Analysis of xx-top95-086-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .32.....58..3.....9.428...1...4...39...6...5.....1.....2...67.8.....4....95....6. initial

Autosolve

position: .32.....585.3..9..964285371...4...39...6...5.....1....42...67.8.....45...95....6. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A4: 1,7 => CTR => A4: 2,5,6
* DIS # A5: 1,7 => CTR => A5: 2,3
* DIS # A8: 1,7 => CTR => A8: 3,6
* DIS # A8: 1,3 => CTR => A8: 6,7
* PRF # C8: 1,3 => SOL
* DIS # D8: 7 => CTR => D8: 1,9
* PRF # E8: 7,9 => SOL
* CNT   7 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 # A4: 1,7 => CTR => A4: 2,5,6
* DIS A4: 2,5,6 # A5: 1,7 => CTR => A5: 2,3
* DIS A4: 2,5,6 + A5: 2,3 # A8: 1,7 => CTR => A8: 3,6
* DIS A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 3 => CTR => A9: 1,7
* PRF A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C8: 1,3 => SOL
* STA A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 + C8: 1,3
* CNT   5 HDP CHAINS /  30 HYP OPENED

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

Details

Positions

.32.....58..3.....9.428...1...4...39...6...5.....1.....2...67.8.....4....95....6. initial
.32.....585.3..9..964285371...4...39...6...5.....1....42...67.8.....45...95....6. autosolve
132749685857361924964285371216457839348692157579813246421536798683974512795128463 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
A1: 1,7
C2: 1,7
E1: 4,6
E2: 4,6
F2: 1,7
H1: 4,8
H2: 2,4
C7: 1,3
H7: 1,9
H8: 1,9
I8: 2,3
G9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C2: 1.. / A1 = 1  => 23 pairs (_) / C2 = 1  =>  0 pairs (X)
G4,G5: 1.. / G4 = 1  => 13 pairs (_) / G5 = 1  => 12 pairs (_)
H7,H8: 1.. / H7 = 1  => 16 pairs (_) / H8 = 1  => 14 pairs (_)
C2,F2: 1.. / C2 = 1  =>  0 pairs (X) / F2 = 1  => 23 pairs (_)
H2,I2: 2.. / H2 = 2  => 13 pairs (_) / I2 = 2  => 11 pairs (_)
E8,I8: 2.. / E8 = 2  => 14 pairs (_) / I8 = 2  => 17 pairs (_)
H2,H6: 2.. / H2 = 2  => 13 pairs (_) / H6 = 2  => 11 pairs (_)
I8,I9: 3.. / I8 = 3  => 14 pairs (_) / I9 = 3  => 17 pairs (_)
C7,E7: 3.. / C7 = 3  => 16 pairs (_) / E7 = 3  => 22 pairs (_)
E1,E2: 4.. / E1 = 4  => 11 pairs (_) / E2 = 4  => 11 pairs (_)
B5,B6: 4.. / B5 = 4  => 14 pairs (_) / B6 = 4  => 15 pairs (_)
G9,I9: 4.. / G9 = 4  => 15 pairs (_) / I9 = 4  => 14 pairs (_)
A4,A6: 5.. / A4 = 5  => 18 pairs (_) / A6 = 5  => 13 pairs (_)
E4,D6: 5.. / E4 = 5  => 13 pairs (_) / D6 = 5  => 18 pairs (_)
D7,E7: 5.. / D7 = 5  => 13 pairs (_) / E7 = 5  => 18 pairs (_)
