Analysis of xx-top500-089-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....2.8..5.......4.1.......2.8.4.......3..1.........7....7...3.6..1.....4.......2 initial

Autosolve

position: ...42.81.582.173.4.148..2..278.41..394.37.12.1.32..47.82.7.4631637182.4.4.1...782 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D4: 6,9 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # D9: 6,9 => SOL
* DIS # D9: 5 => CTR => D9: 6,9
* DIS # I3: 5,7 => CTR => I3: 6,9
* DIS # H3: 6,9 => CTR => H3: 5
* DIS # H4: 5 => CTR => H4: 6,9
* DIS # F6: 5,6 => CTR => F6: 8,9
* PRF # I6: 5,6 => SOL
* DIS # H4: 5,9 => CTR => H4: 6
* PRF # I6: 5,9 => SOL
* DIS # D4: 6 => CTR => D4: 5,9
* DIS # E9: 5,9 => CTR => E9: 3,6
* DIS # F9: 5,9 => CTR => F9: 3,6
* DIS # E9: 5,9 => CTR => E9: 3,6
* DIS # F9: 5,9 => CTR => F9: 3,6
* DIS # E3: 5,9 => CTR => E3: 3,6
* DIS # I3: 5,9 => CTR => I3: 6,7
* PRF # I6: 5,9 => SOL
* CNT  19 HDP CHAINS /  47 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 # D4: 6,9 => CTR => D4: 5
* PRF D4: 5 => SOL
* STA D4: 5
* CNT   2 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

