Analysis of xx-top500-158-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1..5....6...4...2..3...........2.89.7.5......6...........6..1....9.3.....2....... initial

Autosolve

position: 1..5923.695.4.372123.1..95..1.7268957859142636923..417...6.91.2.6923157..218..6.9 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C1: 4,7 => SOL
* DIS # C1: 8 => CTR => C1: 4,7
* PRF # C3: 6,8 => SOL
* DIS # C3: 4 => CTR => C3: 6,8
* DIS # E3: 6,8 => CTR => E3: 7
* PRF # E3: 7 => SOL
* PRF # E3: 7,8 => SOL
* DIS # E3: 6 => CTR => E3: 7,8
* DIS # C1: 4,8 => CTR => C1: 7
* PRF # C1: 7 => SOL
* DIS # H7: 3 => CTR => H7: 4,8
* DIS # C3: 4,8 => CTR => C3: 6
* PRF # C3: 6 => SOL
* DIS # A7: 3,4 => CTR => A7: 5,8
* DIS # A9: 3,4 => CTR => A9: 5
* PRF # A9: 5 => SOL
* PRF # C7: 3,4 => SOL
* DIS # C7: 7 => CTR => C7: 3,4
* DIS # C7: 4,7 => CTR => C7: 3
* PRF # C7: 3 => SOL
* PRF # A7: 4,8 => SOL
* DIS # A7: 3,5 => CTR => A7: 4,8
* PRF # E9: 4,5 => SOL
* DIS # E9: 7 => CTR => E9: 4,5
* DIS # A7: 4,5 => CTR => A7: 3,8
* PRF # A7: 3,8 => SOL
* DIS # E9: 5,7 => CTR => E9: 4
* PRF # E9: 4 => SOL
* DIS # H7: 3 => CTR => H7: 4,8
* PRF # H7: 3,4 => SOL
* DIS # H7: 8 => CTR => H7: 3,4
* DIS # A9: 3,4 => CTR => A9: 5
* PRF # A9: 5 => SOL
* CNT  33 HDP CHAINS /  36 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C1: 4,7 => SOL
* STA C1: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

1..5....6...4...2..3...........2.89.7.5......6...........6..1....9.3.....2....... initial
1..5923.695.4.372123.1..95..1.7268957859142636923..417...6.91.2.6923157..218..6.9 autosolve
147592386958463721236178954314726895785914263692385417873659142469231578521847639 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
B1: 4,7
C2: 6,8
E2: 6,8
F3: 7,8
H1: 4,8
I3: 4,8
A4: 3,4
C4: 3,4
E6: 5,8
F6: 5,8
B7: 4,7
A8: 4,8
E7: 4,5
F9: 5,7
I8: 4,8
H9: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,C4: 3.. / A4 = 3  =>  0 pairs (*) / C4 = 3  =>  0 pairs (X)
H7,H9: 3.. / H7 = 3  =>  0 pairs (X) / H9 = 3  => 17 pairs (_)
A9,H9: 3.. / A9 = 3  =>  0 pairs (X) / H9 = 3  => 17 pairs (_)
C4,C7: 3.. / C4 = 3  =>  0 pairs (X) / C7 = 3  =>  0 pairs (_)
H1,I3: 4.. / H1 = 4  =>  0 pairs (X) / I3 = 4  =>  0 pairs (_)
A4,C4: 4.. / A4 = 4  =>  0 pairs (X) / C4 = 4  =>  0 pairs (_)
E7,E9: 4.. / E7 = 4  =>  0 pairs (X) / E9 = 4  =>  0 pairs (_)
C3,I3: 4.. / C3 = 4  =>  0 pairs (X) / I3 = 4  =>  0 pairs (_)
A8,I8: 4.. / A8 = 4  =>  0 pairs (*) / I8 = 4  =>  0 pairs (X)
B1,B7: 4.. / B1 = 4  =>  0 pairs (*) / B7 = 4  =>  0 pairs (X)
I3,I8: 4.. / I3 = 4  =>  0 pairs (*) / I8 = 4  =>  0 pairs (X)
E6,F6: 5.. / E6 = 5  =>  0 pairs (X) / F6 = 5  =>  0 pairs (_)
A7,A9: 5.. / A7 = 5  =>  0 pairs (X) / A9 = 5  =>  0 pairs (_)
A7,E7: 5.. / A7 = 5  =>  0 pairs (X) / E7 = 5  =>  0 pairs (_)
F6,F9: 5.. / F6 = 5  =>  0 pairs (*) / F9 = 5  =>  0 pairs (X)
C2,C3: 6.. / C2 = 6  =>  0 pairs (X) / C3 = 6  =>  0 pairs (_)
E2,E3: 6.. / E2 = 6  =>  0 pairs (*) / E3 = 6  =>  0 pairs (X)
C2,E2: 6.. / C2 = 6  =>  0 pairs (X) / E2 = 6  =>  0 pairs (_)