A4,E4: 5.. / A4 = 5  => 18 pairs (_) / E4 = 5  => 13 pairs (_)
A6,D6: 5.. / A6 = 5  => 13 pairs (_) / D6 = 5  => 18 pairs (_)
D6,D7: 5.. / D6 = 5  => 18 pairs (_) / D7 = 5  => 13 pairs (_)
E4,E7: 5.. / E4 = 5  => 13 pairs (_) / E7 = 5  => 18 pairs (_)
E1,E2: 6.. / E1 = 6  => 11 pairs (_) / E2 = 6  => 11 pairs (_)
G1,I2: 6.. / G1 = 6  => 11 pairs (_) / I2 = 6  => 11 pairs (_)
A8,C8: 6.. / A8 = 6  => 12 pairs (_) / C8 = 6  =>  0 pairs (X)
E1,G1: 6.. / E1 = 6  => 11 pairs (_) / G1 = 6  => 11 pairs (_)
E2,I2: 6.. / E2 = 6  => 11 pairs (_) / I2 = 6  => 11 pairs (_)
I2,I6: 6.. / I2 = 6  => 11 pairs (_) / I6 = 6  => 11 pairs (_)
A1,C2: 7.. / A1 = 7  =>  0 pairs (X) / C2 = 7  => 23 pairs (_)
I5,I6: 7.. / I5 = 7  => 12 pairs (_) / I6 = 7  => 15 pairs (_)
C2,F2: 7.. / C2 = 7  => 23 pairs (_) / F2 = 7  =>  0 pairs (X)
G1,H1: 8.. / G1 = 8  =>  9 pairs (_) / H1 = 8  => 13 pairs (_)
B8,C8: 8.. / B8 = 8  => 16 pairs (_) / C8 = 8  => 14 pairs (_)
D9,F9: 8.. / D9 = 8  => 12 pairs (_) / F9 = 8  => 24 pairs (_)
D6,D9: 8.. / D6 = 8  => 24 pairs (_) / D9 = 8  => 12 pairs (_)
H1,H6: 8.. / H1 = 8  => 13 pairs (_) / H6 = 8  =>  9 pairs (_)
D1,F1: 9.. / D1 = 9  => 16 pairs (_) / F1 = 9  => 13 pairs (_)
C5,C6: 9.. / C5 = 9  => 14 pairs (_) / C6 = 9  => 12 pairs (_)
H7,H8: 9.. / H7 = 9  => 14 pairs (_) / H8 = 9  => 16 pairs (_)
* DURATION: 0:00:52.761292  START: 00:55:48.657675  END: 00:56:41.418967 2017-05-04
* CP COUNT: (36)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C2,C7,E1,E2,F2,G9,H1,H2,H7,H8,I8)
* .32.....585.3..9..964285371...4...39...6...5.....1....42...67.8.....45...95....6.
* PAIR A1: 1,7 ROW 1
D1: 1,7,9                                # reduction candidate for 1,7
D1: 1,7                                  # 13 pairs
F1: 1,7,9                                # reduction candidate for 1,7
F1: 1,7                                  # 16 pairs
* PAIR A1: 1,7 COL A
A4: 1,7,2,5,6                            # reduction candidate for 1,7
A4: 1,7 => CTR
* 1327.9.858573.19.69642853717.6452.392.3697.54549813627421536798678924513395178.6.
A4: 2,5,6                                # 12 pairs
A5: 1,7,2,3                              # reduction candidate for 1,7
A5: 1,7 => CTR
* 132769.858573419269642853712.6457.397..69..5.54.81.6.7421536798678924513395178.6.
A5: 2,3                                  # 13 pairs
A8: 1,7,3,6                              # reduction candidate for 1,7
A8: 1,7 => CTR
* 1327.9.858573.19..9642853716.845.13921.69.854549813.27421536798786924513395178.6.