....2.8..5.......4.1.......2.8.4.......3..1.........7....7...3.6..1.....4.......2 initial
...42.81.582.173.4.148..2..278.41..394.37.12.1.32..47.82.7.4631637182.4.4.1...782 autosolve
396425817582617394714839256278541963945376128163298475829754631637182549451963782 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A1: 3,7
B1: 6,9
C1: 6,9
A3: 3,7
F1: 3,5
D2: 6,9
I1: 5,7
H2: 6,9
C5: 5,6
B6: 5,6
G4: 5,9
C7: 5,9
B9: 5,9
E7: 5,9
G8: 5,9
I8: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 3.. / A1 = 3  => 13 pairs (_) / A3 = 3  =>  0 pairs (X)
E9,F9: 3.. / E9 = 3  => 16 pairs (_) / F9 = 3  => 14 pairs (_)
A1,F1: 3.. / A1 = 3  => 13 pairs (_) / F1 = 3  =>  0 pairs (X)
E3,E9: 3.. / E3 = 3  => 14 pairs (_) / E9 = 3  => 16 pairs (_)
C5,B6: 5.. / C5 = 5  =>  0 pairs (*) / B6 = 5  =>  0 pairs (X)
C7,B9: 5.. / C7 = 5  =>  0 pairs (X) / B9 = 5  =>  0 pairs (_)
G8,I8: 5.. / G8 = 5  => 15 pairs (_) / I8 = 5  =>  0 pairs (X)
F1,I1: 5.. / F1 = 5  => 13 pairs (_) / I1 = 5  =>  0 pairs (X)
C7,E7: 5.. / C7 = 5  =>  0 pairs (X) / E7 = 5  =>  0 pairs (_)
B6,B9: 5.. / B6 = 5  =>  0 pairs (X) / B9 = 5  =>  0 pairs (_)
C5,C7: 5.. / C5 = 5  =>  0 pairs (*) / C7 = 5  =>  0 pairs (X)
D4,D9: 5.. / D4 = 5  =>  0 pairs (*) / D9 = 5  =>  0 pairs (X)
G4,G8: 5.. / G4 = 5  =>  0 pairs (X) / G8 = 5  => 15 pairs (_)
H3,H4: 5.. / H3 = 5  => 15 pairs (_) / H4 = 5  =>  0 pairs (X)
B1,C1: 6.. / B1 = 6  =>  0 pairs (X) / C1 = 6  =>  0 pairs (_)
C5,B6: 6.. / C5 = 6  =>  0 pairs (X) / B6 = 6  =>  0 pairs (_)
D2,H2: 6.. / D2 = 6  => 18 pairs (_) / H2 = 6  =>  0 pairs (X)
D4,H4: 6.. / D4 = 6  =>  0 pairs (X) / H4 = 6  => 18 pairs (_)
B1,B6: 6.. / B1 = 6  =>  0 pairs (X) / B6 = 6  =>  0 pairs (_)
C1,C5: 6.. / C1 = 6  =>  0 pairs (*) / C5 = 6  =>  0 pairs (X)
A1,A3: 7.. / A1 = 7  =>  0 pairs (X) / A3 = 7  => 13 pairs (_)
I1,I3: 7.. / I1 = 7  => 13 pairs (_) / I3 = 7  =>  0 pairs (X)
A1,I1: 7.. / A1 = 7  =>  0 pairs (X) / I1 = 7  => 13 pairs (_)
A3,I3: 7.. / A3 = 7  => 13 pairs (_) / I3 = 7  =>  0 pairs (X)
F5,F6: 8.. / F5 = 8  => 18 pairs (_) / F6 = 8  => 17 pairs (_)
I5,I6: 8.. / I5 = 8  => 17 pairs (_) / I6 = 8  => 18 pairs (_)
F5,I5: 8.. / F5 = 8  => 18 pairs (_) / I5 = 8  => 17 pairs (_)
F6,I6: 8.. / F6 = 8  => 17 pairs (_) / I6 = 8  => 18 pairs (_)
B1,C1: 9.. / B1 = 9  =>  0 pairs (*) / C1 = 9  =>  0 pairs (X)
C7,B9: 9.. / C7 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
G8,I8: 9.. / G8 = 9  =>  0 pairs (X) / I8 = 9  => 15 pairs (_)
D2,H2: 9.. / D2 = 9  =>  0 pairs (X) / H2 = 9  => 18 pairs (_)
C7,E7: 9.. / C7 = 9  =>  0 pairs (*) / E7 = 9  =>  0 pairs (X)
B1,B9: 9.. / B1 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
C1,C7: 9.. / C1 = 9  =>  0 pairs (X) / C7 = 9  =>  0 pairs (_)
G4,G8: 9.. / G4 = 9  => 15 pairs (_) / G8 = 9  =>  0 pairs (X)
* DURATION: 0:01:00.481788  START: 05:49:16.657215  END: 05:50:17.139003 2017-05-04
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,B6,B9,C1,C5,C7,D2,E7,F1,G4,G8,H2,I1,I8)
* ...42.81.582.173.4.148..2..278.41..394.37.12.1.32..47.82.7.4631637182.4.4.1...782
* PAIR F1: 3,5 BLK 2
E3: 3,5,6,9                              # reduction candidate for 3,5
E3: 3,5                                  # 18 pairs
F3: 3,5,6,9                              # reduction candidate for 3,5
F3: 3,5                                  # 20 pairs
* PAIR F1: 3,5 COL F
F9: 3,5,6,9                              # reduction candidate for 3,5
F9: 3,5                                  # 20 pairs
F9: 6,9                                  # 17 pairs
* PAIR D2: 6,9 BLK 2
E3: 6,9,3,5                              # reduction candidate for 6,9
E3: 6,9                                  # 20 pairs
F3: 6,9,3,5                              # reduction candidate for 6,9
F3: 6,9                                  # 18 pairs
* PAIR D2: 6,9 COL D
D4: 6,9,5                                # reduction candidate for 6,9
D4: 6,9 => CTR
* .6942.81.582.173.4.1485.2..278.41.53946375128153268479825794631637182.4.4915..782
D4: 5 => SOLVED
* 396425817582617394714839256278541963945376128163298475829754631637182549451963782
D9: 6,9,5                                # reduction candidate for 6,9
D9: 6,9 => SOLVED
* 396425817582617394714839256278541963945376128163298475829754631637182549451963782
D9: 5 => CTR
* .6942.81.582.173.4.1485.2..278.41.53946375128153268479825794631637182.4.4915..782
* PAIR I1: 5,7 BLK 3
I3: 5,7,6,9                              # reduction candidate for 5,7
I3: 5,7 => CTR
* ...42.81.582917364.148..29.27864195394.37.12.15329.47.82.7.46316371825494.15..782
I3: 6,9                                  # 15 pairs
* PAIR H2: 6,9 BLK 3
H3: 6,9,5                                # reduction candidate for 6,9
H3: 6,9 => CTR
* ...42.81.582.173.4.148..2..27864195394.37.12.15329.47.82.7.46316371825494.15..782
H3: 5                                    # 15 pairs
I3: 6,9,5,7                              # reduction candidate for 6,9
I3: 6,9                                  # 15 pairs
* PAIR H2: 6,9 COL H
H4: 6,9,5                                # reduction candidate for 6,9
H4: 5 => CTR
* ...42.81.582917364.148..29.27864195394.37.12.15329.47.82.7.46316371825494.15..782
H4: 6,9                                  # 15 pairs
* PAIR C5: 5,6 ROW 5
F5: 5,6,8                                # reduction candidate for 5,6
F5: 5,6                                  # 17 pairs
I5: 5,6,8                                # reduction candidate for 5,6
I5: 5,6                                  # 18 pairs
