Analysis of xx-ph-00001036-L84-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1......8...7.....6.....35....4.9....3....5.2..6.7......9..4...7.....2.5.8..5..1.. initial

Autosolve

position: 1......8...7.....6.....35....4.9....3....5.2..6.7......9..4...7.....2.5.8..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: 0:00:23.834703

The following important HDP chains were detected:

* DIS # G7: 3,6 # A2: 2,5 => CTR => A2: 4,9
* DIS # G7: 3,6 + A2: 4,9 # A6: 2,5 => CTR => A6: 9
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 # A4: 7 => CTR => A4: 2,5
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 # C1: 2,5 => CTR => C1: 3,9
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 # C6: 1,8 => CTR => C6: 2,5
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 + C6: 2,5 # C8: 3,6 => CTR => C8: 1
* PRF # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 + C6: 2,5 + C8: 1 => SOL
* STA G7: 3,6
* CNT   7 HDP CHAINS /  18 HYP OPENED

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

Details

Positions

1......8...7.....6.....35....4.9....3....5.2..6.7......9..4...7.....2.5.8..5..1.. initial
1......8...7.....6.....35....4.9....3....5.2..6.7......9..4...7.....2.5.8..5..1.. autosolve
123456789457189236689273541214398675378615924965724813592841367731962458846537192 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
D4: 2,3
E6: 2,3
H7: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,E6: 2.. / D4 = 2  =>  3 pairs (_) / E6 = 2  =>  2 pairs (_)
G7,I9: 2.. / G7 = 2  =>  4 pairs (_) / I9 = 2  =>  6 pairs (_)
D4,E6: 3.. / D4 = 3  =>  2 pairs (_) / E6 = 3  =>  3 pairs (_)
D5,F6: 4.. / D5 = 4  =>  6 pairs (_) / F6 = 4  =>  3 pairs (_)
E1,E2: 5.. / E1 = 5  =>  3 pairs (_) / E2 = 5  =>  3 pairs (_)
I4,I6: 5.. / I4 = 5  =>  4 pairs (_) / I6 = 5  =>  4 pairs (_)
A7,C7: 5.. / A7 = 5  =>  5 pairs (_) / C7 = 5  =>  4 pairs (_)
G1,H3: 7.. / G1 = 7  =>  6 pairs (_) / H3 = 7  =>  3 pairs (_)
E3,H3: 7.. / E3 = 7  =>  6 pairs (_) / H3 = 7  =>  3 pairs (_)
B5,G5: 7.. / B5 = 7  =>  5 pairs (_) / G5 = 7  =>  5 pairs (_)
A4,A8: 7.. / A4 = 7  =>  6 pairs (_) / A8 = 7  =>  5 pairs (_)
F1,F9: 7.. / F1 = 7  =>  4 pairs (_) / F9 = 7  =>  4 pairs (_)
H3,H4: 7.. / H3 = 7  =>  3 pairs (_) / H4 = 7  =>  6 pairs (_)
D8,F9: 9.. / D8 = 9  =>  4 pairs (_) / F9 = 9  =>  3 pairs (_)
* DURATION: 0:00:10.620708  START: 11:12:53.717030  END: 11:13:04.337738 2020-11-24
* CP COUNT: (14)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:23.674878  START: 11:13:10.874656  END: 11:13:34.549534 2020-11-24
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00001036-L84-base-pr-002.dot
* REASONING
* DIS # G7: 3,6 # A2: 2,5 => CTR => A2: 4,9
* DIS # G7: 3,6 + A2: 4,9 # A6: 2,5 => CTR => A6: 9
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 # A4: 7 => CTR => A4: 2,5
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 # C1: 2,5 => CTR => C1: 3,9
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 # C6: 1,8 => CTR => C6: 2,5
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 + C6: 2,5 # C8: 3,6 => CTR => C8: 1
* PRF # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 + C6: 2,5 + C8: 1 => SOL
* STA G7: 3,6
* CNT   7 HDP CHAINS /  18 HYP OPENED

Header Info

1036;L84;elev;21;11.30;11.30;3.40

Solution

position: 123456789457189236689273541214398675378615924965724813592841367731962458846537192 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 # G7: 3,6 => UNS
* INC # G8: 3,6 => UNS
* INC # H9: 3,6 => UNS
* INC # C7: 3,6 => UNS
* INC # D7: 3,6 => UNS
* INC # H4: 3,6 => UNS
* INC # H4: 1,7 => UNS
* CNT   7 HDP CHAINS /   7 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G7: 3,6 => UNS
* INC # G8: 3,6 => UNS
* INC # H9: 3,6 => UNS
* INC # C7: 3,6 => UNS
* INC # D7: 3,6 => UNS
* INC # H4: 3,6 => UNS
* INC # H4: 1,7 => UNS
* CNT   7 HDP CHAINS /   7 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G7: 3,6 => UNS
* INC # G8: 3,6 => UNS
* INC # H9: 3,6 => UNS
* INC # C7: 3,6 => UNS
* INC # D7: 3,6 => UNS
* INC # H4: 3,6 => UNS
* INC # H4: 1,7 => UNS
* DIS # G7: 3,6 # A2: 2,5 => CTR => A2: 4,9
* INC # G7: 3,6 + A2: 4,9 # A4: 2,5 => UNS
* DIS # G7: 3,6 + A2: 4,9 # A6: 2,5 => CTR => A6: 9
* INC # G7: 3,6 + A2: 4,9 + A6: 9 # A4: 2,5 => UNS
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 # A4: 7 => CTR => A4: 2,5
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 # C1: 2,5 => CTR => C1: 3,9
* INC # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 # C6: 2,5 => UNS
* INC # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 # C6: 2,5 => UNS
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 # C6: 1,8 => CTR => C6: 2,5
* DIS # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 + C6: 2,5 # C8: 3,6 => CTR => C8: 1
* PRF # G7: 3,6 + A2: 4,9 + A6: 9 + A4: 2,5 + C1: 3,9 + C6: 2,5 + C8: 1 => SOL
* STA G7: 3,6
* CNT  18 HDP CHAINS /  18 HYP OPENED