Analysis of xx-top95-093-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .5..9....1.....6.....3.8.....8.4...9514.......3....2..........4.8...6..77..15..6. initial

Autosolve

position: 85..9....1.....6.....3.8.....8.4...9514.......3....24.........4.8...6..77..15..6. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D1: 2,7 => CTR => D1: 4,6
* DIS # D2: 2,7 => CTR => D2: 4,5
* PRF # F2: 2,7 => SOL
* DIS # E3: 2,7 => CTR => E3: 1,6
* DIS # E7: 2,7 => CTR => E7: 3,8
* PRF # A3: 6,9 => SOL
* DIS # E7: 2,3 => CTR => E7: 7,8
* CNT   7 HDP CHAINS /  44 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 # D1: 2,7 => CTR => D1: 4,6
* DIS D1: 4,6 # D2: 2,7 => CTR => D2: 4,5
* PRF D1: 4,6 + D2: 4,5 # F2: 2,7 => SOL
* STA D1: 4,6 + D2: 4,5 + F2: 2,7
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

.5..9....1.....6.....3.8.....8.4...9514.......3....2..........4.8...6..77..15..6. initial
85..9....1.....6.....3.8.....8.4...9514.......3....24.........4.8...6..77..15..6. autosolve
856491372143572698927368451278645139514923786639817245361789524485236917792154863 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
E2: 2,7
A4: 2,6
A6: 6,9
C7: 1,5
C8: 1,5
C9: 2,9
E8: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,E3: 1.. / F1 = 1  => 21 pairs (_) / E3 = 1  => 14 pairs (_)
C7,C8: 1.. / C7 = 1  =>  5 pairs (_) / C8 = 1  =>  5 pairs (_)
E3,E6: 1.. / E3 = 1  => 14 pairs (_) / E6 = 1  => 21 pairs (_)
A4,B4: 2.. / A4 = 2  =>  7 pairs (_) / B4 = 2  => 11 pairs (_)
C1,C2: 3.. / C1 = 3  => 15 pairs (_) / C2 = 3  =>  8 pairs (_)
A7,A8: 3.. / A7 = 3  =>  8 pairs (_) / A8 = 3  => 16 pairs (_)
G1,G3: 4.. / G1 = 4  =>  9 pairs (_) / G3 = 4  =>  0 pairs (*)
A8,B9: 4.. / A8 = 4  => 11 pairs (_) / B9 = 4  =>  8 pairs (_)
D8,F9: 4.. / D8 = 4  =>  8 pairs (_) / F9 = 4  => 11 pairs (_)
A8,D8: 4.. / A8 = 4  => 11 pairs (_) / D8 = 4  =>  8 pairs (_)
B9,F9: 4.. / B9 = 4  =>  8 pairs (_) / F9 = 4  => 11 pairs (_)
A3,A8: 4.. / A3 = 4  =>  8 pairs (_) / A8 = 4  => 11 pairs (_)
D2,F2: 5.. / D2 = 5  =>  8 pairs (_) / F2 = 5  =>  8 pairs (_)
C7,C8: 5.. / C7 = 5  =>  5 pairs (_) / C8 = 5  =>  5 pairs (_)
I3,I6: 5.. / I3 = 5  =>  9 pairs (_) / I6 = 5  => 11 pairs (_)
D1,E3: 6.. / D1 = 6  => 12 pairs (_) / E3 = 6  => 21 pairs (_)
I5,I6: 6.. / I5 = 6  =>  9 pairs (_) / I6 = 6  =>  0 pairs (X)
A7,B7: 6.. / A7 = 6  => 18 pairs (_) / B7 = 6  =>  8 pairs (_)
C1,D1: 6.. / C1 = 6  => 21 pairs (_) / D1 = 6  => 12 pairs (_)
B4,C6: 7.. / B4 = 7  => 21 pairs (_) / C6 = 7  => 10 pairs (_)
H2,I2: 8.. / H2 = 8  =>  9 pairs (_) / I2 = 8  => 10 pairs (_)
D7,E7: 8.. / D7 = 8  =>  0 pairs (X) / E7 = 8  =>  7 pairs (_)
G9,I9: 8.. / G9 = 8  =>  9 pairs (_) / I9 = 8  => 11 pairs (_)
G5,G9: 8.. / G5 = 8  => 11 pairs (_) / G9 = 8  =>  9 pairs (_)
H2,H5: 8.. / H2 = 8  =>  9 pairs (_) / H5 = 8  => 10 pairs (_)
A6,C6: 9.. / A6 = 9  =>  7 pairs (_) / C6 = 9  => 21 pairs (_)
D5,F5: 9.. / D5 = 9  =>  8 pairs (_) / F5 = 9  =>  7 pairs (_)
* DURATION: 0:00:35.175395  START: 01:11:22.711752  END: 01:11:57.887147 2017-05-04
* CP COUNT: (27)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C7,C8,C9,E2,E8)
* 85..9....1.....6.....3.8.....8.4...9514.......3....24.........4.8...6..77..15..6.
