,6,8
* DIS # H3: 2,4 + A2: 4,6,8 # C2: 3,7 => CTR => C2: 2,4,6,8
* DIS # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 # C3: 2,4 => CTR => C3: 7,8,9
* PRF # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 + C3: 7,8,9 # B3: 1,8 => SOL
* STA # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 + C3: 7,8,9 + B3: 1,8
* CNT   4 HDP CHAINS /  42 HYP OPENED

Header Info

805;669;elev;22;11.30;11.30;9.90

Solution

position: 123456789456789123789132546217963854835241697964875231391628475548317962672594318 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 # G3: 2,4 => UNS
* INC # H3: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # C2: 3,6,7,8 => UNS
* INC # H8: 2,4 => UNS
* INC # H9: 2,4 => UNS
* INC # D4: 3,5 => UNS
* INC # D4: 7,9 => UNS
* INC # F7: 3,5 => UNS
* INC # F9: 3,5 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 2,4 => UNS
* INC # H3: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # C2: 3,6,7,8 => UNS
* INC # H8: 2,4 => UNS
* INC # H9: 2,4 => UNS
* INC # D4: 3,5 => UNS
* INC # D4: 7,9 => UNS
* INC # F7: 3,5 => UNS
* INC # F9: 3,5 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 2,4 => UNS
* INC # H3: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # C2: 3,6,7,8 => UNS
* INC # H8: 2,4 => UNS
* INC # H9: 2,4 => UNS
* INC # D4: 3,5 => UNS
* INC # D4: 7,9 => UNS
* INC # F7: 3,5 => UNS
* INC # F9: 3,5 => UNS
* INC # G3: 2,4 # C2: 2,4 => UNS
* INC # G3: 2,4 # C2: 3,6,7,8 => UNS
* INC # G3: 2,4 # H8: 2,4 => UNS
* INC # G3: 2,4 # H9: 2,4 => UNS
* INC # G3: 2,4 # G1: 3,7 => UNS
* INC # G3: 2,4 # I1: 3,7 => UNS
* INC # G3: 2,4 # A2: 3,7 => UNS
* INC # G3: 2,4 # C2: 3,7 => UNS
* INC # G3: 2,4 # B3: 2,4 => UNS
* INC # G3: 2,4 # C3: 2,4 => UNS
* INC # G3: 2,4 # G7: 2,4 => UNS
* INC # G3: 2,4 # G9: 2,4 => UNS
* INC # G3: 2,4 # I1: 5,9 => UNS
* INC # G3: 2,4 # I1: 3,7 => UNS
* INC # G3: 2,4 # H4: 5,9 => UNS
* INC # G3: 2,4 # H4: 1 => UNS
* INC # G3: 2,4 # D4: 3,5 => UNS
* INC # G3: 2,4 # D4: 7,9 => UNS
* INC # G3: 2,4 # F7: 3,5 => UNS
* INC # G3: 2,4 # F9: 3,5 => UNS
* INC # G3: 2,4 => UNS
* INC # H3: 2,4 # C2: 2,4 => UNS
* INC # H3: 2,4 # C2: 3,6,7,8 => UNS
* INC # H3: 2,4 # G1: 3,7 => UNS
* INC # H3: 2,4 # G1: 5 => UNS
* DIS # H3: 2,4 # A2: 3,7 => CTR => A2: 4,6,8
* DIS # H3: 2,4 + A2: 4,6,8 # C2: 3,7 => CTR => C2: 2,4,6,8
* INC # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 # B3: 2,4 => UNS
* DIS # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 # C3: 2,4 => CTR => C3: 7,8,9
* INC # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 + C3: 7,8,9 # B3: 2,4 => UNS
* PRF # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 + C3: 7,8,9 # B3: 1,8 => SOL
* STA # H3: 2,4 + A2: 4,6,8 + C2: 2,4,6,8 + C3: 7,8,9 + B3: 1,8
* CNT  41 HDP CHAINS /  42 HYP OPENED