Analysis of xx-top500-097-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .5.1..2..6...4......3..........6...7..1....4..2...7...7..4.8.........13.......... initial

Autosolve

position: .571.32646.274.3.1143...7.....264.17.713..642426.17..371.438.26..4.7.13......147. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A4: 8,9 => CTR => A4: 3,5
* DIS # A8: 8,9 => CTR => A8: 2,5
* DIS # A9: 8,9 => CTR => A9: 2,3,5
* PRF # H2: 5 => SOL
* PRF # B8: 8,9 => SOL
* DIS # B9: 8,9 => CTR => B9: 3,6
* DIS # E3: 8,9 => CTR => E3: 2,5
* DIS # E5: 5 => CTR => E5: 8,9
* DIS # D3: 5,9 => CTR => D3: 6,8
* PRF # E3: 5,9 => SOL
* DIS # H2: 8 => CTR => H2: 5,9
* DIS # H3: 5,9 => CTR => H3: 8
* DIS # D3: 5,9 => CTR => D3: 6,8
* PRF # E3: 5,9 => SOL
* DIS # I8: 5,9 => CTR => I8: 8
* DIS # D6: 5,9 => CTR => D6: 8
* DIS # A5: 5,9 => CTR => A5: 8
* DIS # G4: 5,9 => CTR => G4: 8
* DIS # D6: 5,9 => CTR => D6: 8
* DIS # H3: 5,9 => CTR => H3: 8
* DIS # A9: 5,9 => CTR => A9: 2,3,8
* DIS # C9: 5,9 => CTR => C9: 8
* DIS # C4: 8 => CTR => C4: 5,9
* DIS # I8: 5,9 => CTR => I8: 8
* DIS # G4: 5,9 => CTR => G4: 8
* CNT  25 HDP CHAINS /  61 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 # A4: 8,9 => CTR => A4: 3,5
* DIS A4: 3,5 # A8: 8,9 => CTR => A8: 2,5
* DIS A4: 3,5 + A8: 2,5 # A9: 8,9 => CTR => A9: 2,3,5
* DIS A4: 3,5 + A8: 2,5 + A9: 2,3,5 # H2: 8,9 => CTR => H2: 5
* PRF A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5 => SOL
* STA A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5
* CNT   5 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.5.1..2..6...4......3..........6...7..1....4..2...7...7..4.8.........13.......... initial
.571.32646.274.3.1143...7.....264.17.713..642426.17..371.438.26..4.7.13......147. autosolve
957183264682749351143652789539264817871395642426817593715438926294576138368921475 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
A1: 8,9
B2: 8,9
E1: 8,9
F2: 5,9
F3: 2,6
I3: 5,9
F5: 5,9
H6: 5,9
C7: 5,9
F8: 2,6
G7: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E3,F3: 2.. / E3 = 2  => 12 pairs (_) / F3 = 2  =>  0 pairs (*)
A8,A9: 2.. / A8 = 2  =>  0 pairs (*) / A9 = 2  =>  0 pairs (X)
F8,E9: 2.. / F8 = 2  => 12 pairs (_) / E9 = 2  =>  0 pairs (*)
A8,F8: 2.. / A8 = 2  =>  0 pairs (*) / F8 = 2  =>  0 pairs (X)
A9,E9: 2.. / A9 = 2  => 12 pairs (_) / E9 = 2  =>  0 pairs (*)
E3,E9: 2.. / E3 = 2  => 12 pairs (_) / E9 = 2  =>  0 pairs (*)
F3,F8: 2.. / F3 = 2  =>  0 pairs (*) / F8 = 2  =>  0 pairs (X)
A4,B4: 3.. / A4 = 3  => 12 pairs (_) / B4 = 3  =>  0 pairs (*)
A9,B9: 3.. / A9 = 3  =>  0 pairs (*) / B9 = 3  =>  0 pairs (X)
A4,A9: 3.. / A4 = 3  => 12 pairs (_) / A9 = 3  =>  0 pairs (*)
B4,B9: 3.. / B4 = 3  =>  0 pairs (*) / B9 = 3  =>  0 pairs (X)
F2,H2: 5.. / F2 = 5  => 14 pairs (_) / H2 = 5  =>  0 pairs (*)
C7,G7: 5.. / C7 = 5  => 18 pairs (_) / G7 = 5  =>  0 pairs (X)
F2,F5: 5.. / F2 = 5  => 14 pairs (_) / F5 = 5  =>  0 pairs (*)
D3,F3: 6.. / D3 = 6  =>  0 pairs (*) / F3 = 6  =>  0 pairs (X)
B8,B9: 6.. / B8 = 6  => 12 pairs (_) / B9 = 6  =>  0 pairs (*)
B9,D9: 6.. / B9 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
F3,F8: 6.. / F3 = 6  => 12 pairs (_) / F8 = 6  =>  0 pairs (*)
A1,B2: 8.. / A1 = 8  =>  0 pairs (X) / B2 = 8  => 17 pairs (_)
H2,H3: 8.. / H2 = 8  =>  0 pairs (X) / H3 = 8  => 17 pairs (_)
E5,D6: 8.. / E5 = 8  =>  0 pairs (X) / D6 = 8  => 17 pairs (_)
G4,G6: 8.. / G4 = 8  => 17 pairs (_) / G6 = 8  =>  0 pairs (X)
I8,I9: 8.. / I8 = 8  => 13 pairs (_) / I9 = 8  =>  0 pairs (X)
A1,E1: 8.. / A1 = 8  =>  0 pairs (X) / E1 = 8  => 17 pairs (_)
