Analysis of xx-ph-02488080-2019_08_05_a-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7..6..7..5..9....5.6....8......4..5.3..8....9.....637..2......86..3......3...1 initial

Autosolve

position: 98.7..6..7..5..9....5.6....8......4..5.3..8....9.....637..2......86..3......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: 0:00:31.377107

The following important HDP chains were detected:

* PRF # E2: 1,4 # F4: 7,9 => SOL
* STA # E2: 1,4 + F4: 7,9
* CNT   1 HDP CHAINS /  57 HYP OPENED

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

Details

Positions

98.7..6..7..5..9....5.6....8......4..5.3..8....9.....637..2......86..3......3...1 initial
98.7..6..7..5..9....5.6....8......4..5.3..8....9.....637..2......86..3......3...1 autosolve
983742615726518934415963278867259143154376892239184756371825469548691327692437581 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
E1: 1,4
G7: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I4,H6: 3.. / I4 = 3  =>  2 pairs (_) / H6 = 3  =>  2 pairs (_)
B6,H6: 3.. / B6 = 3  =>  2 pairs (_) / H6 = 3  =>  2 pairs (_)
H1,I1: 5.. / H1 = 5  =>  2 pairs (_) / I1 = 5  =>  2 pairs (_)
A8,A9: 5.. / A8 = 5  =>  2 pairs (_) / A9 = 5  =>  2 pairs (_)
B2,C2: 6.. / B2 = 6  =>  2 pairs (_) / C2 = 6  =>  4 pairs (_)
F4,F5: 6.. / F4 = 6  =>  2 pairs (_) / F5 = 6  =>  4 pairs (_)
H7,H9: 6.. / H7 = 6  =>  3 pairs (_) / H9 = 6  =>  3 pairs (_)
C7,H7: 6.. / C7 = 6  =>  3 pairs (_) / H7 = 6  =>  3 pairs (_)
A5,A9: 6.. / A5 = 6  =>  2 pairs (_) / A9 = 6  =>  4 pairs (_)
C4,C5: 7.. / C4 = 7  =>  2 pairs (_) / C5 = 7  =>  3 pairs (_)
E2,E6: 8.. / E2 = 8  =>  2 pairs (_) / E6 = 8  =>  5 pairs (_)
D3,F3: 9.. / D3 = 9  =>  4 pairs (_) / F3 = 9  =>  2 pairs (_)
B8,B9: 9.. / B8 = 9  =>  4 pairs (_) / B9 = 9  =>  3 pairs (_)
* DURATION: 0:00:07.697774  START: 19:35:20.576042  END: 19:35:28.273816 2020-10-14
* CP COUNT: (13)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:31.102334  START: 19:35:39.320395  END: 19:36:10.422729 2020-10-14
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-02488080-2019_08_05_a-base-pr-002.dot
* REASONING
* PRF # E2: 1,4 # F4: 7,9 => SOL
* STA # E2: 1,4 + F4: 7,9
* CNT   1 HDP CHAINS /  57 HYP OPENED

