Analysis of xx-top500-012-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...3..2..91.................475.......17...........89.....96..42...8...........1. initial

Autosolve

position: ..83612.991.8....6..69..1.8847529361691738425...6148971..296.8426418.9.3.894.3612 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 5,7 => CTR => B3: 2,3
* PRF # B7: 3 => SOL
* PRF # H2: 5,7 => SOL
* DIS # E2: 5,7 => CTR => E2: 4
* DIS # A3: 3,5 => CTR => A3: 4,7
* PRF # B7: 3,5 => SOL
* DIS # B7: 7 => CTR => B7: 3,5
* PRF # B7: 3 => SOL
* DIS # E2: 5,7 => CTR => E2: 4
* PRF # B7: 3 => SOL
* PRF # H2: 5,7 => SOL
* CNT  11 HDP CHAINS /  38 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # B3: 5,7 => CTR => B3: 2,3
* PRF B3: 2,3 # B7: 3 => SOL
* STA B3: 2,3 + B7: 3
* CNT   2 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

...3..2..91.................475.......17...........89.....96..42...8...........1. initial
..83612.991.8....6..69..1.8847529361691738425...6148971..296.8426418.9.3.894.3612 autosolve
578361249913842576426975138847529361691738425352614897135296784264187953789453612 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
B1: 5,7
G2: 5,7
A6: 3,5
C7: 3,5
A9: 5,7
F8: 5,7
E9: 5,7
G7: 5,7
H8: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C2,B3: 2.. / C2 = 2  => 12 pairs (_) / B3 = 2  => 12 pairs (_)
F2,F3: 2.. / F2 = 2  => 12 pairs (_) / F3 = 2  => 12 pairs (_)
B6,C6: 2.. / B6 = 2  => 12 pairs (_) / C6 = 2  => 12 pairs (_)
C2,F2: 2.. / C2 = 2  => 12 pairs (_) / F2 = 2  => 12 pairs (_)
B3,F3: 2.. / B3 = 2  => 12 pairs (_) / F3 = 2  => 12 pairs (_)
B3,B6: 2.. / B3 = 2  => 12 pairs (_) / B6 = 2  => 12 pairs (_)
C2,C6: 2.. / C2 = 2  => 12 pairs (_) / C6 = 2  => 12 pairs (_)
H2,H3: 3.. / H2 = 3  => 11 pairs (_) / H3 = 3  =>  0 pairs (*)
B7,C7: 3.. / B7 = 3  =>  0 pairs (*) / C7 = 3  =>  0 pairs (X)
C2,H2: 3.. / C2 = 3  =>  0 pairs (*) / H2 = 3  =>  0 pairs (X)
A3,A6: 3.. / A3 = 3  =>  0 pairs (X) / A6 = 3  => 12 pairs (_)
A1,A3: 4.. / A1 = 4  => 12 pairs (_) / A3 = 4  => 14 pairs (_)
E2,E3: 4.. / E2 = 4  => 10 pairs (_) / E3 = 4  =>  0 pairs (X)
A1,H1: 4.. / A1 = 4  => 12 pairs (_) / H1 = 4  => 14 pairs (_)
E2,H2: 4.. / E2 = 4  => 10 pairs (_) / H2 = 4  =>  0 pairs (X)
F8,E9: 5.. / F8 = 5  =>  0 pairs (X) / E9 = 5  =>  0 pairs (_)
G7,H8: 5.. / G7 = 5  =>  0 pairs (X) / H8 = 5  =>  0 pairs (_)
F8,H8: 5.. / F8 = 5  =>  0 pairs (X) / H8 = 5  =>  0 pairs (_)
A9,E9: 5.. / A9 = 5  =>  0 pairs (X) / E9 = 5  =>  0 pairs (_)
G2,G7: 5.. / G2 = 5  =>  0 pairs (*) / G7 = 5  =>  0 pairs (X)
B7,A9: 7.. / B7 = 7  =>  0 pairs (X) / A9 = 7  =>  0 pairs (_)
F8,E9: 7.. / F8 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
G7,H8: 7.. / G7 = 7  =>  0 pairs (*) / H8 = 7  =>  0 pairs (X)
B7,G7: 7.. / B7 = 7  =>  0 pairs (X) / G7 = 7  =>  0 pairs (_)
F8,H8: 7.. / F8 = 7  =>  0 pairs (*) / H8 = 7  =>  0 pairs (X)
A9,E9: 7.. / A9 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
G2,G7: 7.. / G2 = 7  =>  0 pairs (X) / G7 = 7  =>  0 pairs (_)
* DURATION: 0:00:46.227368  START: 03:00:22.506989  END: 03:01:08.734357 2017-05-04
* CP COUNT: (27)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B1,C7,E9,F8,G2,G7,H8)
* ..83612.991.8....6..69..1.8847529361691738425...6148971..296.8426418.9.3.894.3612
* PAIR B1: 5,7 BLK 1
A1: 5,7,4                                # reduction candidate for 5,7
A1: 5,7                                  # 14 pairs
A3: 5,7,3,4                              # reduction candidate for 5,7
A3: 5,7                                  # 16 pairs
B3: 5,7,2,3                              # reduction candidate for 5,7
B3: 5,7 => CTR
* ..83612.99128...363.69.21.8847529361691738425523614897135296784264187953789453612
B3: 2,3                                  # 10 pairs
* PAIR B1: 5,7 ROW 1
H1: 5,7,4                                # reduction candidate for 5,7
H1: 4                                    # 14 pairs
H1: 5,7                                  # 12 pairs
* PAIR B1: 5,7 COL B
B7: 5,7,3                                # reduction candidate for 5,7
B7: 3 => SOLVED
* 578361249913842576426975138847529361691738425352614897135296784264187953789453612
B7: 5,7                                  # 14 pairs
* PAIR G2: 5,7 BLK 3
H1: 5,7,4                                # reduction candidate for 5,7
H1: 5,7                                  # 12 pairs
H2: 5,7,3,4                              # reduction candidate for 5,7
H2: 5,7 => SOLVED
* 578361249913842576426975138847529361691738425352614897135296784264187953789453612
H2: 3,4                                  # 10 pairs
H3: 5,7,3,4                              # reduction candidate for 5,7
H3: 5,7                                  # 12 pairs
* PAIR G2: 5,7 ROW 2
E2: 5,7,4                                # reduction candidate for 5,7
E2: 5,7 => CTR