* PAIR E2: 2,7 BLK 2
D1: 2,7,4,6                              # reduction candidate for 2,7
D1: 2,7 => CTR
* 856.914..1.3.7.6....7368..1.78645..9514...786639817245.6.78...4.8...6..77.215.863
D1: 4,6                                  #  8 pairs
F1: 2,7,1,4                              # reduction candidate for 2,7
F1: 2,7                                  # 17 pairs
D2: 2,7,4,5                              # reduction candidate for 2,7
D2: 2,7 => CTR
* 856491...143..5698..73684.1.78.43..9514....8..3981724536..8...448..36..7792154863
D2: 4,5                                  #  8 pairs
F2: 2,7,4,5                              # reduction candidate for 2,7
F2: 2,7 => SOLVED
* 856491372143572698927368451278645139514923786639817245361789524485236917792154863
F2: 4,5                                  #  8 pairs
E3: 2,7,1,6                              # reduction candidate for 2,7
E3: 2,7 => CTR
* 85.6914..1.....6.....3.8..1..8.4...9514.6.....3..1.24.........4.8...6..77..15..6.
E3: 1,6                                  #  8 pairs
* PAIR E2: 2,7 ROW 2
B2: 2,7,4,9                              # reduction candidate for 2,7
B2: 2,7                                  # 12 pairs
C2: 2,7,3,9                              # reduction candidate for 2,7
C2: 2,7                                  # 19 pairs
H2: 2,7,3,8,9                            # reduction candidate for 2,7
H2: 2,7                                  # 15 pairs
* PAIR E2: 2,7 COL E
E5: 2,7,3,6,8                            # reduction candidate for 2,7
E5: 2,7                                  # 12 pairs
E7: 2,7,3,8                              # reduction candidate for 2,7
E7: 2,7 => CTR
* 85.6924.11...75682...318..5628743..95142.9...9375.124.36.827..448.936.2779.15..6.
E7: 3,8                                  #  8 pairs
* PAIR A4: 2,6 BLK 4
B4: 2,6,7                                # reduction candidate for 2,6
B4: 7                                    # 21 pairs
B4: 2,6                                  # 10 pairs
* PAIR A4: 2,6 COL A
A3: 2,6,4,9                              # reduction candidate for 2,6
A3: 2,6                                  # 12 pairs
A7: 2,6,3,9                              # reduction candidate for 2,6
A7: 2,6                                  # 17 pairs
* PAIR A6: 6,9 BLK 4
C6: 6,9,7                                # reduction candidate for 6,9
C6: 6,9                                  # 21 pairs
C6: 7                                    # 10 pairs
* PAIR A6: 6,9 COL A
A3: 6,9,2,4                              # reduction candidate for 6,9
A3: 6,9 => SOLVED
* 856491372143572698927368451278645139514923786639817245361789524485236917792154863
A3: 2,4                                  #  8 pairs
A7: 6,9,2,3                              # reduction candidate for 6,9
A7: 6,9                                  # 17 pairs
* PAIR C7: 1,5 ROW 7
G7: 1,5,3,9                              # reduction candidate for 1,5
G7: 1,5                                  #  8 pairs
H7: 1,5,2,3,9                            # reduction candidate for 1,5
H7: 1,5                                  #  9 pairs
* PAIR C8: 1,5 ROW 8
G8: 1,5,3,9                              # reduction candidate for 1,5
G8: 1,5                                  #  8 pairs
H8: 1,5,2,3,9                            # reduction candidate for 1,5
H8: 1,5                                  #  9 pairs
* PAIR C9: 2,9 BLK 7
A7: 2,9,3,6                              # reduction candidate for 2,9
A7: 2,9                                  # 20 pairs
B7: 2,9,6                                # reduction candidate for 2,9
B7: 2,9                                  # 18 pairs
A8: 2,9,3,4                              # reduction candidate for 2,9
A8: 2,9                                  # 11 pairs
B9: 2,9,4                                # reduction candidate for 2,9
B9: 2,9                                  # 11 pairs
* PAIR C9: 2,9 ROW 9
F9: 2,9,3,4                              # reduction candidate for 2,9
F9: 2,9                                  # 11 pairs
F9: 3,4                                  #  8 pairs
* PAIR C9: 2,9 COL C
C2: 2,9,3,7                              # reduction candidate for 2,9
C2: 2,9                                  # 15 pairs
C3: 2,9,6,7                              # reduction candidate for 2,9
C3: 2,9                                  #  9 pairs
* PAIR E8: 2,3 BLK 8
E7: 2,3,7,8                              # reduction candidate for 2,3
E7: 2,3 => CTR
* 85.6924.11...75682...318..5..8743..95142.9....375.124....8.7..4.8.9.6..77..154.6.