Header Info

2488080;2019_08_05_a;PAQ;24;11.50;11.50;8.30

Solution

position: 983742615726518934415963278867259143154376892239184756371825469548691327692437581 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 # F1: 1,4 => UNS
* INC # E2: 1,4 => UNS
* INC # F2: 1,4 => UNS
* INC # D3: 1,4 => UNS
* INC # F3: 1,4 => UNS
* INC # C1: 1,4 => UNS
* INC # C1: 2,3 => UNS
* INC # E5: 1,4 => UNS
* INC # E6: 1,4 => UNS
* INC # E8: 1,4 => UNS
* INC # I7: 4,5 => UNS
* INC # I8: 4,5 => UNS
* INC # G9: 4,5 => UNS
* INC # F7: 4,5 => UNS
* INC # F7: 1,8,9 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 1,4 => UNS
* INC # E2: 1,4 => UNS
* INC # F2: 1,4 => UNS
* INC # D3: 1,4 => UNS
* INC # F3: 1,4 => UNS
* INC # C1: 1,4 => UNS
* INC # C1: 2,3 => UNS
* INC # E5: 1,4 => UNS
* INC # E6: 1,4 => UNS
* INC # E8: 1,4 => UNS
* INC # I7: 4,5 => UNS
* INC # I8: 4,5 => UNS
* INC # G9: 4,5 => UNS
* INC # F7: 4,5 => UNS
* INC # F7: 1,8,9 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 1,4 => UNS
* INC # E2: 1,4 => UNS
* INC # F2: 1,4 => UNS
* INC # D3: 1,4 => UNS
* INC # F3: 1,4 => UNS
* INC # C1: 1,4 => UNS
* INC # C1: 2,3 => UNS
* INC # E5: 1,4 => UNS
* INC # E6: 1,4 => UNS
* INC # E8: 1,4 => UNS
* INC # I7: 4,5 => UNS
* INC # I8: 4,5 => UNS
* INC # G9: 4,5 => UNS
* INC # F7: 4,5 => UNS
* INC # F7: 1,8,9 => UNS
* INC # F1: 1,4 # B2: 2,3 => UNS
* INC # F1: 1,4 # C2: 2,3 => UNS
* INC # F1: 1,4 # B3: 2,3 => UNS
* INC # F1: 1,4 # H1: 2,3 => UNS
* INC # F1: 1,4 # I1: 2,3 => UNS
* INC # F1: 1,4 # C4: 2,3 => UNS
* INC # F1: 1,4 # C4: 1,6,7 => UNS
* INC # F1: 1,4 # E5: 1,4 => UNS
* INC # F1: 1,4 # E6: 1,4 => UNS
* INC # F1: 1,4 # E8: 1,4 => UNS
* INC # F1: 1,4 # F5: 1,4 => UNS
* INC # F1: 1,4 # F6: 1,4 => UNS
* INC # F1: 1,4 # F7: 1,4 => UNS
* INC # F1: 1,4 # F8: 1,4 => UNS
* INC # F1: 1,4 # F3: 2,3 => UNS
* INC # F1: 1,4 # F3: 9 => UNS
* INC # F1: 1,4 # B2: 2,3 => UNS
* INC # F1: 1,4 # C2: 2,3 => UNS
* INC # F1: 1,4 # H2: 2,3 => UNS
* INC # F1: 1,4 # I2: 2,3 => UNS
* INC # F1: 1,4 # F3: 2,9 => UNS
* INC # F1: 1,4 # F3: 3 => UNS
* INC # F1: 1,4 # D4: 2,9 => UNS
* INC # F1: 1,4 # D4: 1 => UNS
* INC # F1: 1,4 # I7: 4,5 => UNS
* INC # F1: 1,4 # I8: 4,5 => UNS
* INC # F1: 1,4 # G9: 4,5 => UNS
* INC # F1: 1,4 # F7: 4,5 => UNS
* INC # F1: 1,4 # F7: 1,8,9 => UNS
* INC # F1: 1,4 => UNS
* INC # E2: 1,4 # C1: 1,4 => UNS
* INC # E2: 1,4 # C1: 2,3 => UNS
* INC # E2: 1,4 # F2: 2,3 => UNS
* INC # E2: 1,4 # F3: 2,3 => UNS
* INC # E2: 1,4 # C1: 2,3 => UNS
* INC # E2: 1,4 # H1: 2,3 => UNS
* INC # E2: 1,4 # I1: 2,3 => UNS
* INC # E2: 1,4 # B2: 1,4 => UNS
* INC # E2: 1,4 # C2: 1,4 => UNS
* INC # E2: 1,4 # E4: 7,9 => UNS
* PRF # E2: 1,4 # F4: 7,9 => SOL
* STA # E2: 1,4 + F4: 7,9
* CNT  56 HDP CHAINS /  57 HYP OPENED