Analysis of xx-ph-00028844-2011_12-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7..6..5...9..7...7..6...43.9.......5.6.9.......2.3...8.5.7.....1....2.....4.1. initial

Autosolve

position: 98.7..6..5...9..7...7..6...43.9.......5.6.9.......2.3...8.5.7.....1....2.....4.1. 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: 0:00:28.440896

The following important HDP chains were detected:

* DIS # F8: 3,9 # E3: 1,8 => CTR => E3: 2,3,4
* DIS # F8: 3,9 + E3: 2,3,4 # E6: 1,8 => CTR => E6: 4
* DIS # F8: 3,9 + E3: 2,3,4 + E6: 4 # D9: 8 => CTR => D9: 2,6
* DIS # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 # A7: 2,6 => CTR => A7: 1,3
* DIS # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 + A7: 1,3 # B7: 2,6 => CTR => B7: 1,4,9
* PRF # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 + A7: 1,3 + B7: 1,4,9 # I7: 3,9 => SOL
* STA # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 + A7: 1,3 + B7: 1,4,9 + I7: 3,9
* CNT   6 HDP CHAINS /  28 HYP OPENED

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

Details

Positions

98.7..6..5...9..7...7..6...43.9.......5.6.9.......2.3...8.5.7.....1....2.....4.1. initial
98.7..6..5...9..7...7..6...43.9.......5.6.9.......2.3...8.5.7.....1....2.....4.1. autosolve
984731625562498173317526894436915287825367941791842536148253769673189452259674318 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
F7: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A7,B7: 1.. / A7 = 1  =>  2 pairs (_) / B7 = 1  =>  3 pairs (_)
D5,F5: 3.. / D5 = 3  =>  2 pairs (_) / F5 = 3  =>  5 pairs (_)
F1,D3: 5.. / F1 = 5  =>  2 pairs (_) / D3 = 5  =>  3 pairs (_)
F4,D6: 5.. / F4 = 5  =>  3 pairs (_) / D6 = 5  =>  2 pairs (_)
B8,B9: 5.. / B8 = 5  =>  1 pairs (_) / B9 = 5  =>  2 pairs (_)
D3,D6: 5.. / D3 = 5  =>  3 pairs (_) / D6 = 5  =>  2 pairs (_)
F1,F4: 5.. / F1 = 5  =>  2 pairs (_) / F4 = 5  =>  3 pairs (_)
B2,C2: 6.. / B2 = 6  =>  1 pairs (_) / C2 = 6  =>  3 pairs (_)
D7,D9: 6.. / D7 = 6  =>  4 pairs (_) / D9 = 6  =>  2 pairs (_)
A5,A6: 8.. / A5 = 8  =>  3 pairs (_) / A6 = 8  =>  2 pairs (_)
H3,I3: 9.. / H3 = 9  =>  2 pairs (_) / I3 = 9  =>  1 pairs (_)
B6,C6: 9.. / B6 = 9  =>  2 pairs (_) / C6 = 9  =>  1 pairs (_)
F7,F8: 9.. / F7 = 9  =>  1 pairs (_) / F8 = 9  =>  5 pairs (_)
* DURATION: 0:00:07.718879  START: 15:48:10.138691  END: 15:48:17.857570 2020-12-10
* CP COUNT: (13)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:28.305578  START: 15:48:20.933759  END: 15:48:49.239337 2020-12-10
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00028844-2011_12-base-pr-002.dot
* REASONING
* DIS # F8: 3,9 # E3: 1,8 => CTR => E3: 2,3,4
* DIS # F8: 3,9 + E3: 2,3,4 # E6: 1,8 => CTR => E6: 4
* DIS # F8: 3,9 + E3: 2,3,4 + E6: 4 # D9: 8 => CTR => D9: 2,6
* DIS # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 # A7: 2,6 => CTR => A7: 1,3
* DIS # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 + A7: 1,3 # B7: 2,6 => CTR => B7: 1,4,9
* PRF # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 + A7: 1,3 + B7: 1,4,9 # I7: 3,9 => SOL
* STA # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 + A7: 1,3 + B7: 1,4,9 + I7: 3,9
* CNT   6 HDP CHAINS /  28 HYP OPENED

Header Info

28844;2011_12;GP;24;11.30;11.30;9.90

Solution

position: 984731625562498173317526894436915287825367941791842536148253769673189452259674318 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 # F8: 3,9 => UNS
* INC # F8: 7,8 => UNS
* INC # I7: 3,9 => UNS
* INC # I7: 4,6 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F8: 3,9 => UNS
* INC # F8: 7,8 => UNS
* INC # I7: 3,9 => UNS
* INC # I7: 4,6 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F8: 3,9 => UNS
* INC # F8: 7,8 => UNS
* INC # I7: 3,9 => UNS
* INC # I7: 4,6 => UNS
* INC # F8: 3,9 # I1: 1,5 => UNS
* INC # F8: 3,9 # I1: 3,4 => UNS
* INC # F8: 3,9 # F4: 1,5 => UNS
* INC # F8: 3,9 # F4: 7,8 => UNS
* DIS # F8: 3,9 # E3: 1,8 => CTR => E3: 2,3,4
* INC # F8: 3,9 + E3: 2,3,4 # G2: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 # I2: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 # F4: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 # F5: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 # F4: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 # F5: 1,8 => UNS
* DIS # F8: 3,9 + E3: 2,3,4 # E6: 1,8 => CTR => E6: 4
* INC # F8: 3,9 + E3: 2,3,4 + E6: 4 # G4: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 + E6: 4 # I4: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 + E6: 4 # F4: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 + E6: 4 # F5: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 + E6: 4 # G4: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 + E6: 4 # I4: 1,8 => UNS
* INC # F8: 3,9 + E3: 2,3,4 + E6: 4 # D9: 2,6 => UNS
* DIS # F8: 3,9 + E3: 2,3,4 + E6: 4 # D9: 8 => CTR => D9: 2,6
* DIS # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 # A7: 2,6 => CTR => A7: 1,3
* DIS # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 + A7: 1,3 # B7: 2,6 => CTR => B7: 1,4,9
* PRF # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 + A7: 1,3 + B7: 1,4,9 # I7: 3,9 => SOL
* STA # F8: 3,9 + E3: 2,3,4 + E6: 4 + D9: 2,6 + A7: 1,3 + B7: 1,4,9 + I7: 3,9
* CNT  27 HDP CHAINS /  28 HYP OPENED