Analysis of xx-ph-00067391-12_11-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.76....5.....4....3..5.7.2..........83...6......81.4.9...32....5.8..3....5....1 initial

Autosolve

position: 98.76....5...3.4....3..5.7.2..........83...6......81.4.9...32....5.8..3....5....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: 0:00:43.275565

The following important HDP chains were detected:

* DIS # I1: 2 # D3: 1,4 => CTR => D3: 2,8,9
* DIS # I1: 2 + D3: 2,8,9 # F5: 1,4 => CTR => F5: 2,7,9
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 # F8: 2,9 => CTR => F8: 1,4,6,7
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 # F9: 2,9 => CTR => F9: 4,6,7
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 # F5: 7 => CTR => F5: 2,9
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 # G9: 6,9 => CTR => G9: 7,8
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 # G8: 7 => CTR => G8: 6,9
* PRF # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 + G8: 6,9 # H9: 8,9 => SOL
* STA # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 + G8: 6,9 + H9: 8,9
* CNT   8 HDP CHAINS /  42 HYP OPENED

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

Details

Positions

98.76....5.....4....3..5.7.2..........83...6......81.4.9...32....5.8..3....5....1 initial
98.76....5...3.4....3..5.7.2..........83...6......81.4.9...32....5.8..3....5....1 autosolve
984761352572839416613245978261497583458312769739658124896173245125984637347526891 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
G1: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H2: 1.. / H1 = 1  =>  4 pairs (_) / H2 = 1  =>  5 pairs (_)
I5,H6: 2.. / I5 = 2  =>  5 pairs (_) / H6 = 2  =>  3 pairs (_)
G1,I1: 3.. / G1 = 3  =>  3 pairs (_) / I1 = 3  =>  2 pairs (_)
A6,B6: 3.. / A6 = 3  =>  1 pairs (_) / B6 = 3  =>  3 pairs (_)
G4,I4: 3.. / G4 = 3  =>  2 pairs (_) / I4 = 3  =>  3 pairs (_)
A9,B9: 3.. / A9 = 3  =>  3 pairs (_) / B9 = 3  =>  1 pairs (_)
A6,A9: 3.. / A6 = 3  =>  1 pairs (_) / A9 = 3  =>  3 pairs (_)
B6,B9: 3.. / B6 = 3  =>  3 pairs (_) / B9 = 3  =>  1 pairs (_)
G1,G4: 3.. / G1 = 3  =>  3 pairs (_) / G4 = 3  =>  2 pairs (_)
I1,I4: 3.. / I1 = 3  =>  2 pairs (_) / I4 = 3  =>  3 pairs (_)
H7,H9: 4.. / H7 = 4  =>  5 pairs (_) / H9 = 4  =>  2 pairs (_)
C1,F1: 4.. / C1 = 4  =>  3 pairs (_) / F1 = 4  =>  2 pairs (_)
H7,I7: 5.. / H7 = 5  =>  5 pairs (_) / I7 = 5  =>  3 pairs (_)
B2,C2: 7.. / B2 = 7  =>  1 pairs (_) / C2 = 7  =>  2 pairs (_)
D2,D3: 8.. / D2 = 8  =>  1 pairs (_) / D3 = 8  =>  2 pairs (_)
A7,A9: 8.. / A7 = 8  =>  2 pairs (_) / A9 = 8  =>  3 pairs (_)
C4,C6: 9.. / C4 = 9  =>  3 pairs (_) / C6 = 9  =>  3 pairs (_)
* DURATION: 0:00:11.055980  START: 13:35:18.786733  END: 13:35:29.842713 2020-12-22
* CP COUNT: (17)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:42.989030  START: 13:35:33.296174  END: 13:36:16.285204 2020-12-22
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00067391-12_11-base-pr-002.dot
* REASONING
* DIS # I1: 2 # D3: 1,4 => CTR => D3: 2,8,9
* DIS # I1: 2 + D3: 2,8,9 # F5: 1,4 => CTR => F5: 2,7,9
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 # F8: 2,9 => CTR => F8: 1,4,6,7
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 # F9: 2,9 => CTR => F9: 4,6,7
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 # F5: 7 => CTR => F5: 2,9
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 # G9: 6,9 => CTR => G9: 7,8
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 # G8: 7 => CTR => G8: 6,9
* PRF # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 + G8: 6,9 # H9: 8,9 => SOL
* STA # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 + G8: 6,9 + H9: 8,9
* CNT   8 HDP CHAINS /  42 HYP OPENED

Header Info

67391;12_11;GP;24;11.30;1.20;1.20

Solution

position: 984761352572839416613245978261497583458312769739658124896173245125984637347526891 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: 3,5 => UNS
* INC # I1: 2 => UNS
* INC # G4: 3,5 => UNS
* INC # G4: 7,8,9 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 3,5 => UNS
* INC # I1: 2 => UNS
* INC # G4: 3,5 => UNS
* INC # G4: 7,8,9 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 3,5 => UNS
* INC # I1: 2 => UNS
* INC # G4: 3,5 => UNS
* INC # G4: 7,8,9 => UNS
* INC # I1: 3,5 # G4: 3,5 => UNS
* INC # I1: 3,5 # G4: 7,8,9 => UNS
* INC # I1: 3,5 # H2: 1,2 => UNS
* INC # I1: 3,5 # H2: 8,9 => UNS
* INC # I1: 3,5 # C1: 1,2 => UNS
* INC # I1: 3,5 # F1: 1,2 => UNS
* INC # I1: 3,5 # I4: 3,5 => UNS
* INC # I1: 3,5 # I4: 7,8,9 => UNS
* INC # I1: 3,5 => UNS
* INC # I1: 2 # A3: 1,4 => UNS
* INC # I1: 2 # B3: 1,4 => UNS
* INC # I1: 2 # C4: 1,4 => UNS
* INC # I1: 2 # C7: 1,4 => UNS
* DIS # I1: 2 # D3: 1,4 => CTR => D3: 2,8,9
* INC # I1: 2 + D3: 2,8,9 # F4: 1,4 => UNS
* DIS # I1: 2 + D3: 2,8,9 # F5: 1,4 => CTR => F5: 2,7,9
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 # F8: 1,4 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 # F4: 1,4 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 # F8: 1,4 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 # D2: 2,9 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 # D3: 2,9 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 # F5: 2,9 => UNS
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 # F8: 2,9 => CTR => F8: 1,4,6,7
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 # F9: 2,9 => CTR => F9: 4,6,7
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 # F5: 2,9 => UNS
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 # F5: 7 => CTR => F5: 2,9
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 # D2: 2,9 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 # D3: 2,9 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 # I2: 6,9 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 # I3: 6,9 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 # G8: 6,9 => UNS
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 # G9: 6,9 => CTR => G9: 7,8
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 # G8: 6,9 => UNS
* DIS # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 # G8: 7 => CTR => G8: 6,9
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 + G8: 6,9 # I2: 6,9 => UNS
* INC # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 + G8: 6,9 # I3: 6,9 => UNS
* PRF # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 + G8: 6,9 # H9: 8,9 => SOL
* STA # I1: 2 + D3: 2,8,9 + F5: 2,7,9 + F8: 1,4,6,7 + F9: 4,6,7 + F5: 2,9 + G9: 7,8 + G8: 6,9 + H9: 8,9
* CNT  41 HDP CHAINS /  42 HYP OPENED