A8: 3,6                                  # 13 pairs
A9: 1,7,3                                # reduction candidate for 1,7
A9: 1,7                                  # 15 pairs
* PAIR C2: 1,7 COL C
C4: 1,7,6,8                              # reduction candidate for 1,7
C4: 1,7                                  # 18 pairs
C5: 1,7,3,8,9                            # reduction candidate for 1,7
C5: 1,7                                  # 18 pairs
C8: 1,7,3,6,8                            # reduction candidate for 1,7
C8: 1,7                                  # 21 pairs
* PAIR E1: 4,6 ROW 1
G1: 4,6,8                                # reduction candidate for 4,6
G1: 4,6                                  # 13 pairs
G1: 8                                    #  9 pairs
* PAIR E2: 4,6 ROW 2
I2: 4,6,2                                # reduction candidate for 4,6
I2: 4,6                                  # 13 pairs
I2: 2                                    # 11 pairs
* PAIR F2: 1,7 BLK 2
D1: 1,7,9                                # reduction candidate for 1,7
D1: 1,7                                  # 13 pairs
F1: 1,7,9                                # reduction candidate for 1,7
F1: 1,7                                  # 16 pairs
* PAIR F2: 1,7 COL F
F9: 1,7,2,3,8                            # reduction candidate for 1,7
F9: 1,7                                  # 17 pairs
F9: 2,3,8                                # 13 pairs
* PAIR H1: 4,8 BLK 3
G1: 4,8,6                                # reduction candidate for 4,8
G1: 6                                    # 11 pairs
G1: 4,8                                  # 11 pairs
* PAIR H1: 4,8 COL H
H6: 4,8,2                                # reduction candidate for 4,8
H6: 4,8                                  # 13 pairs
H6: 2                                    # 11 pairs
* PAIR H2: 2,4 BLK 3
I2: 2,4,6                                # reduction candidate for 2,4
I2: 6                                    # 11 pairs
I2: 2,4                                  # 11 pairs
* PAIR H2: 2,4 COL H
H6: 2,4,8                                # reduction candidate for 2,4
H6: 2,4                                  # 13 pairs
H6: 8                                    #  9 pairs
* PAIR C7: 1,3 BLK 7
A8: 1,3,6,7                              # reduction candidate for 1,3
A8: 1,3 => CTR
* 132.....58573.192.964285371..845..392..6..85.5..81..4.421536798386..4512795128463
A8: 6,7                                  # 13 pairs
C8: 1,3,6,7,8                            # reduction candidate for 1,3
C8: 1,3 => SOLVED
* 132749685857361924964285371216457839348692157579813246421536798683974512795128463
C8: 6,7,8                                # 12 pairs
A9: 1,3,7                                # reduction candidate for 1,3
A9: 1,3                                  # 17 pairs
* PAIR C7: 1,3 COL C
C5: 1,3,7,8,9                            # reduction candidate for 1,3
C5: 1,3                                  # 24 pairs
C5: 7,8,9                                # 12 pairs
* PAIR H7: 1,9 ROW 7
D7: 1,9,5                                # reduction candidate for 1,9
D7: 1,9                                  # 18 pairs
D7: 5                                    # 13 pairs
* PAIR H8: 1,9 ROW 8
D8: 1,9,7                                # reduction candidate for 1,9
D8: 7 => CTR
* 1329.7.858573.19.696428537167.452.392..67..5454.81.62742.5.67.8...7.45..7951.8.6.
D8: 1,9                                  # 14 pairs
* PAIR I8: 2,3 BLK 9
I9: 2,3,4                                # reduction candidate for 2,3
I9: 2,3                                  # 15 pairs
I9: 4                                    # 14 pairs
* PAIR I8: 2,3 ROW 8
E8: 2,3,7,9                              # reduction candidate for 2,3
E8: 7,9 => SOLVED
* 132749685857361924964285371216457839348692157579813246421536798683974512795128463
E8: 2,3                                  # 13 pairs
* PAIR G9: 2,4 BLK 9
I9: 2,4,3                                # reduction candidate for 2,4
I9: 3                                    # 17 pairs
I9: 2,4                                  # 14 pairs
* PAIR G9: 2,4 COL G
G5: 2,4,1,8                              # reduction candidate for 2,4
G5: 2,4                                  # 17 pairs
G6: 2,4,6,8                              # reduction candidate for 2,4
G6: 2,4                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-086-base-pr-000.dot
* REASONING
* DIS # A4: 1,7 => CTR => A4: 2,5,6
* DIS # A5: 1,7 => CTR => A5: 2,3
* DIS # A8: 1,7 => CTR => A8: 3,6
* DIS # A8: 1,3 => CTR => A8: 6,7
* PRF # C8: 1,3 => SOL
* DIS # D8: 7 => CTR => D8: 1,9
* PRF # E8: 7,9 => SOL
* CNT   7 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C2,C7,E1,E2,F2,G9,H1,H2,H7,H8,I8)
* .32.....585.3..9..964285371...4...39...6...5.....1....42...67.8.....45...95....6.