C3,E3: 6.. / C3 = 6  =>  0 pairs (*) / E3 = 6  =>  0 pairs (X)
B1,C1: 7.. / B1 = 7  =>  0 pairs (X) / C1 = 7  =>  0 pairs (_)
E3,F3: 7.. / E3 = 7  =>  0 pairs (*) / F3 = 7  =>  0 pairs (X)
B7,C7: 7.. / B7 = 7  =>  0 pairs (*) / C7 = 7  =>  0 pairs (X)
E9,F9: 7.. / E9 = 7  =>  0 pairs (X) / F9 = 7  =>  0 pairs (_)
B1,B7: 7.. / B1 = 7  =>  0 pairs (X) / B7 = 7  =>  0 pairs (_)
C1,C7: 7.. / C1 = 7  =>  0 pairs (*) / C7 = 7  =>  0 pairs (X)
E3,E9: 7.. / E3 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
F3,F9: 7.. / F3 = 7  =>  0 pairs (X) / F9 = 7  =>  0 pairs (_)
H1,I3: 8.. / H1 = 8  =>  0 pairs (*) / I3 = 8  =>  0 pairs (X)
E6,F6: 8.. / E6 = 8  =>  0 pairs (*) / F6 = 8  =>  0 pairs (X)
A7,A8: 8.. / A7 = 8  =>  0 pairs (*) / A8 = 8  =>  0 pairs (X)
H7,I8: 8.. / H7 = 8  =>  0 pairs (X) / I8 = 8  =>  0 pairs (_)
C1,H1: 8.. / C1 = 8  =>  0 pairs (X) / H1 = 8  =>  0 pairs (_)
C2,E2: 8.. / C2 = 8  =>  0 pairs (*) / E2 = 8  =>  0 pairs (X)
A7,H7: 8.. / A7 = 8  =>  0 pairs (*) / H7 = 8  =>  0 pairs (X)
A8,I8: 8.. / A8 = 8  =>  0 pairs (X) / I8 = 8  =>  0 pairs (_)
F3,F6: 8.. / F3 = 8  =>  0 pairs (*) / F6 = 8  =>  0 pairs (X)
H1,H7: 8.. / H1 = 8  =>  0 pairs (*) / H7 = 8  =>  0 pairs (X)
I3,I8: 8.. / I3 = 8  =>  0 pairs (X) / I8 = 8  =>  0 pairs (_)
* DURATION: 0:01:08.269524  START: 08:08:43.841244  END: 08:09:52.110768 2017-05-04
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B1,B7,C2,C4,E2,E6,E7,F3,F6,F9,H1,H9,I3,I8)
* 1..5923.695.4.372123.1..95..1.7268957859142636923..417...6.91.2.6923157..218..6.9
* PAIR B1: 4,7 BLK 1
C1: 4,7,8                                # reduction candidate for 4,7
C1: 4,7 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
C1: 8 => CTR
* 17859234695648372123416795841372689578591426369235.417...6.91.2.6923157..218..6.9
* PAIR C2: 6,8 BLK 1
C3: 6,8,4                                # reduction candidate for 6,8
C3: 6,8 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
C3: 4 => CTR
* 1..5923.695648372123416795841372689578591426369235841754.6.91.2.6923157..218..6.9
* PAIR E2: 6,8 BLK 2
E3: 6,8,7                                # reduction candidate for 6,8
E3: 6,8 => CTR
* 14.5923.695.4.372123.1.795..1.7268957859142636923584175..649182869231574421875639
E3: 7 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
* PAIR F3: 7,8 BLK 2
E3: 7,8,6                                # reduction candidate for 7,8
E3: 7,8 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
E3: 6 => CTR
* 14.5923.695648372123.16795..1.7268957859142636923584175..649182869231574421875639
* PAIR H1: 4,8 ROW 1
C1: 4,8,7                                # reduction candidate for 4,8
C1: 4,8 => CTR
* 17.5923.695.4.372123.1..95..1.7268957859142636923..417.476591.2869231574521847639
C1: 7 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
* PAIR H1: 4,8 COL H
H7: 4,8,3                                # reduction candidate for 4,8
H7: 3 => CTR
* 1..59238695.4.372123.1..954.1.7268957859142636923..4178..65913246923157..218..6.9