* PAIR B6: 5,6 ROW 6
E6: 5,6,9                                # reduction candidate for 5,6
E6: 5,6                                  # 19 pairs
F6: 5,6,8,9                              # reduction candidate for 5,6
F6: 5,6 => CTR
* .9642.81.582.173.4.148..2..2785419.394.37812.1.329.478829754631637182.4.451...782
F6: 8,9                                  # 17 pairs
I6: 5,6,8,9                              # reduction candidate for 5,6
I6: 5,6 => SOLVED
* 396425817582617394714839256278541963945376128163298475829754631637182549451963782
I6: 8,9                                  # 17 pairs
* PAIR G4: 5,9 BLK 6
H4: 5,9,6                                # reduction candidate for 5,9
H4: 5,9 => CTR
* ...42.81.582917364.148..2..278641..394.37.12.15329.47.82.7.4631637182.4.4.15..782
H4: 6                                    # 18 pairs
I6: 5,9,6,8                              # reduction candidate for 5,9
I6: 5,9 => SOLVED
* 396425817582617394714839256278541963945376128163298475829754631637182549451963782
I6: 6,8                                  # 18 pairs
* PAIR G4: 5,9 ROW 4
D4: 5,9,6                                # reduction candidate for 5,9
D4: 6 => CTR
* ...42.81.582917364.148..2..278641..394.37.12.15329.47.82.7.4631637182.4.4.15..782
D4: 5,9                                  # 18 pairs
* PAIR B9: 5,9 ROW 9
D9: 5,9,6                                # reduction candidate for 5,9
D9: 5,9                                  # 19 pairs
E9: 5,9,3,6                              # reduction candidate for 5,9
E9: 5,9 => CTR
* 369425817582.173.47148362..2785419639463781251532694788257946316371825494.1..3782
E9: 3,6                                  # 17 pairs
F9: 5,9,3,6                              # reduction candidate for 5,9
F9: 5,9 => CTR
* ...42.81.582917364.148..2..2785419.394.37.12.1.32..47.82.7.4631637182.4.4.163.782
F9: 3,6                                  # 17 pairs
* PAIR E7: 5,9 BLK 8
D9: 5,9,6                                # reduction candidate for 5,9
D9: 5,9                                  # 19 pairs
E9: 5,9,3,6                              # reduction candidate for 5,9
E9: 5,9 => CTR
* 369425817582.173.47148362..2785419639463781251532694788257946316371825494.1..3782
E9: 3,6                                  # 17 pairs
F9: 5,9,3,6                              # reduction candidate for 5,9
F9: 5,9 => CTR
* ...42.81.582917364.148..2..2785419.394.37.12.1.32..47.82.7.4631637182.4.4.163.782
F9: 3,6                                  # 17 pairs
* PAIR E7: 5,9 COL E
E3: 5,9,3,6                              # reduction candidate for 5,9
E3: 5,9 => CTR
* .6942.81.582617394.1485.2..278.41.6394637.12.15326.47.825794631637182.4.491.3.782
E3: 3,6                                  # 18 pairs
E6: 5,9,6                                # reduction candidate for 5,9
E6: 5,9                                  # 20 pairs
* PAIR I8: 5,9 COL I
I3: 5,9,6,7                              # reduction candidate for 5,9
I3: 5,9 => CTR
* 3..425817582.173.47148..2..278641..394.37812.1.3259478825794631637182.4.4915..782
I3: 6,7                                  # 18 pairs
I6: 5,9,6,8                              # reduction candidate for 5,9
I6: 5,9 => SOLVED
* 396425817582617394714839256278541963945376128163298475829754631637182549451963782
I6: 6,8                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-089-base-pr-000.dot
* REASONING
* DIS # D4: 6,9 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # D9: 6,9 => SOL
* DIS # D9: 5 => CTR => D9: 6,9
* DIS # I3: 5,7 => CTR => I3: 6,9
* DIS # H3: 6,9 => CTR => H3: 5
* DIS # H4: 5 => CTR => H4: 6,9
* DIS # F6: 5,6 => CTR => F6: 8,9
* PRF # I6: 5,6 => SOL
* DIS # H4: 5,9 => CTR => H4: 6
* PRF # I6: 5,9 => SOL
* DIS # D4: 6 => CTR => D4: 5,9
* DIS # E9: 5,9 => CTR => E9: 3,6
* DIS # F9: 5,9 => CTR => F9: 3,6
* DIS # E9: 5,9 => CTR => E9: 3,6
* DIS # F9: 5,9 => CTR => F9: 3,6
* DIS # E3: 5,9 => CTR => E3: 3,6
* DIS # I3: 5,9 => CTR => I3: 6,7
* PRF # I6: 5,9 => SOL
* CNT  19 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,B6,B9,C1,C5,C7,D2,E7,F1,G4,G8,H2,I1,I8)
* ...42.81.582.173.4.148..2..278.41..394.37.12.1.32..47.82.7.4631637182.4.4.1...782
* PAIR F1: 3,5 BLK 2
E3: 3,5,6,9                              # reduction candidate for 3,5
E3: 3,5                                  # 18 pairs
F3: 3,5,6,9                              # reduction candidate for 3,5
F3: 3,5                                  # 20 pairs
* PAIR F1: 3,5 COL F
F9: 3,5,6,9                              # reduction candidate for 3,5
F9: 3,5                                  # 20 pairs
F9: 6,9                                  # 17 pairs
* PAIR D2: 6,9 BLK 2
E3: 6,9,3,5                              # reduction candidate for 6,9
E3: 6,9                                  # 20 pairs
F3: 6,9,3,5                              # reduction candidate for 6,9
F3: 6,9                                  # 18 pairs
* PAIR D2: 6,9 COL D
D4: 6,9,5                                # reduction candidate for 6,9
D4: 6,9 => CTR
* .6942.81.582.173.4.1485.2..278.41.53946375128153268479825794631637182.4.4915..782
D4: 5 => SOLVED
* 396425817582617394714839256278541963945376128163298475829754631637182549451963782
* DURATION: 0:00:07.001277  START: 05:51:01.108626  END: 05:51:08.109903 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-089-base-pr-001.dot
* REASONING
* DIS # D4: 6,9 => CTR => D4: 5
* PRF D4: 5 => SOL
* STA D4: 5
* CNT   2 HDP CHAINS /   7 HYP OPENED