* PAIR A1: 1,7 ROW 1
D1: 1,7,9                                # reduction candidate for 1,7
D1: 1,7                                  # 13 pairs
F1: 1,7,9                                # reduction candidate for 1,7
F1: 1,7                                  # 16 pairs
* PAIR A1: 1,7 COL A
A4: 1,7,2,5,6                            # reduction candidate for 1,7
A4: 1,7 => CTR
* 1327.9.858573.19.69642853717.6452.392.3697.54549813627421536798678924513395178.6.
A5: 1,7,2,3                              # reduction candidate for 1,7
A5: 1,7 => CTR
* 132769.858573419269642853712.6457.397..69..5.54.81.6.7421536798678924513395178.6.
A8: 1,7,3,6                              # reduction candidate for 1,7
A8: 1,7 => CTR
* 1327.9.858573.19..9642853716.845.13921.69.854549813.27421536798786924513395178.6.
A9: 1,7,3                                # reduction candidate for 1,7
A9: 1,7                                  # 15 pairs
* RESTART
* PAIR A1: 1,7 COL A
A9: 1,7,3                                # reduction candidate for 1,7
A9: 3 => CTR
* 132.....58573.19..964285371...4...39...6...5.7..51....42..567.8.....45...95....6.
* PAIR RESTART
* PAIR A1: 1,7 ROW 1
D1: 1,7,9                                # reduction candidate for 1,7
D1: 1,7                                  # 16 pairs
F1: 1,7,9                                # reduction candidate for 1,7
F1: 1,7                                  # 19 pairs
* PAIR C2: 1,7 COL C
C4: 1,7,6,8                              # reduction candidate for 1,7
C4: 1,7                                  # 18 pairs
C5: 1,7,3,8,9                            # reduction candidate for 1,7
C5: 1,7                                  # 18 pairs
C8: 1,7,3,6,8                            # reduction candidate for 1,7
C8: 1,7                                  # 21 pairs
* PAIR E1: 4,6 ROW 1
G1: 4,6,8                                # reduction candidate for 4,6
G1: 4,6                                  # 16 pairs
G1: 8                                    # 12 pairs
* PAIR E2: 4,6 ROW 2
I2: 4,6,2                                # reduction candidate for 4,6
I2: 4,6                                  # 16 pairs
I2: 2                                    # 15 pairs
* PAIR F2: 1,7 BLK 2
D1: 1,7,9                                # reduction candidate for 1,7
D1: 1,7                                  # 16 pairs
F1: 1,7,9                                # reduction candidate for 1,7
F1: 1,7                                  # 19 pairs
* PAIR F2: 1,7 COL F
F9: 1,7,2,3,8                            # reduction candidate for 1,7
F9: 1,7                                  # 21 pairs
F9: 2,3,8                                # 16 pairs
* PAIR H1: 4,8 BLK 3
G1: 4,8,6                                # reduction candidate for 4,8
G1: 6                                    # 14 pairs
G1: 4,8                                  # 14 pairs
* PAIR H1: 4,8 COL H
H6: 4,8,2                                # reduction candidate for 4,8
H6: 4,8                                  # 16 pairs
H6: 2                                    # 15 pairs
* PAIR H2: 2,4 BLK 3
I2: 2,4,6                                # reduction candidate for 2,4
I2: 6                                    # 14 pairs
I2: 2,4                                  # 14 pairs
* PAIR H2: 2,4 COL H
H6: 2,4,8                                # reduction candidate for 2,4
H6: 2,4                                  # 16 pairs
H6: 8                                    # 12 pairs
* PAIR C7: 1,3 BLK 7
C8: 1,3,6,7,8                            # reduction candidate for 1,3
C8: 1,3 => SOLVED
* 132749685857361924964285371216457839348692157579813246421536798683974512795128463
* DURATION: 0:00:27.635091  START: 00:57:20.405120  END: 00:57:48.040211 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-086-base-pr-001.dot