H7: 4,8                                  # 17 pairs
* PAIR I3: 4,8 ROW 3
C3: 4,8,6                                # reduction candidate for 4,8
C3: 4,8 => CTR
* 14.5923.695648372123.16795..1.7268957859142636923584175..649182869231574421875639
C3: 6 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
* PAIR A4: 3,4 COL A
A7: 3,4,5,8                              # reduction candidate for 3,4
A7: 3,4 => CTR
* 1..5923.695.4.372123.1..95..1.7268957859142636923..417...659182869231574521847639
A7: 5,8                                  # 17 pairs
A9: 3,4,5                                # reduction candidate for 3,4
A9: 3,4 => CTR
* 14.5923.695.4.372123.1..95..1.7268957859142636923..4175..6491828692315744218..639
A9: 5 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
* PAIR C4: 3,4 COL C
C7: 3,4,7                                # reduction candidate for 3,4
C7: 3,4 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
C7: 7 => CTR
* 17.5923.695.4.372123.1..95.4137268957859142636923..417.476591.2869231574521847639
* PAIR B7: 4,7 BLK 7
C7: 4,7,3                                # reduction candidate for 4,7
C7: 4,7 => CTR
* 1..5923.695.4.372123.1..95.4137268957859142636923..417...6.91.2869231574.21847639
C7: 3 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
* PAIR A8: 4,8 BLK 7
A7: 4,8,3,5                              # reduction candidate for 4,8
A7: 4,8 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
A7: 3,5 => CTR
* 1.859234695648372123416795841372689578591426369235.417...6.9182869231574.218..639
* PAIR E7: 4,5 BLK 8
E9: 4,5,7                                # reduction candidate for 4,5
E9: 4,5 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
E9: 7 => CTR
* 14759238695.4.372123.1.7954.14726895785914263692358417...6491.2.6923157..218756.9
* PAIR E7: 4,5 ROW 7
A7: 4,5,3,8                              # reduction candidate for 4,5
A7: 4,5 => CTR
* 1.85923469564.372123.1..95..1.7268957859142636923..417...6.9182869231574.218..639
A7: 3,8 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
* PAIR F9: 5,7 BLK 8
E9: 5,7,4                                # reduction candidate for 5,7
E9: 5,7 => CTR
* 14759238695.4.372123.1..954.147268957859142636923..417...6491.2.6923157..218..6.9
E9: 4 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
* PAIR I8: 4,8 BLK 9
H7: 4,8,3                                # reduction candidate for 4,8
H7: 3 => CTR
* 1..59238695.4.372123.1..954.1.7268957859142636923..4178..65913246923157..218..6.9
H7: 4,8                                  # 17 pairs
* PAIR H9: 3,4 BLK 9
H7: 3,4,8                                # reduction candidate for 3,4
H7: 3,4 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
H7: 8 => CTR
* 1.859234695648372123416795841372689578591426369235.417...6.9182869231574.218..639
* PAIR H9: 3,4 ROW 9
A9: 3,4,5                                # reduction candidate for 3,4
A9: 3,4 => CTR
* 14.5923.695.4.372123.1..95..1.7268957859142636923..4175..6491828692315744218..639
A9: 5 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-158-base-pr-000.dot