B2,H2: 8.. / B2 = 8  => 17 pairs (_) / H2 = 8  =>  0 pairs (X)
A5,E5: 8.. / A5 = 8  => 17 pairs (_) / E5 = 8  =>  0 pairs (X)
D6,G6: 8.. / D6 = 8  => 17 pairs (_) / G6 = 8  =>  0 pairs (X)
C4,C9: 8.. / C4 = 8  =>  0 pairs (X) / C9 = 8  => 14 pairs (_)
D3,D6: 8.. / D3 = 8  =>  0 pairs (X) / D6 = 8  => 17 pairs (_)
A1,B2: 9.. / A1 = 9  => 17 pairs (_) / B2 = 9  =>  0 pairs (X)
A1,E1: 9.. / A1 = 9  => 17 pairs (_) / E1 = 9  =>  0 pairs (X)
C7,G7: 9.. / C7 = 9  =>  0 pairs (X) / G7 = 9  => 18 pairs (_)
F2,F5: 9.. / F2 = 9  =>  0 pairs (*) / F5 = 9  =>  0 pairs (X)
* DURATION: 0:00:59.382802  START: 06:05:00.002424  END: 06:05:59.385226 2017-05-04
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,C7,E1,F2,F3,F5,F8,G7,H6,I3)
* .571.32646.274.3.1143...7.....264.17.713..642426.17..371.438.26..4.7.13......147.
* PAIR A1: 8,9 COL A
A4: 8,9,3,5                              # reduction candidate for 8,9
A4: 8,9 => CTR
* .571.32646.274.3.11436.27...3.264.1757138.642426.17..371.438.262.4.7613.36..2147.
A4: 3,5                                  # 12 pairs
A5: 8,9,5                                # reduction candidate for 8,9
A5: 8,9                                  # 16 pairs
A8: 8,9,2,5                              # reduction candidate for 8,9
A8: 8,9 => CTR
* .571.32646.274.3.1143.267..3..264.1757138964242651789371.438926.64972135239651478
A8: 2,5                                  # 12 pairs
A9: 8,9,2,3,5                            # reduction candidate for 8,9
A9: 8,9 => CTR
* .571.32646.274.3.1143...7..3..264.17.713..642426.17..371.438.262.4.7613......147.
A9: 2,3,5                                # 11 pairs
* PAIR B2: 8,9 ROW 2
H2: 8,9,5                                # reduction candidate for 8,9
H2: 5 => SOLVED
* 957183264682749351143652789539264817871395642426817593715438926294576138368921475
H2: 8,9                                  # 14 pairs
* PAIR B2: 8,9 COL B
B4: 8,9,3                                # reduction candidate for 8,9
B4: 8,9                                  # 12 pairs
B8: 8,9,6                                # reduction candidate for 8,9
B8: 8,9 => SOLVED
* 957183264682749351143652789539264817871395642426817593715438926294576138368921475
B8: 6                                    # 12 pairs
B9: 8,9,3,6                              # reduction candidate for 8,9
B9: 8,9 => CTR
* .571.32646.274.3.1143...7...3.264.17.713..642426.17..371.438.26.64.7213......147.
B9: 3,6                                  # 12 pairs
* PAIR E1: 8,9 BLK 2
D3: 8,9,5,6                              # reduction candidate for 8,9
D3: 8,9                                  # 16 pairs
E3: 8,9,2,5                              # reduction candidate for 8,9
E3: 8,9 => CTR
* 9571832646827453911436.27..539264817871359642426817..3715438926294576138368921475
E3: 2,5                                  # 12 pairs
* PAIR E1: 8,9 COL E
E5: 8,9,5                                # reduction candidate for 8,9
E5: 5 => CTR
* 957183264682745391143...785...264817871359642426817953719438526.64.72138238..147.
E5: 8,9                                  # 18 pairs
* PAIR F2: 5,9 BLK 2
D3: 5,9,6,8                              # reduction candidate for 5,9
D3: 5,9 => CTR
* .571.32646.274.3.1143.2678.3..2648178713..642426817..371.438.26564972138238651479
D3: 6,8                                  # 12 pairs
E3: 5,9,2,8                              # reduction candidate for 5,9
E3: 5,9 => SOLVED
* 957183264682749351143652789539264817871395642426817593715438926294576138368921475
E3: 2,8                                  # 12 pairs
* PAIR F2: 5,9 ROW 2