* 4583612.991.8...46..694.1388475293616917384253..614897135296784264187953789453612
E2: 4                                    # 10 pairs
F2: 5,7,2                                # reduction candidate for 5,7
F2: 5,7                                  # 12 pairs
* PAIR A6: 3,5 BLK 4
B6: 3,5,2                                # reduction candidate for 3,5
B6: 3,5                                  # 12 pairs
C6: 3,5,2                                # reduction candidate for 3,5
C6: 3,5                                  # 12 pairs
* PAIR A6: 3,5 COL A
A3: 3,5,4,7                              # reduction candidate for 3,5
A3: 3,5 => CTR
* 45836127991.87.5463.69..1.8847529361691738425...6148971..296784264187953789453612
A3: 4,7                                  # 14 pairs
* PAIR C7: 3,5 BLK 7
B7: 3,5,7                                # reduction candidate for 3,5
B7: 3,5 => SOLVED
* 578361249913842576426975138847529361691738425352614897135296784264187953789453612
B7: 7 => CTR
* 75836124991284...6..69..1.8847529361691738425...614897173296584264185973589473612
* PAIR C7: 3,5 COL C
C2: 3,5,2                                # reduction candidate for 3,5
C2: 3,5                                  # 12 pairs
C6: 3,5,2                                # reduction candidate for 3,5
C6: 3,5                                  # 12 pairs
* PAIR A9: 5,7 BLK 7
B7: 5,7,3                                # reduction candidate for 5,7
B7: 3 => SOLVED
* 578361249913842576426975138847529361691738425352614897135296784264187953789453612
B7: 5,7                                  # 14 pairs
* PAIR A9: 5,7 COL A
A1: 5,7,4                                # reduction candidate for 5,7
A1: 5,7                                  # 14 pairs
A3: 5,7,3,4                              # reduction candidate for 5,7
A3: 5,7                                  # 16 pairs
* PAIR F8: 5,7 COL F
F2: 5,7,2                                # reduction candidate for 5,7
F2: 5,7                                  # 12 pairs
F3: 5,7,2                                # reduction candidate for 5,7
F3: 5,7                                  # 12 pairs
* PAIR E9: 5,7 COL E
E2: 5,7,4                                # reduction candidate for 5,7
E2: 5,7 => CTR
* 4583612.991.8...46..694.1388475293616917384253..614897135296784264187953789453612
E2: 4                                    # 10 pairs
E3: 5,7,4                                # reduction candidate for 5,7
E3: 5,7                                  # 10 pairs
* PAIR G7: 5,7 ROW 7
B7: 5,7,3                                # reduction candidate for 5,7
B7: 3 => SOLVED
* 578361249913842576426975138847529361691738425352614897135296784264187953789453612
B7: 5,7                                  # 14 pairs
* PAIR H8: 5,7 COL H
H1: 5,7,4                                # reduction candidate for 5,7
H1: 5,7                                  # 12 pairs
H2: 5,7,3,4                              # reduction candidate for 5,7
H2: 5,7 => SOLVED
* 578361249913842576426975138847529361691738425352614897135296784264187953789453612
H2: 3,4                                  # 10 pairs
H3: 5,7,3,4                              # reduction candidate for 5,7
H3: 5,7                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-012-base-pr-000.dot
* REASONING
* DIS # B3: 5,7 => CTR => B3: 2,3
* PRF # B7: 3 => SOL
* PRF # H2: 5,7 => SOL
* DIS # E2: 5,7 => CTR => E2: 4
* DIS # A3: 3,5 => CTR => A3: 4,7
* PRF # B7: 3,5 => SOL
* DIS # B7: 7 => CTR => B7: 3,5
* PRF # B7: 3 => SOL
* DIS # E2: 5,7 => CTR => E2: 4
* PRF # B7: 3 => SOL
* PRF # H2: 5,7 => SOL
* CNT  11 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B1,C7,E9,F8,G2,G7,H8)
* ..83612.991.8....6..69..1.8847529361691738425...6148971..296.8426418.9.3.894.3612
* PAIR B1: 5,7 BLK 1
A1: 5,7,4                                # reduction candidate for 5,7
A1: 5,7                                  # 14 pairs
A3: 5,7,3,4                              # reduction candidate for 5,7
A3: 5,7                                  # 16 pairs
B3: 5,7,2,3                              # reduction candidate for 5,7
B3: 5,7 => CTR
* ..83612.99128...363.69.21.8847529361691738425523614897135296784264187953789453612
* PAIR B1: 5,7 ROW 1
H1: 5,7,4                                # reduction candidate for 5,7
H1: 4                                    # 14 pairs
H1: 5,7                                  # 13 pairs
* PAIR B1: 5,7 COL B
B7: 5,7,3                                # reduction candidate for 5,7
B7: 3 => SOLVED
* 578361249913842576426975138847529361691738425352614897135296784264187953789453612
* DURATION: 0:00:07.707472  START: 03:01:46.392753  END: 03:01:54.100225 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-012-base-pr-001.dot
* REASONING
* DIS # B3: 5,7 => CTR => B3: 2,3
* PRF B3: 2,3 # B7: 3 => SOL
* STA B3: 2,3 + B7: 3
* CNT   2 HDP CHAINS /   7 HYP OPENED