Header Info

Top 500 Minimum 17 089

solution: 396425817582617394714839256278541963945376128163298475829754631637182549451963782
info: 1565     FNBTWXY  S8.f     3431

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

Solution

position: 396425817582617394714839256278541963945376128163298475829754631637182549451963782 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 # E3: 3,5 => UNS
* INC # F3: 3,5 => UNS
* INC # F9: 3,5 => UNS
* INC # F9: 6,9 => UNS
* INC # E3: 6,9 => UNS
* INC # F3: 6,9 => UNS
* DIS # D4: 6,9 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # D9: 6,9 => SOL
* DIS # D9: 5 => CTR => D9: 6,9
* DIS # I3: 5,7 => CTR => I3: 6,9
* INC # I3: 6,9 => UNS
* DIS # H3: 6,9 => CTR => H3: 5
* INC # H3: 5 => UNS
* INC # I3: 6,9 => UNS
* INC # H4: 6,9 => UNS
* DIS # H4: 5 => CTR => H4: 6,9
* INC # F5: 5,6 => UNS
* INC # I5: 5,6 => UNS
* INC # E6: 5,6 => UNS
* DIS # F6: 5,6 => CTR => F6: 8,9
* INC # F6: 8,9 => UNS
* PRF # I6: 5,6 => SOL
* INC # I6: 8,9 => UNS
* DIS # H4: 5,9 => CTR => H4: 6
* INC # H4: 6 => UNS
* PRF # I6: 5,9 => SOL
* INC # I6: 6,8 => UNS
* INC # D4: 5,9 => UNS
* DIS # D4: 6 => CTR => D4: 5,9
* INC # D9: 5,9 => UNS
* DIS # E9: 5,9 => CTR => E9: 3,6
* INC # E9: 3,6 => UNS
* DIS # F9: 5,9 => CTR => F9: 3,6
* INC # F9: 3,6 => UNS
* INC # D9: 5,9 => UNS
* DIS # E9: 5,9 => CTR => E9: 3,6
* INC # E9: 3,6 => UNS
* DIS # F9: 5,9 => CTR => F9: 3,6
* INC # F9: 3,6 => UNS
* DIS # E3: 5,9 => CTR => E3: 3,6
* INC # E3: 3,6 => UNS
* INC # E6: 5,9 => UNS
* DIS # I3: 5,9 => CTR => I3: 6,7
* INC # I3: 6,7 => UNS
* PRF # I6: 5,9 => SOL
* INC # I6: 6,8 => UNS
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E3: 3,5 => UNS
* INC # F3: 3,5 => UNS
* INC # F9: 3,5 => UNS
* INC # F9: 6,9 => UNS
* INC # E3: 6,9 => UNS
* INC # F3: 6,9 => UNS
* DIS # D4: 6,9 => CTR => D4: 5
* PRF D4: 5 => SOL
* STA D4: 5
* CNT   8 HDP CHAINS /   7 HYP OPENED