H2: 5,9,8                                # reduction candidate for 5,9
H2: 8 => CTR
* 857193264692745381143826759..8264517571389642426517893715438926.846721352...51478
H2: 5,9                                  # 17 pairs
* PAIR I3: 5,9 BLK 3
H2: 5,9,8                                # reduction candidate for 5,9
H2: 5,9                                  # 17 pairs
H3: 5,9,8                                # reduction candidate for 5,9
H3: 5,9 => CTR
* 857193264692745381143826759..8264517571389642426517893715438926.846721352...51478
H3: 8                                    # 17 pairs
* PAIR I3: 5,9 ROW 3
D3: 5,9,6,8                              # reduction candidate for 5,9
D3: 5,9 => CTR
* .571.32646.274.3.1143.2678.3..2648178713..642426817..371.438.26564972138238651479
D3: 6,8                                  # 12 pairs
E3: 5,9,2,8                              # reduction candidate for 5,9
E3: 5,9 => SOLVED
* 957183264682749351143652789539264817871395642426817593715438926294576138368921475
E3: 2,8                                  # 12 pairs
* PAIR I3: 5,9 COL I
I8: 5,9,8                                # reduction candidate for 5,9
I8: 5,9 => CTR
* 8571932646927453811438267...38264.1757138.642426.178.371.438.26..4.7.13......1478
I8: 8                                    # 13 pairs
I9: 5,9,8                                # reduction candidate for 5,9
I9: 5,9                                  # 13 pairs
* PAIR F5: 5,9 BLK 5
E5: 5,9,8                                # reduction candidate for 5,9
E5: 5,9                                  # 17 pairs
D6: 5,9,8                                # reduction candidate for 5,9
D6: 5,9 => CTR
* 8571932646927453811438267..38.264.1757138964242651789371.438926..4.7213.23.6.147.
D6: 8                                    # 17 pairs
* PAIR F5: 5,9 ROW 5
A5: 5,9,8                                # reduction candidate for 5,9
A5: 5,9 => CTR
* 8571932646927453811438267.....264.1757138964242651789371.438926..4.7213523.651478
A5: 8                                    # 17 pairs
* PAIR H6: 5,9 BLK 6
G4: 5,9,8                                # reduction candidate for 5,9
G4: 5,9 => CTR
* 8571932646927453811438267..38.264.1757138964242651789371.438926..4.7213.23.6.147.
G4: 8                                    # 17 pairs
G6: 5,9,8                                # reduction candidate for 5,9
G6: 5,9                                  # 17 pairs
* PAIR H6: 5,9 ROW 6
D6: 5,9,8                                # reduction candidate for 5,9
D6: 5,9 => CTR
* 8571932646927453811438267..38.264.1757138964242651789371.438926..4.7213.23.6.147.
D6: 8                                    # 17 pairs
* PAIR H6: 5,9 COL H
H2: 5,9,8                                # reduction candidate for 5,9
H2: 5,9                                  # 17 pairs
H3: 5,9,8                                # reduction candidate for 5,9
H3: 5,9 => CTR
* 857193264692745381143826759..8264517571389642426517893715438926.846721352...51478
H3: 8                                    # 17 pairs
* PAIR C7: 5,9 BLK 7
A8: 5,9,2,8                              # reduction candidate for 5,9
A8: 5,9                                  # 15 pairs
A9: 5,9,2,3,8                            # reduction candidate for 5,9
A9: 5,9 => CTR
* .571.32646.274.3.1143...7..3..264.17.713..642426.17..371.438.262.4.7613......147.
A9: 2,3,8                                # 11 pairs
C9: 5,9,8                                # reduction candidate for 5,9
C9: 5,9 => CTR
* 8571932646927453811438267...38264.1757138.642426.178.371.438.26..4.7.13......147.
