Analysis of xx-ph-00067507-12_11-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.76....5..4..3....4..5.8.6....4.5..4......2....7.1...5...6.9...6...2.3...1..... initial

Autosolve

position: 98.76....5..4..3....4..5.8.6....4.5..4......2....7.1...5...6.9...6...2.3...1..... 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: 0:00:33.636067

The following important HDP chains were detected:

* DIS # I1: 1 # B3: 2,3 => CTR => B3: 1,6,7
* DIS # I1: 1 + B3: 1,6,7 # C6: 2,3 => CTR => C6: 5,8,9
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 # C7: 2,3 => CTR => C7: 1,7,8
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 # C4: 1,7 => CTR => C4: 2,3,8,9
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 # C5: 1,7 => CTR => C5: 3,5,8,9
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 # C7: 8 => CTR => C7: 1,7
* PRF # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 + C7: 1,7 # E3: 2,3 => SOL
* STA # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 + C7: 1,7 + E3: 2,3
* CNT   7 HDP CHAINS /  33 HYP OPENED

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

Details

Positions

98.76....5..4..3....4..5.8.6....4.5..4......2....7.1...5...6.9...6...2.3...1..... initial
98.76....5..4..3....4..5.8.6....4.5..4......2....7.1...5...6.9...6...2.3...1..... autosolve
982763541567481329314925786673214958149538672825679134251346897496857213738192465 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
G1: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I7,H8: 1.. / I7 = 1  =>  5 pairs (_) / H8 = 1  =>  3 pairs (_)
H1,H2: 2.. / H1 = 2  =>  4 pairs (_) / H2 = 2  =>  5 pairs (_)
H5,H6: 3.. / H5 = 3  =>  2 pairs (_) / H6 = 3  =>  5 pairs (_)
C1,F1: 3.. / C1 = 3  =>  2 pairs (_) / F1 = 3  =>  3 pairs (_)
H6,I6: 4.. / H6 = 4  =>  5 pairs (_) / I6 = 4  =>  3 pairs (_)
G1,I1: 5.. / G1 = 5  =>  3 pairs (_) / I1 = 5  =>  2 pairs (_)
C5,C6: 5.. / C5 = 5  =>  4 pairs (_) / C6 = 5  =>  1 pairs (_)
D8,E8: 5.. / D8 = 5  =>  1 pairs (_) / E8 = 5  =>  4 pairs (_)
G9,I9: 5.. / G9 = 5  =>  2 pairs (_) / I9 = 5  =>  3 pairs (_)
C6,D6: 5.. / C6 = 5  =>  1 pairs (_) / D6 = 5  =>  4 pairs (_)
E5,E8: 5.. / E5 = 5  =>  1 pairs (_) / E8 = 5  =>  4 pairs (_)
G1,G9: 5.. / G1 = 5  =>  3 pairs (_) / G9 = 5  =>  2 pairs (_)
I1,I9: 5.. / I1 = 5  =>  2 pairs (_) / I9 = 5  =>  3 pairs (_)
B2,B3: 6.. / B2 = 6  =>  1 pairs (_) / B3 = 6  =>  2 pairs (_)
D5,D6: 6.. / D5 = 6  =>  3 pairs (_) / D6 = 6  =>  2 pairs (_)
F8,F9: 7.. / F8 = 7  =>  3 pairs (_) / F9 = 7  =>  3 pairs (_)
E2,F2: 8.. / E2 = 8  =>  1 pairs (_) / F2 = 8  =>  2 pairs (_)
* DURATION: 0:00:11.076126  START: 13:48:19.595413  END: 13:48:30.671539 2020-12-22
* CP COUNT: (17)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:33.467015  START: 13:48:34.031527  END: 13:49:07.498542 2020-12-22
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00067507-12_11-base-pr-002.dot
* REASONING
* DIS # I1: 1 # B3: 2,3 => CTR => B3: 1,6,7
* DIS # I1: 1 + B3: 1,6,7 # C6: 2,3 => CTR => C6: 5,8,9
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 # C7: 2,3 => CTR => C7: 1,7,8
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 # C4: 1,7 => CTR => C4: 2,3,8,9
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 # C5: 1,7 => CTR => C5: 3,5,8,9
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 # C7: 8 => CTR => C7: 1,7
* PRF # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 + C7: 1,7 # E3: 2,3 => SOL
* STA # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 + C7: 1,7 + E3: 2,3
* CNT   7 HDP CHAINS /  33 HYP OPENED

Header Info

67507;12_11;GP;24;11.30;11.30;2.60

Solution

position: 982763541567481329314925786673214958149538672825679134251346897496857213738192465 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 # I1: 4,5 => UNS
* INC # I1: 1 => UNS
* INC # G9: 4,5 => UNS
* INC # G9: 6,7,8 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 4,5 => UNS
* INC # I1: 1 => UNS
* INC # G9: 4,5 => UNS
* INC # G9: 6,7,8 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 4,5 => UNS
* INC # I1: 1 => UNS
* INC # G9: 4,5 => UNS
* INC # G9: 6,7,8 => UNS
* INC # I1: 4,5 # G9: 4,5 => UNS
* INC # I1: 4,5 # G9: 6,7,8 => UNS
* INC # I1: 4,5 # H2: 1,2 => UNS
* INC # I1: 4,5 # H2: 6,7 => UNS
* INC # I1: 4,5 # C1: 1,2 => UNS
* INC # I1: 4,5 # F1: 1,2 => UNS
* INC # I1: 4,5 # I9: 4,5 => UNS
* INC # I1: 4,5 # I9: 6,7,8 => UNS
* INC # I1: 4,5 => UNS
* INC # I1: 1 # A3: 2,3 => UNS
* DIS # I1: 1 # B3: 2,3 => CTR => B3: 1,6,7
* INC # I1: 1 + B3: 1,6,7 # C4: 2,3 => UNS
* DIS # I1: 1 + B3: 1,6,7 # C6: 2,3 => CTR => C6: 5,8,9
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 # C7: 2,3 => CTR => C7: 1,7,8
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 # C9: 2,3 => UNS
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 # C4: 2,3 => UNS
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 # C9: 2,3 => UNS
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 # B2: 1,7 => UNS
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 # B3: 1,7 => UNS
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 # C4: 1,7 => CTR => C4: 2,3,8,9
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 # C5: 1,7 => CTR => C5: 3,5,8,9
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 # C7: 1,7 => UNS
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 # C7: 1,7 => UNS
* DIS # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 # C7: 8 => CTR => C7: 1,7
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 + C7: 1,7 # B2: 1,7 => UNS
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 + C7: 1,7 # B3: 1,7 => UNS
* INC # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 + C7: 1,7 # D3: 2,3 => UNS
* PRF # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 + C7: 1,7 # E3: 2,3 => SOL
* STA # I1: 1 + B3: 1,6,7 + C6: 5,8,9 + C7: 1,7,8 + C4: 2,3,8,9 + C5: 3,5,8,9 + C7: 1,7 + E3: 2,3
* CNT  32 HDP CHAINS /  33 HYP OPENED