Header Info

Top 500 Minimum 17 012

solution: 578361249913842576426975138847529361691738425352614897135296784264187953789453612
info: 1308     FNBWXY   S8.f     48865

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

Solution

position: 578361249913842576426975138847529361691738425352614897135296784264187953789453612 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:

* INC # A1: 5,7 => UNS
* INC # A3: 5,7 => UNS
* DIS # B3: 5,7 => CTR => B3: 2,3
* INC # B3: 2,3 => UNS
* INC # H1: 5,7 => UNS
* INC # H1: 4 => UNS
* INC # B7: 5,7 => UNS
* PRF # B7: 3 => SOL
* INC # H1: 5,7 => UNS
* PRF # H2: 5,7 => SOL
* INC # H2: 3,4 => UNS
* INC # H3: 5,7 => UNS
* DIS # E2: 5,7 => CTR => E2: 4
* INC # E2: 4 => UNS
* INC # F2: 5,7 => UNS
* INC # B6: 3,5 => UNS
* INC # C6: 3,5 => UNS
* DIS # A3: 3,5 => CTR => A3: 4,7
* INC # A3: 4,7 => UNS
* PRF # B7: 3,5 => SOL
* DIS # B7: 7 => CTR => B7: 3,5
* INC # C2: 3,5 => UNS
* INC # C6: 3,5 => UNS
* INC # B7: 5,7 => UNS
* PRF # B7: 3 => SOL
* INC # A1: 5,7 => UNS
* INC # A3: 5,7 => UNS
* INC # F2: 5,7 => UNS
* INC # F3: 5,7 => UNS
* DIS # E2: 5,7 => CTR => E2: 4
* INC # E2: 4 => UNS
* INC # E3: 5,7 => UNS
* INC # B7: 5,7 => UNS
* PRF # B7: 3 => SOL
* INC # H1: 5,7 => UNS
* PRF # H2: 5,7 => SOL
* INC # H2: 3,4 => UNS
* INC # H3: 5,7 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 5,7 => UNS
* INC # A3: 5,7 => UNS
* DIS # B3: 5,7 => CTR => B3: 2,3
* INC B3: 2,3 # H1: 5,7 => UNS
* INC B3: 2,3 # H1: 4 => UNS
* INC B3: 2,3 # B7: 5,7 => UNS
* PRF B3: 2,3 # B7: 3 => SOL
* STA B3: 2,3 + B7: 3
* CNT   7 HDP CHAINS /   7 HYP OPENED