C9: 8                                    # 14 pairs
* PAIR C7: 5,9 COL C
C4: 5,9,8                                # reduction candidate for 5,9
C4: 8 => CTR
* 8571932646927453811438267...38264.1757138.642426.178.371.438.26..4.7.13......147.
C4: 5,9                                  # 14 pairs
* PAIR G7: 5,9 BLK 9
I8: 5,9,8                                # reduction candidate for 5,9
I8: 5,9 => CTR
* 8571932646927453811438267...38264.1757138.642426.178.371.438.26..4.7.13......1478
I8: 8                                    # 13 pairs
I9: 5,9,8                                # reduction candidate for 5,9
I9: 5,9                                  # 13 pairs
* PAIR G7: 5,9 COL G
G4: 5,9,8                                # reduction candidate for 5,9
G4: 5,9 => CTR
* 8571932646927453811438267..38.264.1757138964242651789371.438926..4.7213.23.6.147.
G4: 8                                    # 17 pairs
G6: 5,9,8                                # reduction candidate for 5,9
G6: 5,9                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-097-base-pr-000.dot
* REASONING
* DIS # A4: 8,9 => CTR => A4: 3,5
* DIS # A8: 8,9 => CTR => A8: 2,5
* DIS # A9: 8,9 => CTR => A9: 2,3,5
* PRF # H2: 5 => SOL
* PRF # B8: 8,9 => SOL
* DIS # B9: 8,9 => CTR => B9: 3,6
* DIS # E3: 8,9 => CTR => E3: 2,5
* DIS # E5: 5 => CTR => E5: 8,9
* DIS # D3: 5,9 => CTR => D3: 6,8
* PRF # E3: 5,9 => SOL
* DIS # H2: 8 => CTR => H2: 5,9
* DIS # H3: 5,9 => CTR => H3: 8
* DIS # D3: 5,9 => CTR => D3: 6,8
* PRF # E3: 5,9 => SOL
* DIS # I8: 5,9 => CTR => I8: 8
* DIS # D6: 5,9 => CTR => D6: 8
* DIS # A5: 5,9 => CTR => A5: 8
* DIS # G4: 5,9 => CTR => G4: 8
* DIS # D6: 5,9 => CTR => D6: 8
* DIS # H3: 5,9 => CTR => H3: 8
* DIS # A9: 5,9 => CTR => A9: 2,3,8
* DIS # C9: 5,9 => CTR => C9: 8
* DIS # C4: 8 => CTR => C4: 5,9
* DIS # I8: 5,9 => CTR => I8: 8
* DIS # G4: 5,9 => CTR => G4: 8
* CNT  25 HDP CHAINS /  61 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,C7,E1,F2,F3,F5,F8,G7,H6,I3)
* .571.32646.274.3.1143...7.....264.17.713..642426.17..371.438.26..4.7.13......147.
* PAIR A1: 8,9 COL A
A4: 8,9,3,5                              # reduction candidate for 8,9
A4: 8,9 => CTR
* .571.32646.274.3.11436.27...3.264.1757138.642426.17..371.438.262.4.7613.36..2147.
A5: 8,9,5                                # reduction candidate for 8,9
A5: 8,9                                  # 16 pairs
A8: 8,9,2,5                              # reduction candidate for 8,9
A8: 8,9 => CTR
* .571.32646.274.3.1143.267..3..264.1757138964242651789371.438926.64972135239651478
A9: 8,9,2,3,5                            # reduction candidate for 8,9
A9: 8,9 => CTR
* .571.32646.274.3.1143...7..3..264.17.713..642426.17..371.438.262.4.7613......147.
* RESTART
* PAIR RESTART
* PAIR B2: 8,9 ROW 2
H2: 8,9,5                                # reduction candidate for 8,9
H2: 8,9 => CTR
* 957183264682745391143...785...264817871359642426817953719438526.64.72138238..147.
H2: 5 => SOLVED
* 957183264682749351143652789539264817871395642426817593715438926294576138368921475
* DURATION: 0:00:07.310846  START: 06:06:56.828576  END: 06:07:04.139422 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-097-base-pr-001.dot
* REASONING
* DIS # A4: 8,9 => CTR => A4: 3,5
* DIS A4: 3,5 # A8: 8,9 => CTR => A8: 2,5
* DIS A4: 3,5 + A8: 2,5 # A9: 8,9 => CTR => A9: 2,3,5
* DIS A4: 3,5 + A8: 2,5 + A9: 2,3,5 # H2: 8,9 => CTR => H2: 5
* PRF A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5 => SOL
* STA A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5
* CNT   5 HDP CHAINS /   5 HYP OPENED