* REASONING
* DIS # A4: 1,7 => CTR => A4: 2,5,6
* DIS A4: 2,5,6 # A5: 1,7 => CTR => A5: 2,3
* DIS A4: 2,5,6 + A5: 2,3 # A8: 1,7 => CTR => A8: 3,6
* DIS A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 3 => CTR => A9: 1,7
* PRF A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C8: 1,3 => SOL
* STA A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 + C8: 1,3
* CNT   5 HDP CHAINS /  30 HYP OPENED

Header Info

Top 95 Sudokus 086
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 132749685857361924964285371216457839348692157579813246421536798683974512795128463 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 # D1: 1,7 => UNS
* INC # F1: 1,7 => UNS
* DIS # A4: 1,7 => CTR => A4: 2,5,6
* INC # A4: 2,5,6 => UNS
* DIS # A5: 1,7 => CTR => A5: 2,3
* INC # A5: 2,3 => UNS
* DIS # A8: 1,7 => CTR => A8: 3,6
* INC # A8: 3,6 => UNS
* INC # A9: 1,7 => UNS
* INC # C4: 1,7 => UNS
* INC # C5: 1,7 => UNS
* INC # C8: 1,7 => UNS
* INC # G1: 4,6 => UNS
* INC # G1: 8 => UNS
* INC # I2: 4,6 => UNS
* INC # I2: 2 => UNS
* INC # D1: 1,7 => UNS
* INC # F1: 1,7 => UNS
* INC # F9: 1,7 => UNS
* INC # F9: 2,3,8 => UNS
* INC # G1: 4,8 => UNS
* INC # G1: 6 => UNS
* INC # H6: 4,8 => UNS
* INC # H6: 2 => UNS
* INC # I2: 2,4 => UNS
* INC # I2: 6 => UNS
* INC # H6: 2,4 => UNS
* INC # H6: 8 => UNS
* DIS # A8: 1,3 => CTR => A8: 6,7
* INC # A8: 6,7 => UNS
* PRF # C8: 1,3 => SOL
* INC # C8: 6,7,8 => UNS
* INC # A9: 1,3 => UNS
* INC # C5: 1,3 => UNS
* INC # C5: 7,8,9 => UNS
* INC # D7: 1,9 => UNS
* INC # D7: 5 => UNS
* INC # D8: 1,9 => UNS
* DIS # D8: 7 => CTR => D8: 1,9
* INC # I9: 2,3 => UNS
* INC # I9: 4 => UNS
* INC # E8: 2,3 => UNS
* PRF # E8: 7,9 => SOL
* INC # I9: 2,4 => UNS
* INC # I9: 3 => UNS
* INC # G5: 2,4 => UNS
* INC # G6: 2,4 => UNS
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 1,7 => UNS
* INC # F1: 1,7 => UNS
* DIS # A4: 1,7 => CTR => A4: 2,5,6
* DIS A4: 2,5,6 # A5: 1,7 => CTR => A5: 2,3
* DIS A4: 2,5,6 + A5: 2,3 # A8: 1,7 => CTR => A8: 3,6
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 1,7 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 1,7 => UNS
* DIS A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 3 => CTR => A9: 1,7
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # D1: 1,7 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # F1: 1,7 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C4: 1,7 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C5: 1,7 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C8: 1,7 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # G1: 4,6 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # G1: 8 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # I2: 4,6 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # I2: 2 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # D1: 1,7 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # F1: 1,7 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # F9: 1,7 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # F9: 2,3,8 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # G1: 4,8 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # G1: 6 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # H6: 4,8 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # H6: 2 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # I2: 2,4 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # I2: 6 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # H6: 2,4 => UNS
* INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # H6: 8 => UNS
* PRF A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C8: 1,3 => SOL
* STA A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 + C8: 1,3
* CNT  30 HDP CHAINS /  30 HYP OPENED