E7: 7,8                                  #  8 pairs
F7: 2,3,7,9                              # reduction candidate for 2,3
F7: 2,3                                  # 15 pairs
F9: 2,3,4,9                              # reduction candidate for 2,3
F9: 2,3                                  # 12 pairs
* PAIR E8: 2,3 ROW 8
A8: 2,3,4,9                              # reduction candidate for 2,3
A8: 2,3                                  # 10 pairs
H8: 2,3,1,5,9                            # reduction candidate for 2,3
H8: 2,3                                  # 13 pairs
* PAIR E8: 2,3 COL E
E5: 2,3,6,7,8                            # reduction candidate for 2,3
E5: 6,7,8                                # 12 pairs
E5: 2,3                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-093-base-pr-000.dot
* REASONING
* DIS # D1: 2,7 => CTR => D1: 4,6
* DIS # D2: 2,7 => CTR => D2: 4,5
* PRF # F2: 2,7 => SOL
* DIS # E3: 2,7 => CTR => E3: 1,6
* DIS # E7: 2,7 => CTR => E7: 3,8
* PRF # A3: 6,9 => SOL
* DIS # E7: 2,3 => CTR => E7: 7,8
* CNT   7 HDP CHAINS /  44 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C7,C8,C9,E2,E8)
* 85..9....1.....6.....3.8.....8.4...9514.......3....24.........4.8...6..77..15..6.
* PAIR E2: 2,7 BLK 2
D1: 2,7,4,6                              # reduction candidate for 2,7
D1: 2,7 => CTR
* 856.914..1.3.7.6....7368..1.78645..9514...786639817245.6.78...4.8...6..77.215.863
F1: 2,7,1,4                              # reduction candidate for 2,7
F1: 2,7                                  # 17 pairs
D2: 2,7,4,5                              # reduction candidate for 2,7
D2: 2,7 => CTR
* 856491...143..5698..73684.1.78.43..9514....8..3981724536..8...448..36..7792154863
F2: 2,7,4,5                              # reduction candidate for 2,7
F2: 2,7 => SOLVED
* 856491372143572698927368451278645139514923786639817245361789524485236917792154863
* DURATION: 0:00:05.242630  START: 01:12:31.021993  END: 01:12:36.264623 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-093-base-pr-001.dot
* REASONING
* DIS # D1: 2,7 => CTR => D1: 4,6
* DIS D1: 4,6 # D2: 2,7 => CTR => D2: 4,5
* PRF D1: 4,6 + D2: 4,5 # F2: 2,7 => SOL
* STA D1: 4,6 + D2: 4,5 + F2: 2,7
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

Top 95 Sudokus 093
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 856491372143572698927368451278645139514923786639817245361789524485236917792154863 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 # D1: 2,7 => CTR => D1: 4,6
* INC # D1: 4,6 => UNS
* INC # F1: 2,7 => UNS
* DIS # D2: 2,7 => CTR => D2: 4,5
* INC # D2: 4,5 => UNS
* PRF # F2: 2,7 => SOL
* INC # F2: 4,5 => UNS
* DIS # E3: 2,7 => CTR => E3: 1,6
* INC # E3: 1,6 => UNS
* INC # B2: 2,7 => UNS
* INC # C2: 2,7 => UNS
* INC # H2: 2,7 => UNS
* INC # E5: 2,7 => UNS
* DIS # E7: 2,7 => CTR => E7: 3,8
* INC # E7: 3,8 => UNS
* INC # B4: 2,6 => UNS
* INC # B4: 7 => UNS
* INC # A3: 2,6 => UNS
* INC # A7: 2,6 => UNS
* INC # C6: 6,9 => UNS
* INC # C6: 7 => UNS
* PRF # A3: 6,9 => SOL
* INC # A3: 2,4 => UNS
* INC # A7: 6,9 => UNS
* INC # G7: 1,5 => UNS
* INC # H7: 1,5 => UNS
* INC # G8: 1,5 => UNS
* INC # H8: 1,5 => UNS
* INC # A7: 2,9 => UNS
* INC # B7: 2,9 => UNS
* INC # A8: 2,9 => UNS
* INC # B9: 2,9 => UNS
* INC # F9: 2,9 => UNS
* INC # F9: 3,4 => UNS
* INC # C2: 2,9 => UNS
* INC # C3: 2,9 => UNS
* DIS # E7: 2,3 => CTR => E7: 7,8
* INC # E7: 7,8 => UNS
* INC # F7: 2,3 => UNS
* INC # F9: 2,3 => UNS
* INC # A8: 2,3 => UNS
* INC # H8: 2,3 => UNS
* INC # E5: 2,3 => UNS
* INC # E5: 6,7,8 => UNS
* CNT  44 HDP CHAINS /  44 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D1: 2,7 => CTR => D1: 4,6
* INC D1: 4,6 # F1: 2,7 => UNS
* DIS D1: 4,6 # D2: 2,7 => CTR => D2: 4,5
* PRF D1: 4,6 + D2: 4,5 # F2: 2,7 => SOL
* STA D1: 4,6 + D2: 4,5 + F2: 2,7
* CNT   4 HDP CHAINS /   4 HYP OPENED