Header Info

Top 500 Minimum 17 097

solution: 957183264682749351143652789539264817871395642426817593715438926294576138368921475
info: 1574     FNBTWXY  S8.f     20107

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

Solution

position: 957183264682749351143652789539264817871395642426817593715438926294576138368921475 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:

* DIS # A4: 8,9 => CTR => A4: 3,5
* INC # A4: 3,5 => UNS
* INC # A5: 8,9 => UNS
* DIS # A8: 8,9 => CTR => A8: 2,5
* INC # A8: 2,5 => UNS
* DIS # A9: 8,9 => CTR => A9: 2,3,5
* INC # A9: 2,3,5 => UNS
* INC # H2: 8,9 => UNS
* PRF # H2: 5 => SOL
* INC # B4: 8,9 => UNS
* PRF # B8: 8,9 => SOL
* INC # B8: 6 => UNS
* DIS # B9: 8,9 => CTR => B9: 3,6
* INC # B9: 3,6 => UNS
* INC # D3: 8,9 => UNS
* DIS # E3: 8,9 => CTR => E3: 2,5
* INC # E3: 2,5 => UNS
* INC # E5: 8,9 => UNS
* DIS # E5: 5 => CTR => E5: 8,9
* DIS # D3: 5,9 => CTR => D3: 6,8
* INC # D3: 6,8 => UNS
* PRF # E3: 5,9 => SOL
* INC # E3: 2,8 => UNS
* INC # H2: 5,9 => UNS
* DIS # H2: 8 => CTR => H2: 5,9
* INC # H2: 5,9 => UNS
* DIS # H3: 5,9 => CTR => H3: 8
* INC # H3: 8 => UNS
* DIS # D3: 5,9 => CTR => D3: 6,8
* INC # D3: 6,8 => UNS
* PRF # E3: 5,9 => SOL
* INC # E3: 2,8 => UNS
* DIS # I8: 5,9 => CTR => I8: 8
* INC # I8: 8 => UNS
* INC # I9: 5,9 => UNS
* INC # E5: 5,9 => UNS
* DIS # D6: 5,9 => CTR => D6: 8
* INC # D6: 8 => UNS
* DIS # A5: 5,9 => CTR => A5: 8
* INC # A5: 8 => UNS
* DIS # G4: 5,9 => CTR => G4: 8
* INC # G4: 8 => UNS
* INC # G6: 5,9 => UNS
* DIS # D6: 5,9 => CTR => D6: 8
* INC # D6: 8 => UNS
* INC # H2: 5,9 => UNS
* DIS # H3: 5,9 => CTR => H3: 8
* INC # H3: 8 => UNS
* INC # A8: 5,9 => UNS
* DIS # A9: 5,9 => CTR => A9: 2,3,8
* INC # A9: 2,3,8 => UNS
* DIS # C9: 5,9 => CTR => C9: 8
* INC # C9: 8 => UNS
* INC # C4: 5,9 => UNS
* DIS # C4: 8 => CTR => C4: 5,9
* DIS # I8: 5,9 => CTR => I8: 8
* INC # I8: 8 => UNS
* INC # I9: 5,9 => UNS
* DIS # G4: 5,9 => CTR => G4: 8
* INC # G4: 8 => UNS
* INC # G6: 5,9 => UNS
* CNT  61 HDP CHAINS /  61 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A4: 8,9 => CTR => A4: 3,5
* INC A4: 3,5 # A5: 8,9 => UNS
* DIS A4: 3,5 # A8: 8,9 => CTR => A8: 2,5
* DIS A4: 3,5 + A8: 2,5 # A9: 8,9 => CTR => A9: 2,3,5
* DIS A4: 3,5 + A8: 2,5 + A9: 2,3,5 # H2: 8,9 => CTR => H2: 5
* PRF A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5 => SOL
* STA A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5
* CNT   6 HDP CHAINS /   5 HYP OPENED