* REASONING
* PRF # C1: 4,7 => SOL
* DIS # C1: 8 => CTR => C1: 4,7
* PRF # C3: 6,8 => SOL
* DIS # C3: 4 => CTR => C3: 6,8
* DIS # E3: 6,8 => CTR => E3: 7
* PRF # E3: 7 => SOL
* PRF # E3: 7,8 => SOL
* DIS # E3: 6 => CTR => E3: 7,8
* DIS # C1: 4,8 => CTR => C1: 7
* PRF # C1: 7 => SOL
* DIS # H7: 3 => CTR => H7: 4,8
* DIS # C3: 4,8 => CTR => C3: 6
* PRF # C3: 6 => SOL
* DIS # A7: 3,4 => CTR => A7: 5,8
* DIS # A9: 3,4 => CTR => A9: 5
* PRF # A9: 5 => SOL
* PRF # C7: 3,4 => SOL
* DIS # C7: 7 => CTR => C7: 3,4
* DIS # C7: 4,7 => CTR => C7: 3
* PRF # C7: 3 => SOL
* PRF # A7: 4,8 => SOL
* DIS # A7: 3,5 => CTR => A7: 4,8
* PRF # E9: 4,5 => SOL
* DIS # E9: 7 => CTR => E9: 4,5
* DIS # A7: 4,5 => CTR => A7: 3,8
* PRF # A7: 3,8 => SOL
* DIS # E9: 5,7 => CTR => E9: 4
* PRF # E9: 4 => SOL
* DIS # H7: 3 => CTR => H7: 4,8
* PRF # H7: 3,4 => SOL
* DIS # H7: 8 => CTR => H7: 3,4
* DIS # A9: 3,4 => CTR => A9: 5
* PRF # A9: 5 => SOL
* CNT  33 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B1,B7,C2,C4,E2,E6,E7,F3,F6,F9,H1,H9,I3,I8)
* 1..5923.695.4.372123.1..95..1.7268957859142636923..417...6.91.2.6923157..218..6.9
* PAIR B1: 4,7 BLK 1
C1: 4,7,8                                # reduction candidate for 4,7
C1: 4,7 => SOLVED
* 147592386958463721236178954314726895785914263692385417873659142469231578521847639
* DURATION: 0:00:02.011635  START: 08:10:35.339133  END: 08:10:37.350768 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-158-base-pr-001.dot
* REASONING
* PRF # C1: 4,7 => SOL
* STA C1: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 158

solution: 147592386958463721236178954314726895785914263692385417873659142469231578521847639
info: 1819     FNBWY    S8.f     25664

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 147592386958463721236178954314726895785914263692385417873659142469231578521847639 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* PRF # C1: 4,7 => SOL
* DIS # C1: 8 => CTR => C1: 4,7
* PRF # C3: 6,8 => SOL
* DIS # C3: 4 => CTR => C3: 6,8
* DIS # E3: 6,8 => CTR => E3: 7
* PRF # E3: 7 => SOL
* PRF # E3: 7,8 => SOL
* DIS # E3: 6 => CTR => E3: 7,8
* DIS # C1: 4,8 => CTR => C1: 7
* PRF # C1: 7 => SOL
* INC # H7: 4,8 => UNS
* DIS # H7: 3 => CTR => H7: 4,8
* DIS # C3: 4,8 => CTR => C3: 6
* PRF # C3: 6 => SOL
* DIS # A7: 3,4 => CTR => A7: 5,8
* INC # A7: 5,8 => UNS
* DIS # A9: 3,4 => CTR => A9: 5
* PRF # A9: 5 => SOL
* PRF # C7: 3,4 => SOL
* DIS # C7: 7 => CTR => C7: 3,4
* DIS # C7: 4,7 => CTR => C7: 3
* PRF # C7: 3 => SOL
* PRF # A7: 4,8 => SOL
* DIS # A7: 3,5 => CTR => A7: 4,8
* PRF # E9: 4,5 => SOL
* DIS # E9: 7 => CTR => E9: 4,5
* DIS # A7: 4,5 => CTR => A7: 3,8
* PRF # A7: 3,8 => SOL
* DIS # E9: 5,7 => CTR => E9: 4
* PRF # E9: 4 => SOL
* INC # H7: 4,8 => UNS
* DIS # H7: 3 => CTR => H7: 4,8
* PRF # H7: 3,4 => SOL
* DIS # H7: 8 => CTR => H7: 3,4
* DIS # A9: 3,4 => CTR => A9: 5
* PRF # A9: 5 => SOL
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C1: 4,7 => SOL
* STA C1: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED